Demo of error and fix

FindPointsGSLIB for surface meshes

.github/actions/sanitize/mfem/action.yml

@@ -82,7 +82,7 @@ runs:
       run: find . -type f -name '*.o' -delete
       shell: bash
 
-    - uses: actions/upload-artifact@v4
+    - uses: actions/upload-artifact@v7
       with:
         name: build-${{inputs.par}}-${{inputs.sanitizer}}
         path: mfem/build

.github/actions/sanitize/restore/action.yml

@@ -49,7 +49,7 @@ runs:
         par: ${{inputs.par}}
         sanitizer: ${{inputs.sanitizer}}
 
-    - uses: actions/download-artifact@v4
+    - uses: actions/download-artifact@v8
       with:
         name: build-${{inputs.par}}-${{inputs.sanitizer}}
         path: mfem/build

.github/workflows/sanitize-tests.yml

@@ -146,7 +146,7 @@ jobs:
         if: ${{steps.restore.outputs.cache-hit != 'true'}}
         working-directory: mfem/build/tests/unit
         run: find . -type f -name '*.o' -delete
-      - uses: actions/upload-artifact@v4
+      - uses: actions/upload-artifact@v7
         with:
           name: tests-${{inputs.par}}-${{inputs.sanitizer}}
           path: mfem/build/tests/unit/${{env.unit_tests}}
@@ -172,7 +172,7 @@ jobs:
           par: ${{inputs.par}}
           sanitizer: ${{inputs.sanitizer}}
           cache-path: mfem/build/tests/unit/${{env.unit_tests}}
-      - uses: actions/download-artifact@v4
+      - uses: actions/download-artifact@v8
         if: ${{steps.restore.outputs.cache-hit != 'true'}}
         with:
           name: tests-${{inputs.par}}-${{inputs.sanitizer}}

CHANGELOG

@@ -15,6 +15,8 @@ Version 4.9.1 (development)
 
 Discretization improvements
 ---------------------------
+- Extend FindPointsGSLIB to support surface meshes.
+
 - Replaced legacy simplex quadrature rules with symmetric positive-weight
   rules for triangles (orders 0-25) and tetrahedra (orders 0-20). These
   rules guarantee all-positive weights and interior quadrature points,

NOTICE

@@ -28,6 +28,7 @@ license files. These software products and their licenses are as follows:
 * AmgXWrapper (linalg/amgxsolver.{hpp,cpp}) -- MIT license
 * Catch++ (tests/unit/catch.hpp) -- Boost 1.0 license
 * Gecko (general/gecko.{cpp,hpp}) -- BSD 3-clause license
+* gslib (fem/gslib.{cpp,hpp}, mesh/bb_grid_map.{cpp,hpp}) -- BSD 3-clause license
 * Picojson (fem/picojson.h) -- Custom 2-clause license
 * TinyXML2 (general/tinyxml2.{cpp,h}) -- zlib license
 * Zstr (general/zstr.hpp) -- MIT license

examples/ex1.cpp

@@ -137,6 +137,32 @@ int main(int argc, char *argv[])
       }
    }
 
+   mesh.EnsureNodes();
+   GridFunction *nodes = mesh.GetNodes();
+   GridFunction nodes2(nodes->FESpace());
+   nodes2 = *nodes; // 1-to-1 copy
+
+   VisItDataCollection vdc("check", &mesh);
+   vdc.RegisterField("d", nodes);
+   vdc.RegisterField("d2", &nodes2);
+   vdc.SetCycle(0);
+   vdc.Save();
+
+   // byNODES byVDIm shuffle
+   int nnode = nodes2.Size()/2;
+   for (int i = 0; i < nnode; i++)
+   {
+      for (int j = 0; j < dim; j++)
+      {
+         int xi = i + j*nnode;
+         int ni = j + i*dim;
+         nodes2[xi] = nodes->Elem(ni);
+      }
+   } 
+   vdc.SetCycle(1);
+   vdc.Save();
+
+
    // 5. Define a finite element space on the mesh. Here we use continuous
    //    Lagrange finite elements of the specified order. If order < 1, we
    //    instead use an isoparametric/isogeometric space.

fem/CMakeLists.txt

@@ -171,8 +171,12 @@ set(SRCS
   tmop_tools.cpp
   tmop_amr.cpp
   gslib.cpp
+  gslib/findptsedge_local_2.cpp
+  gslib/findptsedge_local_3.cpp
+  gslib/findptssurf_local_3.cpp
   gslib/findpts_local_2.cpp
   gslib/findpts_local_3.cpp
+  gslib/interpolate_local_1.cpp
   gslib/interpolate_local_2.cpp
   gslib/interpolate_local_3.cpp
   transfer.cpp

fem/gridfunc.hpp

@@ -1767,8 +1767,8 @@ public:
                              const int ref_factor=1, const int vdim=-1) const;
 
    /// Computes the \ref PLBound for the gridfunction with number of control
-   /// points based on \p ref_factor, and returns the bounds for each element
-   /// ordered byNodes:
+   /// points based on @a ref_factor, and returns the bounds for each element
+   /// ordered byNODES:
    /// lower_{0,0}, lower_{1,0}, ..., lower_{ne-1,0},
    /// lower_{0,1}, ..., lower_{ne-1,vdim-1}. We also return the
    /// PLBound object used to compute the bounds.
@@ -1802,7 +1802,7 @@ public:
                          const int vdim = -1) const;
 
    /// Compute bounds on the grid function for all the elements. The bounds
-   /// are returned in @b lower and @b upper, ordered byNodes:
+   /// are returned in @b lower and @b upper, ordered byNODES:
    /// lower_{0,0}, lower_{1,0}, ..., lower_{ne-1,0},
    /// lower_{0,1}, ..., lower_{ne-1,vdim-1}
    void GetElementBounds(const PLBound &plb, Vector &lower, Vector &upper,

fem/gslib.hpp

@@ -21,6 +21,45 @@
 
 #ifdef MFEM_USE_GSLIB
 
+/* gslib license and copyright statement for code adapted from gslib:
+
+Copyright (c) 2008-2024, UCHICAGO ARGONNE, LLC.
+
+The UChicago Argonne, LLC as Operator of Argonne National
+Laboratory holds copyright in the Software. The copyright holder
+reserves all rights except those expressly granted to licensees,
+and U.S. Government license rights.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
+
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the disclaimer below.
+
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the disclaimer (as noted below)
+in the documentation and/or other materials provided with the
+distribution.
+
+3. Neither the name of ANL nor the names of its contributors
+may be used to endorse or promote products derived from this software
+without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
+UCHICAGO ARGONNE, LLC, THE U.S. DEPARTMENT OF
+ENERGY OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
 namespace gslib
 {
 struct comm;
@@ -86,7 +125,7 @@ protected:
    void *fdataD;
    struct gslib::crystal *cr;             // gslib's internal data
    struct gslib::comm *gsl_comm;          // gslib's internal data
-   int dim, points_cnt;                   // mesh dimension and number of points
+   int dim, spacedim, points_cnt;         // mesh dimension and number of points
    Array<unsigned int> gsl_code, gsl_proc, gsl_elem, gsl_mfem_elem;
    Vector gsl_mesh, gsl_ref, gsl_dist, gsl_mfem_ref;
    Array<unsigned int> recv_proc, recv_index; // data for custom interpolation
@@ -104,18 +143,23 @@ protected:
    bool       gpu_to_cpu_fallback = false;
 
    // Device specific data used for FindPoints
-   struct
+   struct DEV_STRUCT
    {
       bool setup_device = false;
       bool find_device  = false;
-      int local_hash_size, dof1d, dof1d_sol, h_o_size, h_nx;
+      int local_hash_size, dof1d, dof1d_sol, lh_nx, gh_nx;
       double newt_tol; // Tolerance specified during setup for Newton solve
       struct gslib::crystal *cr;
       struct gslib::hash_data_3 *hash3;
       struct gslib::hash_data_2 *hash2;
       mutable Vector bb, wtend, gll1d, lagcoeff, gll1d_sol, lagcoeff_sol;
-      mutable Array<unsigned int> loc_hash_offset;
-      mutable Vector loc_hash_min, loc_hash_fac;
+      mutable Array<unsigned int> lh_offset, gh_offset;
+      mutable Vector lh_min, lh_fac, gh_min, gh_fac;
+      // Tolerance to mark points found on the surface as CODE_INTERNAL
+      // or CODE_BORDER. This is needed because we cannot only use reference
+      // space coordinates to determine if a point is located inside the
+      // element or not.
+      mutable double surf_dist_tol;
    } DEV;
 
    /// Use GSLIB for communication and interpolation
@@ -127,80 +171,143 @@ protected:
                                    Vector &field_out,
                                    const int field_out_ordering);
 
-   /// Since GSLIB is designed to work with quads/hexes, we split every
-   /// triangle/tet/prism/pyramid element into quads/hexes.
+   /** @brief Since GSLIB is designed to work with quads/hexes, we split every
+    *  triangle/tet/prism/pyramid element into quads/hexes. */
    virtual void SetupSplitMeshes();
 
-   /// Setup integration points that will be used to interpolate the nodal
-   /// location at points expected by GSLIB.
+   /** @brief Setup integration points that will be used to interpolate the
+    *  nodal location at points expected by GSLIB. */
    virtual void SetupIntegrationRuleForSplitMesh(Mesh *mesh,
                                                  IntegrationRule *irule,
                                                  int order);
 
-   /// Helper function that calls \ref SetupSplitMeshes and
-   /// \ref SetupIntegrationRuleForSplitMesh.
+   /** @brief Helper function that calls \ref SetupSplitMeshes and
+    * \ref SetupIntegrationRuleForSplitMesh. */
    virtual void SetupSplitMeshesAndIntegrationRules(const int order);
 
    /// Get GridFunction value at the points expected by GSLIB.
    virtual void GetNodalValues(const GridFunction *gf_in, Vector &node_vals) const;
 
-   /// Map {r,s,t} coordinates from [-1,1] to [0,1] for MFEM. For simplices,
-   /// find the original element number (that was split into micro quads/hexes)
-   /// during the setup phase.
+   /** @brief Map {r,s,t} coordinates from [-1,1] to [0,1] for MFEM. For
+    *  simplices, find the original element number (that was split into
+    *  micro quads/hexes) during the setup phase. */
    virtual void MapRefPosAndElemIndices();
 
-   // Device functions
-   // FindPoints locally on device for 3D.
+   /// FindPoints locally on device for 3D.
    void FindPointsLocal3(const Vector &point_pos, int point_pos_ordering,
                          Array<unsigned int> &gsl_code_dev_l,
                          Array<unsigned int> &gsl_elem_dev_l, Vector &gsl_ref_l,
                          Vector &gsl_dist_l, int npt);
 
-   // FindPoints locally on device for 2D.
+   /// FindPoints locally on device for 2D.
    void FindPointsLocal2(const Vector &point_pos, int point_pos_ordering,
                          Array<unsigned int> &gsl_code_dev_l,
                          Array<unsigned int> &gsl_elem_dev_l, Vector &gsl_ref_l,
                          Vector &gsl_dist_l, int npt);
 
-   // Interpolate on device for 3D.
+   /// FindPoints locally on device for 3D surface elements.
+   void FindPointsSurfLocal3(const Vector &point_pos,
+                             int point_pos_ordering,
+                             Array<unsigned int> &gsl_code_dev_l,
+                             Array<unsigned int> &gsl_elem_dev_l,
+                             Vector &gsl_ref_l,
+                             Vector &gsl_dist_l,
+                             int npt);
+
+   /// FindPoints locally on device for 3D edge elements.
+   void FindPointsEdgeLocal3(const Vector &point_pos,
+                             int point_pos_ordering,
+                             Array<unsigned int> &gsl_code_dev_l,
+                             Array<unsigned int> &gsl_elem_dev_l,
+                             Vector &gsl_ref_l,
+                             Vector &gsl_dist_l,
+                             int npt);
+
+   /// FindPoints locally on device for 2D edge elements.
+   void FindPointsEdgeLocal2(const Vector &point_pos,
+                             int point_pos_ordering,
+                             Array<unsigned int> &gsl_code_dev_l,
+                             Array<unsigned int> &gsl_elem_dev_l,
+                             Vector &gsl_ref_l,
+                             Vector &gsl_dist_l,
+                             int npt);
+
+   /// Interpolate on device for 3D.
    void InterpolateLocal3(const Vector &field_in,
                           Array<int> &gsl_elem_dev_l,
                           Vector &gsl_ref_l,
                           Vector &field_out,
                           int npt, int ncomp,
-                          int nel, int dof1dsol);
-   // Interpolate on device for 2D.
+                          int dof1dsol);
+
+   /// Interpolate on device for 2D.
    void InterpolateLocal2(const Vector &field_in,
                           Array<int> &gsl_elem_dev_l,
                           Vector &gsl_ref_l,
                           Vector &field_out,
                           int npt, int ncomp,
-                          int nel, int dof1dsol);
+                          int dof1dsol);
 
-   // Prepare data for device functions.
+   /// Interpolate on device for 1D.
+   void InterpolateLocal1(const Vector &field_in,
+                          Array<int> &gsl_elem_dev_l,
+                          Vector &gsl_ref_l,
+                          Vector &field_out,
+                          int npt, int ncomp, int dof1dsol);
+
+   /// Prepare data for device execution for volume meshes.
    void SetupDevice();
 
-   /** Searches positions given in physical space by @a point_pos.
+   /** @brief Searches positions given in physical space by @a point_pos.
        These positions can be ordered byNodes: (XXX...,YYY...,ZZZ) or
        byVDim: (XYZ,XYZ,....XYZ) specified by @a point_pos_ordering. */
    void FindPointsOnDevice(const Vector &point_pos,
                            const int point_pos_ordering = Ordering::byNODES);
 
-   /** Interpolation of field values at prescribed reference space positions.
-       @param[in] field_in_evec E-vector of grid function to be interpolated.
-                                Assumed ordering is NDOFSxVDIMxNEL
-       @param[in] nel           Number of elements in the mesh.
-       @param[in] ncomp         Number of components in the field.
-       @param[in] dof1dsol      Number of degrees of freedom in each reference
-                                space direction.
-       @param[in] ordering      Ordering of the out field values: byNodes/byVDIM
-
-       @param[out] field_out  Interpolated values. For points that are not found
-                              the value is set to #default_interp_value. */
+   /** @brief Interpolation of field values at prescribed reference space
+    *         positions.
+    *  @param[in] field_in_evec E-vector of grid function to be interpolated.
+    *                           Assumed ordering is NDOFSxVDIMxNEL
+    *  @param[in] nel           Number of elements in the mesh.
+    *  @param[in] ncomp         Number of components in the field.
+    *  @param[in] dof1dsol      Number of degrees of freedom in each reference
+    *                           space direction.
+    *  @param[in] ordering      Ordering of the out field values: byNodes/byVDIM
+    *
+    *  @param[out] field_out    Interpolated values. For points that are not
+    *                           found the value is set to
+    *                           #default_interp_value. */
    void InterpolateOnDevice(const Vector &field_in_evec, Vector &field_out,
                             const int nel, const int ncomp,
                             const int dof1dsol, const int ordering);
 
+   /** @brief Interpolation of field values at prescribed reference space
+    *         positions for surface meshes. */
+   void InterpolateSurfBase(const Vector &field_in, Vector &field_out,
+                            const int nel, const int ncomp,
+                            const int dof1dsol, const int field_out_ordering);
+
+   /// Preprocess 2D surface mesh needed for FindPoints.
+   void findptsedge_setup_2(DEV_STRUCT &devs,
+                            const double *const elx[2],
+                            const unsigned n,
+                            const uint nel,
+                            const unsigned m,
+                            const double bbox_tol,
+                            const uint local_hash_size,
+                            const uint global_hash_size);
+
+   /// Preprocess 3D surface mesh needed for FindPoints.
+   void findptssurf_setup_3(DEV_STRUCT &devs,
+                            const double *const elx[3],
+                            const unsigned n,
+                            const uint nel,
+                            const unsigned m,
+                            const double bbox_tol,
+                            const uint local_hash_size,
+                            const uint global_hash_size,
+                            const int rD);
+
 public:
    /// Serial constructor
    FindPointsGSLIB();
@@ -224,8 +331,10 @@ public:
    FindPointsGSLIB(const FindPointsGSLIB&) = delete;
    FindPointsGSLIB& operator=(const FindPointsGSLIB&) = delete;
 
-   /** Initializes the internal mesh in gslib, by sending the positions of the
-       Gauss-Lobatto nodes of the input Mesh object \p m.
+   /** @brief Preprocess the internal mesh in gslib.
+
+       @details Initializes the internal mesh in gslib, by sending the
+       positions of the Gauss-Lobatto nodes of the input Mesh object \p m.
        Note: not tested with periodic (L2).
        Note: the input mesh \p m must have Nodes set.
 
@@ -236,13 +345,22 @@ public:
                             search methods.
        @param[in] npt_max   (Optional) Number of points for simultaneous
                             iteration. This alters performance and
-                            memory footprint.*/
-
+                            memory footprint.
+   */
    void Setup(Mesh &m, const double bb_t = 0.1, const double newt_tol = 1.0e-12,
               const int npt_max = 256);
-   /** Searches positions given in physical space by \p point_pos.
-       These positions can be ordered byNodes: (XXX...,YYY...,ZZZ) or
+
+   /// Preprocess the surface mesh to compute data for FindPoints.
+   void SetupSurf(Mesh &m,
+                  const double bb_t = 0.1,
+                  const double newt_tol = 1.0e-12,
+                  const int npt_max = 256);
+
+   /** @brief Searches positions given in physical space by \p point_pos.
+
+       @details These positions can be ordered byNodes: (XXX...,YYY...,ZZZ) or
        byVDim: (XYZ,XYZ,....XYZ) specified by \p point_pos_ordering.
+
        This function populates the following member variables:
        #gsl_code        Return codes for each point: inside element (0),
                         element boundary (1), not found (2).
@@ -261,19 +379,34 @@ public:
        #gsl_dist        Distance between the sought and the found point
                         in physical space. */
    void FindPoints(const Vector &point_pos,
-                   const int point_pos_ordering = Ordering::byNODES);
+                   int point_pos_ordering = Ordering::byNODES);
+
    /// Convenience function when point positions are in a ParticleVector
    void FindPoints(const ParticleVector &point_pos)
    {
       FindPoints(point_pos, point_pos.GetOrdering());
    }
+
+   /** @brief Searches positions given in physical space by \p point_pos on
+    *  surface mesh. */
+   void FindPointsSurf(const Vector &point_pos,
+                       int point_pos_ordering = Ordering::byNODES);
+
+   /// Convenience function when point positions are in a ParticleVector
+   void FindPointsSurf(const ParticleVector &point_pos)
+   {
+      FindPointsSurf(point_pos, point_pos.GetOrdering());
+   }
+
    /// Setup FindPoints and search positions
    void FindPoints(Mesh &m, const Vector &point_pos,
                    const int point_pos_ordering = Ordering::byNODES,
                    const double bb_t = 0.1, const double newt_tol = 1.0e-12,
                    const int npt_max = 256);
 
-   /** Interpolation of field values at prescribed reference space positions.
+   /** @brief Interpolation of field values at prescribed reference space
+    *  positions.
+
        @param[in] field_in    Function values that will be interpolated on the
                               reference positions. Note: it is assumed that
                               \p field_in is in H1 and in the same space as the
@@ -282,19 +415,36 @@ public:
                               the value is set to #default_interp_value.
                               The output ordering is determined from field_in.*/
    virtual void Interpolate(const GridFunction &field_in, Vector &field_out);
+
    /// Interpolation of field values, with output ordering specification.
    virtual void Interpolate(const GridFunction &field_in, Vector &field_out,
                             const int field_out_ordering);
-   /** Search positions and interpolate. The ordering (byNODES or byVDIM) of
-       the output values in \p field_out corresponds to the ordering used
-       in the input GridFunction \p field_in. */
+
+   /** @brief Same as Interpolate but for surface meshes */
+   virtual void InterpolateSurf(const GridFunction &field_in,
+                                Vector &field_out);
+
+   /** @brief Same as Interpolate but for surface meshes with specified output
+       ordering */
+   virtual void InterpolateSurf(const GridFunction &field_in,
+                                Vector &field_out,
+                                const int field_out_ordering);
+
+   /** @brief Search positions and interpolate.
+    *
+    *  @details The ordering (byNODES or byVDIM) of the output values in
+    *  \p field_out corresponds to the ordering used in the input
+    *  GridFunction \p field_in.
+    */
    void Interpolate(const Vector &point_pos, const GridFunction &field_in,
                     Vector &field_out,
-                    const int point_pos_ordering = Ordering::byNODES);
+                    int point_pos_ordering = Ordering::byNODES);
+
    /// Search positions and interpolate with given point and output ordering.
    void Interpolate(const Vector &point_pos, const GridFunction &field_in,
                     Vector &field_out, const int point_pos_ordering,
                     const int field_out_ordering);
+
    /** Setup FindPoints, search positions and interpolate. The ordering (byNODES
        or byVDIM) of the output values in \p field_out corresponds to the
        ordering used in the input GridFunction \p field_in. */
@@ -302,32 +452,36 @@ public:
                     const GridFunction &field_in, Vector &field_out,
                     const int point_pos_ordering = Ordering::byNODES);
 
-   /// Average type to be used for L2 functions in-case a point is located at
-   /// an element boundary where the function might be multi-valued.
+   /** @brief Average type to be used for L2 functions in-case a point is
+    *  located at an element boundary where the function might be multi-valued.
+    */
    virtual void SetL2AvgType(AvgType avgtype_) { avgtype = avgtype_; }
 
-   /// Set the default interpolation value for points that are not found in the
-   /// mesh.
+   /** @brief Set the default interpolation value for points that are not found in the mesh. */
    virtual void SetDefaultInterpolationValue(double interp_value_)
    {
       default_interp_value = interp_value_;
    }
 
-   /// Set the tolerance for detecting points outside the 'curvilinear' boundary
-   /// that gslib may return as found on the boundary. Points found on boundary
-   /// with distance greater than @ bdr_tol are marked as not found.
+   /** @brief Tolerance for detecting points outside the 'curvilinear' boundary.
+    *
+    *  @details When using FindPoints, gslib may return points as found on the
+    *  boundary even when they are slightly outside the domain. This tolerance
+    *  is used to filter such points based on the distance^2 value and mark them
+    *  as not found.*/
    virtual void SetDistanceToleranceForPointsFoundOnBoundary(double bdr_tol_)
    {
       bdr_tol = bdr_tol_;
    }
 
-   /// Enable/Disable use of CPU functions for GPU data if the gslib version
-   /// is older.
+   /** @brief Enable/Disable use of CPU functions for GPU data if the gslib
+    *  version is older. */
    virtual void SetGPUtoCPUFallback(bool mode) { gpu_to_cpu_fallback = mode; }
 
-   /** Cleans up memory allocated internally by gslib.
-       Note that in parallel, this must be called before MPI_Finalize(), as it
-       calls MPI_Comm_free() for internal gslib communicators. FreeData is
+   /** @brief Cleans up memory allocated internally by gslib.
+
+       @details Note that in parallel, this must be called before MPI_Finalize,
+       as it calls MPI_Comm_free() for internal gslib communicators. FreeData is
        also called by the class destructor and there are no memory leaks if the
        destructor is called before MPI_Finalize(). If the destructor is called
        after MPI_Finalize(), there will be an error because gslib will try to
@@ -335,8 +489,8 @@ public:
    */
    virtual void FreeData();
 
-   /// Return code for each point searched by FindPoints: inside element (0), on
-   /// element boundary (1), or not found (2).
+   /** @brief Return code for each point searched by FindPoints:
+    *  inside element (0), element boundary (1), or not found (2). */
    virtual const Array<unsigned int> &GetCode() const { return gsl_code; }
    /// Return element number for each point found by FindPoints.
    virtual const Array<unsigned int> &GetElem() const { return gsl_mfem_elem; }
@@ -344,15 +498,15 @@ public:
    virtual const Array<unsigned int> &GetProc() const { return gsl_proc; }
    /// Return reference coordinates for each point found by FindPoints.
    virtual const Vector &GetReferencePosition() const { return gsl_mfem_ref;  }
-   /// Return distance between the sought and the found point in physical space,
-   /// for each point found by FindPoints.
+   /// Return distance between the sought and the found point in physical space.
    virtual const Vector &GetDist()              const { return gsl_dist; }
 
-   /// Return element number for each point found by FindPoints corresponding to
-   /// GSLIB mesh. gsl_mfem_elem != gsl_elem for mesh with simplices.
+   /** @brief Return element number for each point found by FindPoints
+    *  corresponding to GSLIB mesh. gsl_mfem_elem != gsl_elem for mesh with
+    *  simplices. */
    virtual const Array<unsigned int> &GetGSLIBElem() const { return gsl_elem; }
-   /// Return reference coordinates in [-1,1] (internal range in GSLIB) for each
-   /// point found by FindPoints.
+   /** @brief Return reference coordinates in [-1,1] (internal range in GSLIB)
+    *  for each point found by FindPoints. */
    virtual const Vector &GetGSLIBReferencePosition() const { return gsl_ref; }
 
    /// Get array of indices of not-found points.
@@ -395,7 +549,7 @@ public:
 
    /// Return the axis-aligned bounding boxes (AABB) computed during \ref Setup.
    /// The size of the returned vector is (nel x nverts x dim), where nel is the
-   /// number of elements (after splitting for simplcies), nverts is number of
+   /// number of elements (after splitting for simplicies), nverts is number of
    /// vertices (4 in 2D, 8 in 3D), and dim is the spatial dimension.
    void GetAxisAlignedBoundingBoxes(Vector &aabb) const;
 
@@ -409,6 +563,18 @@ public:
    /// \p obbV, a vector of size (nel x nverts x dim) .
    void GetOrientedBoundingBoxes(DenseTensor &obbA, Vector &obbC,
                                  Vector &obbV) const;
+
+   /** @brief Return the bounding boxes as a mesh on rank 0.
+    *
+    *  @param[in] type  Bounding-box type: 0 - AABB, 1 - OBB.
+    *
+    *  @return On rank 0, returns a newly allocated mesh containing the
+    *  bounding boxes. The caller owns the returned pointer and is responsible
+    *  for deleting it. On other ranks, returns nullptr.
+    */
+   Mesh *GetBoundingBoxMesh(int type);
+
+   virtual const Vector &GetGLLMesh()           const { return gsl_mesh; }
 };
 
 /** \brief OversetFindPointsGSLIB enables use of findpts for arbitrary number of
@@ -536,6 +702,116 @@ public:
    void GS(Vector &senddata, GSOp op);
 };
 
+#if defined(MFEM_USE_MPI)
+/** \brief Class to map a point in physical space to candidate ranks.
+ *
+ *  This class builds a Cartesian-aligned tensor grid that covers the entire
+ *  domain and precomputes which ranks have elements intersecting each
+ *  grid cell. Given a point in physical space, the grid cell containing
+ *  the point is determined, and the list of candidate ranks whose
+ *  elements intersect that cell is returned. This yields a fast, conservative
+ *  point-to-rank candidate query. This is used internally by FindPointsGSLIB
+ *  to speed up point searches in parallel.
+ *
+ *  See Mittal et al., "General Field Evaluation in High-Order Meshes on GPUs".
+ *  (2025). Computers & Fluids. for technical details.
+ *
+ */
+class GlobalBBoxTensorGridMap
+{
+private:
+   struct gslib::crystal *cr = nullptr;               // gslib's internal data
+   struct gslib::comm *gsl_comm = nullptr;            // gslib's internal data
+   int sdim, n_local_cells, num_procs;
+   Array<int> gmap_n;
+   Vector gmap_bnd_min, gmap_bnd_max;
+   Vector gmap_fac;
+   Array<int> ggrid_map;
+
+   void SetupCrystal(const MPI_Comm &comm);
+public:
+   /// Constructor for a given mesh and number of tensor grid divisions
+   GlobalBBoxTensorGridMap(ParMesh &pmesh, int nx);
+
+   /** @brief Constructor for given element bounds and spatial dimension.
+    *
+    *  @details This constructor must be called collectively on \a comm.
+    *  Supports spatial dimensions 1, 2, and 3, and accepts nel == 0 on a rank.
+    *
+    *  Assumes elmin, elmax Ordering::byNodes:
+    *  elmin -> [x_{0,min},x_{1,min},... ,y_{0,min},y_{1,min},..,z_{nel-1,min}]
+    *  elmax -> [x_{0,max},x_{1,max},... ,y_{0,max},y_{1,max},..,z_{nel-1,max}]
+    *  Note elmin, elmax can be obtained using GridFunction::GetElementBounds()
+    *
+    *  When by_max_size=false, n gives the number of tensor-grid divisions in
+    *  each direction. When by_max_size=true, n is a per-rank size hint used to
+    *  derive a uniform global resolution. The communicator-wide sum of n is
+    *  converted to nx = ceil(pow(sum(n), 1./sdim)) in each direction, so n is
+    *  not a hard cap on ggrid_map.Size().
+    */
+   GlobalBBoxTensorGridMap(const MPI_Comm &comm, Vector &elmin,
+                           Vector &elmax, int nel, int sdim, int n,
+                           bool by_max_size);
+
+   /** @brief Constructor for given element bounds, spatial dimension, and
+    *  tensor-grid divisions in each direction.
+    *
+    *  @details This constructor must be called collectively on \a comm.
+    *  Supports spatial dimensions 1, 2, and 3, and accepts nel == 0 on a rank.
+    *  Requires nx.Size() == sdim and positive entries in nx.
+    *
+    *  Assumes elmin, elmax Ordering::byNodes:
+    *  elmin -> [x_{0,min},x_{1,min},... ,y_{0,min},y_{1,min},..,z_{nel-1,min}]
+    *  elmax -> [x_{0,max},x_{1,max},... ,y_{0,max},y_{1,max},..,z_{nel-1,max}]
+    *  Note elmin, elmax can be obtained using GridFunction::GetElementBounds()
+    */
+   GlobalBBoxTensorGridMap(const MPI_Comm &comm, Vector &elmin,
+                           Vector &elmax, int nel, int sdim, Array<int> &nx);
+
+   ~GlobalBBoxTensorGridMap();
+
+   /** @brief Get list of procs corresponding to the list of points.
+    *
+    *  @details This method must be called collectively on the communicator
+    *  used to construct the map. The input points can be ordered byNodes:
+    *  (XXX...,YYY...,ZZZ) or byVDIM: (XYZ,XYZ,...), as specified by
+    *  \a ordering.
+    *
+    *  The output map contains one entry for each input point, keyed by the
+    *  point's local index in \a xyz. Points with no candidate ranks, including
+    *  points outside the global bounding box, have an empty list of candidate
+    *  ranks.
+    */
+   void MapPointsToProcs(Vector &xyz, int ordering,
+                         std::map<int, std::vector<int>> &pt_to_procs) const;
+
+   // Some getters
+   const Array<int> &GetGridMap() const { return ggrid_map; }
+   const Vector &GetGridFac() const { return gmap_fac; }
+   const Vector &GetGridMin() const { return gmap_bnd_min; }
+   const Vector &GetGridMax() const { return gmap_bnd_max; }
+   const Array<int> &GetGridN() const { return gmap_n; }
+
+private:
+   /// Setup the map given element bounds and number of tensor grid divisions.
+   void Setup(const MPI_Comm &comm, Vector &elmin, Vector &elmax,
+              int nel, Array<int> &nx);
+
+   /// Get global hash cell index for a given point.
+   int GetGlobalGridCellFromPoint(Vector &xyz) const;
+
+   /** @brief Get owning proc and local index on that proc for given global
+    *  grid cell index. */
+   void GlobalGridCellToProcAndLocalIndex(int i, int &proc, int &idx) const;
+
+   /// Map a point to proc and local index of the corresponding grid cell
+   void GetProcAndLocalIndexFromPoint(Vector &xyz, int &proc, int &idx) const;
+
+   /// Given local cell index, return list of procs saved in the map
+   Array<int> MapCellToProcs(int l_idx) const;
+};
+#endif // MFEM_USE_MPI
+
 } // namespace mfem
 
 #endif // MFEM_USE_GSLIB

fem/gslib/findpts_local_2.cpp

@@ -562,7 +562,7 @@ newton_area_fin:
       int f = flags >> (2 * dd) & 3u;
       res->r[dd] = f == 0 ? r0[dd] + dr[dd] : (f == 1 ? -1 : 1);
    }
-   res->flags = flags | (p->flags << 5);
+   res->flags = flags | ((p->flags & FLAG_MASK) << 5);
 }
 
 // Full Newton solve on the face. One of r/s/t is constrained.
@@ -635,7 +635,8 @@ newton_edge_fin:
    res->r[de] = nr;
    res->r[dn]=p->r[dn];
    res->dist2p = -v;
-   res->flags = flags | new_flags | (p->flags << 5);
+   res->flags = flags | new_flags | ((p->flags & FLAG_MASK) << 5);
+#undef EVAL
 }
 
 // Find closest mesh node to the sought point.
@@ -714,7 +715,6 @@ static void FindPointsLocal2D_Kernel(const int npt,
                                      const double *lagcoeff,
                                      const int pN = 0)
 {
-#define MAX_CONST(a, b) (((a) > (b)) ? (a) : (b))
    const int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
    const int D1D = T_D1D ? T_D1D : pN;
    const int p_NE = D1D*D1D;
@@ -729,7 +729,7 @@ static void FindPointsLocal2D_Kernel(const int npt,
       // 3D1D for seed, 10D1D+6 for area, 3D1D+9 for edge
       constexpr int size1 = 10*MD1 + 6;
       constexpr int size2 = MD1*4;            // edge constraints
-      constexpr int size3 = MD1*MD1*MD1*DIM;  // local element coordinates
+      constexpr int size3 = MD1*MD1*DIM;  // local element coordinates
 
       MFEM_SHARED double r_workspace[size1];
       MFEM_SHARED findptsElementPoint_t el_pts[2];
@@ -1162,9 +1162,9 @@ void FindPointsGSLIB::FindPointsLocal2(const Vector &point_pos,
    auto pgslm = gsl_mesh.Read();
    auto pwt = DEV.wtend.Read();
    auto pbb = DEV.bb.Read();
-   auto plhm = DEV.loc_hash_min.Read();
-   auto plhf = DEV.loc_hash_fac.Read();
-   auto plho = DEV.loc_hash_offset.ReadWrite();
+   auto plhm = DEV.lh_min.Read();
+   auto plhf = DEV.lh_fac.Read();
+   auto plho = DEV.lh_offset.ReadWrite();
    auto pcode = code.Write();
    auto pelem = elem.Write();
    auto pref = ref.Write();
@@ -1177,30 +1177,32 @@ void FindPointsGSLIB::FindPointsLocal2(const Vector &point_pos,
       case 2:
          return FindPointsLocal2D_Kernel<2>(
                    npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.h_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
+                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
                    pgll1d, plc);
       case 3:
          return FindPointsLocal2D_Kernel<3>(
                    npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.h_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
+                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
                    pgll1d, plc);
       case 4:
          return FindPointsLocal2D_Kernel<4>(
                    npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.h_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
+                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
                    pgll1d, plc);
       case 5:
          return FindPointsLocal2D_Kernel<5>(
                    npt, DEV.newt_tol, pp, point_pos_ordering, pgslm, NE_split_total, pwt,
-                   pbb, DEV.h_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
+                   pbb, DEV.lh_nx, plhm, plhf, plho, pcode, pelem, pref, pdist,
                    pgll1d, plc);
       default:
          return FindPointsLocal2D_Kernel(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                         pgslm, NE_split_total, pwt, pbb, DEV.h_nx,
+                                         pgslm, NE_split_total, pwt, pbb, DEV.lh_nx,
                                          plhm, plhf, plho, pcode, pelem,
                                          pref, pdist, pgll1d, plc, DEV.dof1d);
    }
 }
+#undef DIM2
+#undef DIM
 #undef CODE_INTERNAL
 #undef CODE_BORDER
 #undef CODE_NOT_FOUND

fem/gslib/findpts_local_3.cpp

@@ -706,7 +706,7 @@ newton_vol_fin:
       int f = flags >> (2*dd) & 3u;
       res->r[dd] = f == 0 ? r0[dd]+dr[dd] : (f == 1 ? -1 : 1);
    }
-   res->flags = flags | (p->flags << 7);
+   res->flags = flags | ((p->flags & FLAG_MASK) << 7);
 }
 
 // Full Newton solve on the face. One of r/s/t is constrained.
@@ -889,7 +889,7 @@ newton_face_fin:
    res->r[dn] = p->r[dn];
    res->r[d1] = r[0];
    res->r[d2] = r[1];
-   res->flags = new_flags | (p->flags << 7);
+   res->flags = new_flags | ((p->flags & FLAG_MASK) << 7);
 }
 
 // Full Newton solve on the edge. Two of r/s/t are constrained.
@@ -973,7 +973,8 @@ newton_edge_fin:
    res->r[dn1] = p->r[dn1];
    res->r[dn2] = p->r[dn2];
    res->dist2p = -v;
-   res->flags = flags | new_flags | (p->flags << 7);
+   res->flags = flags | new_flags | ((p->flags & FLAG_MASK) << 7);
+#undef EVAL
 }
 
 // Find closest mesh node to the sought point.
@@ -1252,7 +1253,6 @@ static void FindPointsLocal3DKernel(const int npt,
                      case 0: // findpt_vol
                      {
                         double *wtr = r_workspace_ptr;
-
                         double *resid = wtr+6*D1D;
                         double *jac = resid+3;
                         double *resid_temp = jac+9;
@@ -1503,7 +1503,7 @@ static void FindPointsLocal3DKernel(const int npt,
                               // Hes_T is transposed version (i.e. in col major)
                               // n1*[2, 1, 1, 0, 0]
                               // j==1 => wt_j = wt+n1
-                              double *wt_j = wt+D1D*(2-(row+1) / 2);
+                              double *wt_j = wt+D1D*(2 - (row+1)/2);
                               const double *x = e_x[row+1][d];
                               hes_T[j] = 0.0;
                               for (int k = 0; k < D1D; ++k)
@@ -1522,7 +1522,6 @@ static void FindPointsLocal3DKernel(const int npt,
                               hes[j] += resid[d]*hes_T[j*3+d];
                            }
                         }
-
                         MFEM_SYNC_THREAD;
 
                         MFEM_FOREACH_THREAD(l,x,1)
@@ -1780,6 +1779,7 @@ static void FindPointsLocal3DKernel(const int npt,
          } //findpts_local
       } //elp
    });
+#undef MAXC
 }
 
 void FindPointsGSLIB::FindPointsLocal3(const Vector &point_pos,
@@ -1796,9 +1796,9 @@ void FindPointsGSLIB::FindPointsLocal3(const Vector &point_pos,
    auto pgslm = gsl_mesh.Read();
    auto pwt = DEV.wtend.Read();
    auto pbb = DEV.bb.Read();
-   auto plhm = DEV.loc_hash_min.Read();
-   auto plhf = DEV.loc_hash_fac.Read();
-   auto plho = DEV.loc_hash_offset.ReadWrite();
+   auto plhm = DEV.lh_min.Read();
+   auto plhf = DEV.lh_fac.Read();
+   auto plho = DEV.lh_offset.ReadWrite();
    auto pcode = code.Write();
    auto pelem = elem.Write();
    auto pref = ref.Write();
@@ -1809,31 +1809,31 @@ void FindPointsGSLIB::FindPointsLocal3(const Vector &point_pos,
    {
       case 2:
          FindPointsLocal3DKernel<2>(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                    pgslm, NE_split_total, pwt, pbb, DEV.h_nx, plhm,
+                                    pgslm, NE_split_total, pwt, pbb, DEV.lh_nx, plhm,
                                     plhf, plho, pcode, pelem, pref, pdist, pgll1d,
                                     plc);
          break;
       case 3:
          FindPointsLocal3DKernel<3>(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                    pgslm, NE_split_total, pwt, pbb, DEV.h_nx, plhm,
+                                    pgslm, NE_split_total, pwt, pbb, DEV.lh_nx, plhm,
                                     plhf, plho, pcode, pelem, pref, pdist, pgll1d,
                                     plc);
          break;
       case 4:
          FindPointsLocal3DKernel<4>(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                    pgslm, NE_split_total, pwt, pbb, DEV.h_nx, plhm,
+                                    pgslm, NE_split_total, pwt, pbb, DEV.lh_nx, plhm,
                                     plhf, plho, pcode, pelem, pref, pdist, pgll1d,
                                     plc);
          break;
       case 5:
          FindPointsLocal3DKernel<5>(npt, DEV.newt_tol, pp, point_pos_ordering,
-                                    pgslm, NE_split_total, pwt, pbb, DEV.h_nx, plhm,
+                                    pgslm, NE_split_total, pwt, pbb, DEV.lh_nx, plhm,
                                     plhf, plho, pcode, pelem, pref, pdist, pgll1d,
                                     plc);
          break;
       default:
          FindPointsLocal3DKernel(npt, DEV.newt_tol, pp, point_pos_ordering, pgslm,
-                                 NE_split_total, pwt, pbb, DEV.h_nx, plhm, plhf,
+                                 NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
                                  plho, pcode, pelem, pref, pdist, pgll1d, plc,
                                  DEV.dof1d);
    }

fem/gslib/findptsedge_local_2.cpp

@@ -0,0 +1,725 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "../gslib.hpp"
+#include "../../general/forall.hpp"
+
+#ifdef MFEM_USE_GSLIB
+
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wunused-function"
+#endif
+#include "gslib.h"
+#ifndef GSLIB_RELEASE_VERSION //gslib v1.0.7
+#define GSLIB_RELEASE_VERSION 10007
+#endif
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+
+namespace mfem
+{
+#if GSLIB_RELEASE_VERSION >= 10009
+#define CODE_INTERNAL 0
+#define CODE_BORDER 1
+#define CODE_NOT_FOUND 2
+#define sDIM 2
+#define sDIM2 4
+#define rDIM 1
+
+struct findptsElementPoint_t
+{
+   double x[sDIM], r, oldr, dist2, dist2p, tr;
+   int flags;
+};
+
+struct findptsElementGEdge_t
+{
+   double *x[sDIM];
+};
+
+struct findptsElementGPT_t
+{
+   double x[sDIM], jac[sDIM*rDIM], hes[sDIM*rDIM];
+};
+
+struct dbl_range_t
+{
+   double min, max;
+};
+
+struct obbox_t
+{
+   double c0[sDIM], A[sDIM*sDIM];
+   dbl_range_t x[sDIM];
+};
+
+struct findptsLocalHashData_t
+{
+   int hash_n;
+   dbl_range_t bnd[sDIM];
+   double fac[sDIM];
+   unsigned int *offset;
+};
+
+static MFEM_HOST_DEVICE inline void lag_eval_second_der(double *p0, double x,
+                                                        int i, const double *z,
+                                                        const double *lCoeff,
+                                                        int pN)
+{
+   double u0 = 1, u1 = 0, u2 = 0;
+   for (int j = 0; j < pN; ++j)
+   {
+      if (i != j)
+      {
+         double d_j = 2 * (x-z[j]);
+         u2 = d_j * u2 + u1;
+         u1 = d_j * u1 + u0;
+         u0 = d_j * u0;
+      }
+   }
+   double *p1 = p0 + pN, *p2 = p0 + 2 * pN;
+   p0[i] = lCoeff[i] * u0;
+   p1[i] = 2.0 * lCoeff[i] * u1;
+   p2[i] = 8.0 * lCoeff[i] * u2;
+}
+
+/* positive when possibly inside */
+static MFEM_HOST_DEVICE inline double obbox_axis_test(const obbox_t *const b,
+                                                      const double x[sDIM])
+{
+   double b_d;
+   for (int d=0; d<sDIM; ++d)
+   {
+      b_d = (x[d] - b->x[d].min) * (b->x[d].max - x[d]);
+      if (b_d < 0)   // if outside in any dimension
+      {
+         return b_d;
+      }
+   }
+   return b_d;       // only positive if inside
+}
+
+/* positive when given point is possibly inside given obbox b */
+static MFEM_HOST_DEVICE inline double obbox_test(const obbox_t *const b,
+                                                 const double x[sDIM])
+{
+   const double bxyz = obbox_axis_test(b,x);
+   if (bxyz<0)   // test if point is in AABB
+   {
+      return bxyz;
+   }
+   else   // test OBB only if inside AABB
+   {
+      double dxyz[sDIM];
+      for (int d=0; d<sDIM; ++d)
+      {
+         dxyz[d] = x[d] - b->c0[d];
+      }
+      double test = 1;
+      for (int d=0; d<sDIM; ++d)
+      {
+         double rst = 0;
+         for (int e=0; e<sDIM; ++e)
+         {
+            rst += b->A[d*2 + e] * dxyz[e];
+         }
+         double brst = (rst+1)*(1-rst);
+         test = test<0 ? test : brst;
+      }
+      return test;
+   }
+}
+
+/* Hash index in the hash table to the elements that possibly contain the point x */
+static MFEM_HOST_DEVICE inline int hash_index(const findptsLocalHashData_t *p,
+                                              const double x[2])
+{
+   const int n = p->hash_n;
+   int sum = 0;
+   for (int d=sDIM-1; d>=0; --d)
+   {
+      sum *= n;
+      int i = (int)floor((x[d] - p->bnd[d].min) * p->fac[d]);
+      sum += i<0 ? 0 : (n-1 < i ? n-1 : i);
+   }
+   return sum;
+}
+
+static MFEM_HOST_DEVICE inline double l2norm2(const double x[2])
+{
+   return x[0] * x[0] + x[1] * x[1];
+}
+
+/* the bit structure of flags is CRR
+   the C bit --- 1<<2 --- is set when the point is converged
+   RR is 0 = 00b if r is unconstrained,
+         1 = 01b if r is constrained at -1, i.e., rmin
+         2 = 10b if r is constrained at +1, i.e., rmax
+*/
+
+#define CONVERGED_FLAG (1u<<2)
+#define FLAG_MASK 0x07u // = 111b
+
+/* returns 1 if r direction (the only free direction in 2D) is constrained.
+   returns 1 if either 1st or 2nd bit of flags is set.
+*/
+static MFEM_HOST_DEVICE inline int num_constrained(const int flags)
+{
+   return ((flags | flags>>1) & 1u);
+}
+
+/* pi=0, r=-1; pi=1, r=+1 */
+static MFEM_HOST_DEVICE inline int point_index(const int x)
+{
+   return ((x>>1) & 1u);
+}
+
+/* check reduction in objective against prediction, and adjust
+   trust region radius (p->tr) accordingly;
+   may reject the prior step, returning 1; otherwise returns 0
+   sets out->dist2, out->index, out->x, out->oldr in any event,
+   leaving out->r, out->dr, out->flags to be set when returning 0 */
+static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
+                                                 const double resid[2],
+                                                 const findptsElementPoint_t *p,
+                                                 const double tol)
+{
+   const double dist2 = l2norm2(resid);
+   const double decr = p->dist2 - dist2;
+   const double pred = p->dist2p;
+   out->x[0] = p->x[0];
+   out->x[1] = p->x[1];
+   out->oldr = p->r;
+   out->dist2 = dist2;
+   if (decr >= 0.01*pred)
+   {
+      if (decr >= 0.9*pred)   // very good iteration
+      {
+         out->tr = p->tr*2;
+      }
+      else                    // somewhat good iteration
+      {
+         out->tr = p->tr;
+      }
+      return false;
+   }
+   else
+   {
+      /* reject step; note: the point will pass through this routine
+         again, and we set things up here so it gets classed as a
+         "very good iteration" --- this doubles the trust radius,
+         which is why we divide by 4 below */
+      double v0 = fabs(p->r - p->oldr);
+      out->tr = v0/4.0;
+      out->dist2 = p->dist2;
+      out->r = p->oldr;
+      out->flags = p->flags>>3;
+      out->dist2p = -HUGE_VAL;
+      if (pred < dist2*tol)
+      {
+         out->flags |= CONVERGED_FLAG;
+      }
+      return true;
+   }
+}
+
+static MFEM_HOST_DEVICE inline void newton_edge( findptsElementPoint_t *const
+                                                 out,
+                                                 const double jac[2],
+                                                 const double rhess,
+                                                 const double resid[2],
+                                                 int flags,
+                                                 const findptsElementPoint_t *const p,
+                                                 const double tol )
+{
+   const double tr = p->tr;
+   const double A = jac[0] * jac[0] + jac[1] * jac[1] -
+                    rhess; // A = J^T J - resid_d H_d
+   const double y = jac[0]*resid[0] + jac[1]*resid[1];        // y = J^T resid
+
+   const double oldr = p->r;
+   double dr, newr, tdr, tnewr, v, tv;
+   int new_flags=0, tnew_flags=0;
+
+#define EVAL(dr) ( (dr*A - 2*y) * dr )
+   if (A>0)
+   {
+      dr = y/A;
+      if (fabs(dr)<tol)
+      {
+         dr=0.0;
+         newr = oldr;
+      }
+      else
+      {
+         newr = oldr+dr;
+      }
+
+      if (fabs(dr)<tr && fabs(newr)<1)
+      {
+         v = EVAL(dr);
+         goto newton_edge_fin;
+      }
+   }
+
+   if ((newr=oldr-tr) > -1)
+   {
+      dr = -tr;
+   }
+   else
+   {
+      newr = -1, dr = -1-oldr, new_flags = flags|1u;
+   }
+   v = EVAL(dr);
+
+   if ((tnewr=oldr+tr) < 1)
+   {
+      tdr = tr;
+   }
+   else
+   {
+      tnewr = 1, tdr = 1-oldr, tnew_flags = flags|2u;
+   }
+   tv = EVAL(tdr);
+
+   if (tv<v)
+   {
+      newr = tnewr, dr = tdr, v = tv, new_flags = tnew_flags;
+   }
+#undef EVAL
+
+newton_edge_fin:
+   // check convergence by testing if change in r is less than tol
+   if (fabs(dr)<tol)
+   {
+      new_flags |= CONVERGED_FLAG;
+   }
+   out->r = newr;
+   out->dist2p = -v;
+   out->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<3);
+}
+
+static MFEM_HOST_DEVICE void seed_j( const double *elx[sDIM],
+                                     const double x[sDIM],
+                                     const double *z,
+                                     double       *dist2,
+                                     double       *r,
+                                     const int    ir,
+                                     const int    pN )
+{
+   double dx[sDIM];
+   for (int d=0; d<sDIM; ++d)
+   {
+      dx[d] = x[d] - elx[d][ir];
+   }
+   dist2[ir] = HUGE_VAL;
+   const double dist2_rs = l2norm2(dx);
+   if (dist2[ir]>dist2_rs)
+   {
+      dist2[ir] = dist2_rs;
+      r[ir] = z[ir];
+   }
+}
+
+template<int T_D1D = 0>
+static void FindPointsEdgeLocal2D_Kernel( const int     npt,
+                                          const double  tol,
+                                          const double  dist2tol,
+                                          const double  *x,
+                                          const int     point_pos_ordering,
+                                          const double  *xElemCoord,
+                                          const int     nel,
+                                          const double  *wtend,
+                                          const double  *boxinfo,
+                                          const int     hash_n,
+                                          const double  *hashMin,
+                                          const double  *hashFac,
+                                          unsigned int  *hashOffset,
+                                          unsigned int *const code_base,
+                                          unsigned int *const el_base,
+                                          double *const r_base,
+                                          double *const dist2_base,
+                                          const double  *gll1D,
+                                          const double  *lagcoeff,
+                                          const int     pN = 0 )
+{
+   const int MD1   = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
+   const int D1D   = T_D1D ? T_D1D : pN;
+   const int p_NEL = nel*D1D;
+   MFEM_VERIFY(MD1<=DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(pN<=DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(D1D!=0, "Polynomial order not specified.");
+   const int nThreads = D1D*sDIM;
+
+   mfem::forall_2D(npt, nThreads, 1, [=] MFEM_HOST_DEVICE (int i)
+   {
+      // 2D1D for seed, 3D1D + 7 for edge
+      constexpr int size1 = 3*MD1 + 7;
+      // edge coordinates = D1D*2
+      constexpr int size2 = 2*MD1;
+      // local element coordinates in shared memory
+      constexpr int size3 = MD1*sDIM;
+
+      MFEM_SHARED findptsElementPoint_t el_pts[2];
+      MFEM_SHARED double r_workspace[size1];
+
+      MFEM_SHARED double constraint_workspace[size2];
+
+      MFEM_SHARED double elem_coords[MD1 <= 6 ? size3 : 1];
+
+      double *r_workspace_ptr = r_workspace;
+      findptsElementPoint_t *fpt, *tmp;
+      fpt = el_pts + 0;
+      tmp = el_pts + 1;
+
+      // x and y coord index within point_pos for point i
+      int id_x = point_pos_ordering == 0 ? i     : i*sDIM;
+      int id_y = point_pos_ordering == 0 ? i+npt : i*sDIM+1;
+      double x_i[2] = {x[id_x], x[id_y]};
+
+      unsigned int *code_i = code_base  + i;
+      double *dist2_i      = dist2_base + i;
+
+      //---------------- map_points_to_els --------------------
+      findptsLocalHashData_t hash;
+      for (int d=0; d<sDIM; ++d)
+      {
+         hash.bnd[d].min = hashMin[d];
+         hash.fac[d] = hashFac[d];
+      }
+      hash.hash_n = hash_n;
+      hash.offset = hashOffset;
+
+      const int hi                  = hash_index(&hash, x_i);
+      const unsigned int *elp       = hash.offset + hash.offset[hi];
+      const unsigned int *const ele = hash.offset + hash.offset[hi+1];
+      *code_i  = CODE_NOT_FOUND;
+      *dist2_i = HUGE_VAL;
+
+      for (; elp!=ele; ++elp)
+      {
+         const unsigned int el = *elp;
+
+         obbox_t box;
+         int n_box_ents = 3*sDIM + sDIM2;
+
+         for (int idx = 0; idx < sDIM; ++idx)
+         {
+            box.c0[idx] = boxinfo[n_box_ents*el + idx];
+            box.x[idx].min = boxinfo[n_box_ents*el + sDIM + idx];
+            box.x[idx].max = boxinfo[n_box_ents*el + 2*sDIM + idx];
+         }
+
+         for (int idx = 0; idx < sDIM2; ++idx)
+         {
+            box.A[idx] = boxinfo[n_box_ents*el + 3*sDIM + idx];
+         }
+
+         if (obbox_test(&box,x_i)>=0)
+         {
+            //------------ findpts_local ------------------
+            {
+               if (MD1 <= 6)
+               {
+                  MFEM_FOREACH_THREAD(j,x,D1D*sDIM)
+                  {
+                     const int qp = j % D1D;
+                     const int d = j / D1D;
+                     elem_coords[qp + d*D1D] =
+                        xElemCoord[qp + el*D1D + d*p_NEL];
+                  }
+                  MFEM_SYNC_THREAD;
+               }
+
+               const double *elx[sDIM];
+               for (int d=0; d<sDIM; d++)
+               {
+                  elx[d] = MD1<= 6 ? &elem_coords[d*D1D] :
+                           xElemCoord + d*p_NEL + el*D1D;
+               }
+               MFEM_SYNC_THREAD;
+               //// findpts_el ////
+               {
+                  MFEM_FOREACH_THREAD(j,x,1)
+                  {
+                     fpt->dist2 = HUGE_VAL;
+                     fpt->dist2p = 0;
+                     fpt->tr = 1;
+                  }
+                  MFEM_FOREACH_THREAD(j,x,sDIM)
+                  {
+                     fpt->x[j] = x_i[j];
+                  }
+                  MFEM_SYNC_THREAD;
+
+                  {
+                     double *dist2_temp = r_workspace_ptr;
+                     double *r_temp = dist2_temp + D1D;
+                     MFEM_FOREACH_THREAD(j,x,D1D)
+                     {
+                        seed_j(elx, x_i, gll1D, dist2_temp, r_temp, j, D1D);
+                     }
+                     MFEM_SYNC_THREAD;
+
+                     MFEM_FOREACH_THREAD(j,x,1)
+                     {
+                        for (int ir=0; ir<D1D; ++ir)
+                        {
+                           if (dist2_temp[ir]<fpt->dist2)
+                           {
+                              fpt->dist2 = dist2_temp[ir];
+                              fpt->r = r_temp[ir];
+                           }
+                        }
+                     }
+                     MFEM_SYNC_THREAD;
+                  } //seed done
+
+                  // Initialize tmp struct with fpt values before starting Newton iterations
+                  MFEM_FOREACH_THREAD(j,x,1)
+                  {
+                     tmp->dist2 = HUGE_VAL;
+                     tmp->dist2p = 0;
+                     tmp->tr = 1;
+                     tmp->flags = 0;
+                     tmp->r = fpt->r;
+                  }
+                  MFEM_FOREACH_THREAD(j,x,sDIM)
+                  {
+                     tmp->x[j] = fpt->x[j];
+                  }
+                  MFEM_SYNC_THREAD;
+
+
+                  for (int step=0; step<50; step++)
+                  {
+                     int nc = num_constrained(tmp->flags & FLAG_MASK);
+                     switch (nc)
+                     {
+                        case 0:
+                        {
+                           double *wt = r_workspace_ptr;
+                           double *resid = wt + 3*D1D;
+                           double *jac = resid + sDIM;
+                           double *hess = jac + sDIM*rDIM;
+
+                           findptsElementGEdge_t edge;
+                           MFEM_FOREACH_THREAD(j,x,D1D)
+                           {
+                              for (int d=0; d<sDIM; ++d)
+                              {
+                                 edge.x[d] = constraint_workspace + d*D1D;
+                                 edge.x[d][j] = elx[d][j];
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           // compute basis function info upto 2nd derivative
+                           MFEM_FOREACH_THREAD(j,x,D1D)
+                           {
+                              lag_eval_second_der(wt, tmp->r, j, gll1D,
+                                                  lagcoeff, D1D);
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           MFEM_FOREACH_THREAD(j,x,sDIM)
+                           {
+                              resid[j] = tmp->x[j];
+                              jac[j] = 0.0;
+                              hess[j] = 0.0;
+                              for (int k=0; k<D1D; ++k)
+                              {
+                                 resid[j] -= wt[      k]*edge.x[j][k];
+                                 jac[j]   += wt[D1D+k]*edge.x[j][k];
+                                 hess[j]  += wt[2*D1D+k]*edge.x[j][k];
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           MFEM_FOREACH_THREAD(j,x,1)
+                           {
+                              hess[2] = resid[0]*hess[0] + resid[1]*hess[1];
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           MFEM_FOREACH_THREAD(j,x,1)
+                           {
+                              if (!reject_prior_step_q(fpt, resid, tmp, tol))
+                              {
+                                 newton_edge(fpt, jac, hess[2], resid,
+                                             tmp->flags & FLAG_MASK, tmp, tol);
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+                           break;
+                        }
+                        case 1:    // r is constrained to either -1 or 1
+                        {
+                           MFEM_FOREACH_THREAD(j,x,1)
+                           {
+                              const int pi = point_index(tmp->flags &
+                                                         FLAG_MASK);
+                              const double *wt   = wtend + pi*3*D1D;
+                              findptsElementGPT_t gpt;
+                              for (int d=0; d<sDIM; ++d)
+                              {
+                                 gpt.x[d] = elx[d][pi*(D1D-1)];
+                                 gpt.jac[d] = 0.0;
+                                 gpt.hes[d] = 0.0;
+                                 for (int k=0; k<D1D; ++k)
+                                 {
+                                    gpt.jac[d] += wt[D1D  +k]*elx[d][k];
+                                    gpt.hes[d] += wt[2*D1D+k]*elx[d][k];
+                                 }
+                              }
+
+                              const double *const pt_x = gpt.x;
+                              const double *const jac = gpt.jac;
+                              const double *const hes = gpt.hes;
+                              double resid[sDIM], steep, sr;
+                              resid[0] = fpt->x[0] - pt_x[0];
+                              resid[1] = fpt->x[1] - pt_x[1];
+                              steep = jac[0]*resid[0] + jac[1]*resid[1];
+                              sr = steep*tmp->r;
+                              if ( !reject_prior_step_q(fpt, resid, tmp, tol) )
+                              {
+                                 if (sr<0)
+                                 {
+                                    const double rhess = resid[0]*hes[0] +
+                                                         resid[1]*hes[1];
+                                    newton_edge(fpt, jac, rhess,
+                                                resid, 0, tmp, tol);
+                                 }
+                                 else // sr==0
+                                 {
+                                    fpt->r = tmp->r;
+                                    fpt->dist2p = 0;
+                                    fpt->flags = tmp->flags | CONVERGED_FLAG;
+                                 }
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+                           break;
+                        } // case 1
+                     } //switch
+                     if (fpt->flags & CONVERGED_FLAG)
+                     {
+                        break;
+                     }
+                     MFEM_SYNC_THREAD;
+                     MFEM_FOREACH_THREAD(j,x,1)
+                     {
+                        *tmp = *fpt;
+                     }
+                     MFEM_SYNC_THREAD;
+                  } //for int step<50
+               } //findpts_el
+
+               bool converged_internal =
+                  ((fpt->flags&FLAG_MASK) == CONVERGED_FLAG) &&
+                  (fpt->dist2<dist2tol);
+
+               if (*code_i == CODE_NOT_FOUND || converged_internal ||
+                   fpt->dist2 < *dist2_i)
+               {
+                  MFEM_FOREACH_THREAD(j,x,1)
+                  {
+                     *(el_base+i) = el;
+                     *code_i = converged_internal ? CODE_INTERNAL : CODE_BORDER;
+                     *dist2_i = fpt->dist2;
+                     *(r_base+i) = fpt->r;
+                  }
+                  MFEM_SYNC_THREAD;
+                  if (converged_internal)
+                  {
+                     break;
+                  }
+               }
+            } //findpts_local
+         } //obbox_test
+      } //elp
+   });
+}
+
+void FindPointsGSLIB::FindPointsEdgeLocal2( const Vector &point_pos,
+                                            int point_pos_ordering,
+                                            Array<unsigned int> &code,
+                                            Array<unsigned int> &elem,
+                                            Vector &ref,
+                                            Vector &dist,
+                                            int npt )
+{
+   if (npt==0)
+   {
+      return;
+   }
+   MFEM_VERIFY(dim==1 && spacedim==2,"Function for 2D edges only");
+   bool use_dev = point_pos.UseDevice();
+   auto pp = point_pos.Read(use_dev);
+   auto pgslm = gsl_mesh.Read(use_dev);
+   auto pwt = DEV.wtend.Read(use_dev);
+   auto pbb = DEV.bb.Read(use_dev);
+   auto plhm = DEV.lh_min.Read(use_dev);
+   auto plhf = DEV.lh_fac.Read(use_dev);
+   auto plho = DEV.lh_offset.ReadWrite(use_dev);
+   auto pcode = code.Write(use_dev);
+   auto pelem = elem.Write(use_dev);
+   auto pref = ref.Write(use_dev);
+   auto pdist = dist.Write(use_dev);
+   auto pgll1d = DEV.gll1d.ReadWrite(use_dev);
+   auto plc = DEV.lagcoeff.Read(use_dev);
+   double dist2tol = DEV.surf_dist_tol;
+   switch (DEV.dof1d)
+   {
+      case 2:
+         return FindPointsEdgeLocal2D_Kernel<2>(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+      case 3:
+         return FindPointsEdgeLocal2D_Kernel<3>(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+      case 4:
+         return FindPointsEdgeLocal2D_Kernel<4>(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+      default:
+         return FindPointsEdgeLocal2D_Kernel(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc, DEV.dof1d);
+   }
+}
+#undef sDIM
+#undef rDIM
+#undef sDIM2
+#undef CODE_INTERNAL
+#undef CODE_BORDER
+#undef CODE_NOT_FOUND
+#else
+void FindPointsGSLIB::FindPointsEdgeLocal2( const Vector &point_pos,
+                                            int point_pos_ordering,
+                                            Array<unsigned int> &code,
+                                            Array<unsigned int> &elem,
+                                            Vector &ref,
+                                            Vector &dist,
+                                            int npt ) {} ;
+#endif
+} // namespace mfem
+
+#endif //ifdef MFEM_USE_GSLIB

fem/gslib/findptsedge_local_3.cpp

@@ -0,0 +1,733 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "../gslib.hpp"
+#include "../../general/forall.hpp"
+
+#ifdef MFEM_USE_GSLIB
+
+
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wunused-function"
+#endif
+#include "gslib.h"
+#ifndef GSLIB_RELEASE_VERSION //gslib v1.0.7
+#define GSLIB_RELEASE_VERSION 10007
+#endif
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+
+namespace mfem
+{
+#if GSLIB_RELEASE_VERSION >= 10009
+#define CODE_INTERNAL 0
+#define CODE_BORDER 1
+#define CODE_NOT_FOUND 2
+#define sDIM 3
+#define rDIM 1
+#define sDIM2 (sDIM*sDIM)
+#define rDIM2 (rDIM*rDIM)
+
+struct findptsElementPoint_t
+{
+   double x[sDIM], r, oldr, dist2, dist2p, tr;
+   int flags;
+};
+
+struct findptsElementGEdge_t
+{
+   double *x[sDIM], *dxdn[sDIM], *d2xdn[sDIM];
+};
+
+struct findptsElementGPT_t
+{
+   double x[sDIM], jac[sDIM], hes[sDIM*(1+1)];
+};
+
+struct dbl_range_t
+{
+   double min, max;
+};
+
+struct obbox_t
+{
+   double c0[sDIM], A[sDIM*sDIM];
+   dbl_range_t x[sDIM];
+};
+
+struct findptsLocalHashData_t
+{
+   int hash_n;
+   dbl_range_t bnd[sDIM];
+   double fac[sDIM];
+   unsigned int *offset;
+};
+
+static MFEM_HOST_DEVICE inline void lag_eval_second_der(double *p0, double x,
+                                                        int i, const double *z,
+                                                        const double *lCoeff,
+                                                        int pN)
+{
+   double u0 = 1, u1 = 0, u2 = 0;
+   for (int j=0; j<pN; ++j)
+   {
+      if (i!=j)
+      {
+         double d_j = 2 * (x-z[j]);
+         u2 = d_j * u2 + u1;
+         u1 = d_j * u1 + u0;
+         u0 = d_j * u0;
+      }
+   }
+   double *p1 = p0 + pN, *p2 = p0 + 2 * pN;
+   p0[i] = lCoeff[i] * u0;
+   p1[i] = 2.0 * lCoeff[i] * u1;
+   p2[i] = 8.0 * lCoeff[i] * u2;
+}
+
+/* positive when possibly inside */
+static MFEM_HOST_DEVICE inline double obbox_axis_test(const obbox_t *const b,
+                                                      const double x[sDIM])
+{
+   double b_d;
+   for (int d=0; d<sDIM; ++d)
+   {
+      b_d = (x[d] - b->x[d].min) * (b->x[d].max - x[d]);
+      if (b_d < 0)   // if outside in any dimension
+      {
+         return b_d;
+      }
+   }
+   return b_d;       // only positive if inside in all dimensions
+}
+
+/* positive when possibly inside */
+static MFEM_HOST_DEVICE inline double obbox_test(const obbox_t *const b,
+                                                 const double x[sDIM])
+{
+   const double bxyz = obbox_axis_test(b, x);
+   if (bxyz<0)
+   {
+      return bxyz;
+   }
+   else
+   {
+      double dxyz[3];
+      // dxyz: distance of the point from the center of the OBB
+      for (int d=0; d<sDIM; ++d)
+      {
+         dxyz[d] = x[d] - b->c0[d];
+      }
+      // transform dxyz to the local coordinate system of the OBB,
+      // and check if the point is inside the OBB [-1,1]^sDIM
+      double test = 1;
+      for (int d=0; d<sDIM; ++d)
+      {
+         double rst = 0;
+         for (int e=0; e<sDIM; ++e)
+         {
+            rst += b->A[d*sDIM + e] * dxyz[e];
+         }
+         double brst = (rst+1)*(1-rst);
+         test = test<0 ? test : brst;
+      }
+      return test;
+   }
+}
+
+/* Hash index in the hash table to the elements that possibly contain the point x */
+static MFEM_HOST_DEVICE inline int hash_index(const findptsLocalHashData_t *p,
+                                              const double x[sDIM])
+{
+   const int n = p->hash_n;
+   int sum = 0;
+   for (int d=sDIM-1; d>=0; --d)
+   {
+      sum *= n;
+      int i = (int)floor((x[d] - p->bnd[d].min) * p->fac[d]);
+      sum += i<0 ? 0 : (n-1 < i ? n-1 : i);
+   }
+   return sum;
+}
+
+
+static MFEM_HOST_DEVICE inline double norm2(const double x[sDIM])
+{
+   return ( x[0]*x[0] + x[1]*x[1] + x[2]*x[2] );
+}
+
+/* the bit structure of flags is CRR
+   the C bit --- 1<<2 --- is set when the point is converged
+   RR is 0 = 00b if r is unconstrained,
+         1 = 01b if r is constrained at -1, i.e., rmin
+         2 = 10b if r is constrained at +1, i.e., rmax
+*/
+#define CONVERGED_FLAG (1u<<2)
+#define FLAG_MASK 0x07u
+
+/* returns the number of constrained reference coordinates, max 2
+*/
+static MFEM_HOST_DEVICE inline int num_constrained(const int flags)
+{
+   const int y = (flags | flags>>1);
+   return (y & 1u) + (y>>2 & 1u);
+}
+
+static MFEM_HOST_DEVICE inline int point_index(const int x)
+{
+   return ((x>>1)&1u) | ((x>>2)&2u);
+}
+
+/* check reduction in objective against prediction, and adjust
+   trust region radius (p->tr) accordingly;
+   may reject the prior step, returning 1; otherwise returns 0
+   sets out->dist2, out->index, out->x, out->oldr in any event,
+   leaving out->r, out->dr, out->flags to be set when returning 0 */
+static MFEM_HOST_DEVICE bool reject_prior_step_q(findptsElementPoint_t *out,
+                                                 const double resid[3],
+                                                 const findptsElementPoint_t *p,
+                                                 const double tol)
+{
+   const double dist2 = norm2(resid);
+   const double decr  = p->dist2 - dist2;
+   const double pred  = p->dist2p;
+   for (int d=0; d<sDIM; ++d)
+   {
+      out->x[d] = p->x[d];
+   }
+   out->oldr = p->r;
+   out->dist2 = dist2;
+   if (decr>=0.01*pred)
+   {
+      if (decr>=0.9*pred)   // very good iteration
+      {
+         out->tr = 2*p->tr;
+      }
+      else   // good iteration
+      {
+         out->tr = p->tr;
+      }
+      return false;
+   }
+   else   // if the iteration in not good
+   {
+      /* reject step; note: the point will pass through this routine
+         again, and we set things up here so it gets classed as a
+         "very good iteration" --- this doubles the trust radius,
+         which is why we divide by 4 below */
+      double v0 = fabs(p->r - p->oldr);
+      out->tr = v0/4.0;
+      out->dist2 = p->dist2;
+      out->r = p->oldr;
+      out->flags = p->flags>>3;
+      out->dist2p = -HUGE_VAL;
+      if (pred<dist2*tol)
+      {
+         out->flags |= CONVERGED_FLAG;
+      }
+      return true;
+   }
+}
+
+static MFEM_HOST_DEVICE inline void newton_edge(findptsElementPoint_t *const
+                                                out,
+                                                const double jac[sDIM*rDIM],
+                                                const double rhes,
+                                                const double resid[sDIM],
+                                                int flags,
+                                                const findptsElementPoint_t *const p,
+                                                const double tol)
+{
+   const double tr = p->tr;
+   /* A = J^T J - resid_d H_d */
+   const double A = jac[0]*jac[0]+ jac[1] * jac[1] + jac[2] * jac[2]
+                    - rhes;
+   /* y = J^T r */
+   const double y = jac[0]*resid[0] + jac[1]*resid[1] + jac[0+2]*resid[2];
+
+   const double oldr = p->r;
+   double dr, nr, tdr, tnr;
+   double v, tv;
+   int new_flags = 0, tnew_flags = 0;
+
+#define EVAL(dr) (dr*A - 2*y)*dr
+
+   /* if A is not SPD, quadratic model has no minimum */
+   if (A>0)
+   {
+      dr = y/A;
+
+      if (fabs(dr)<tol)
+      {
+         dr=0.0;
+         nr = oldr;
+      }
+      else
+      {
+         nr = oldr+dr;
+      }
+      if ( fabs(dr)<tr && fabs(nr)<1 )
+      {
+         v = EVAL(dr);
+         goto newton_edge_fin;
+      }
+   }
+
+   if ( (nr=oldr-tr)>-1 )
+   {
+      dr = -tr;
+   }
+   else
+   {
+      nr = -1, dr = -1-oldr, new_flags = flags | 1u;
+   }
+   v = EVAL(dr);
+
+   if ( (tnr = oldr+tr)<1 )
+   {
+      tdr = tr;
+   }
+   else
+   {
+      tnr = 1, tdr = 1-oldr, tnew_flags = flags | 2u;
+   }
+   tv = EVAL(tdr);
+
+   if (tv<v)
+   {
+      nr = tnr, dr = tdr, v = tv, new_flags = tnew_flags;
+   }
+
+newton_edge_fin:
+   /* check convergence */
+   if ( fabs(dr)<tol )
+   {
+      new_flags |= CONVERGED_FLAG;
+   }
+   out->r = nr;
+   out->dist2p = -v;
+   out->flags = flags | new_flags | ((p->flags & FLAG_MASK)<<3);
+#undef EVAL
+}
+
+static MFEM_HOST_DEVICE void seed_j(const double *elx[sDIM],
+                                    const double x[sDIM],
+                                    const double *z,
+                                    double *dist2,
+                                    double *r,
+                                    const int ir,
+                                    const int pN)
+{
+   if (ir>=pN)
+   {
+      return;
+   }
+
+   double dx[sDIM];
+   for (int d=0; d<sDIM; ++d)
+   {
+      dx[d] = x[d] - elx[d][ir];
+   }
+   dist2[ir] = norm2(dx);;
+   r[ir] = z[ir];
+}
+
+template<int T_D1D = 0>
+static void FindPointsEdgeLocal3D_Kernel(const int npt,
+                                         const double tol,
+                                         const double dist2tol,
+                                         const double *x,
+                                         const int point_pos_ordering,
+                                         const double *xElemCoord,
+                                         const int nel,
+                                         const double *wtend,
+                                         const double *boxinfo,
+                                         const int hash_n,
+                                         const double *hashMin,
+                                         const double *hashFac,
+                                         unsigned int *hashOffset,
+                                         unsigned int *const code_base,
+                                         unsigned int *const el_base,
+                                         double *const r_base,
+                                         double *const dist2_base,
+                                         const double *gll1D,
+                                         const double *lagcoeff,
+                                         const int pN = 0)
+{
+   const int MD1   = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
+   const int D1D   = T_D1D ? T_D1D : pN;
+   const int p_NEL = nel*D1D;
+   MFEM_VERIFY(MD1<=DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(pN<=DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(D1D!=0, "Polynomial order not specified.");
+   const int nThreads = D1D*sDIM;
+
+   mfem::forall_2D(npt, nThreads, 1, [=] MFEM_HOST_DEVICE (int i)
+   {
+      constexpr int size1 = 3*MD1 + 13;
+      constexpr int size2 = 3*MD1;
+      constexpr int size3 = MD1*sDIM;
+
+      MFEM_SHARED findptsElementPoint_t el_pts[2];
+      MFEM_SHARED double r_workspace[size1];
+
+      MFEM_SHARED double constraint_workspace[size2];
+
+      MFEM_SHARED double elem_coords[MD1 <= 6 ? size3 : 1];
+
+      double *r_workspace_ptr = r_workspace;
+      findptsElementPoint_t *fpt, *tmp;
+      fpt = el_pts + 0;
+      tmp = el_pts + 1;
+
+      int id_x = point_pos_ordering==0 ?       i :   i*sDIM;
+      int id_y = point_pos_ordering==0 ?   npt+i : 1+i*sDIM;
+      int id_z = point_pos_ordering==0 ? 2*npt+i : 2+i*sDIM;
+      double x_i[3] = {x[id_x], x[id_y], x[id_z]};
+
+      unsigned int *code_i = code_base  + i;
+      double *dist2_i      = dist2_base + i;
+
+      //// map_points_to_els ////
+      findptsLocalHashData_t hash;
+      for (int d=0; d<sDIM; ++d)
+      {
+         hash.bnd[d].min = hashMin[d];
+         hash.fac[d]     = hashFac[d];
+      }
+      hash.hash_n = hash_n;
+      hash.offset = hashOffset;
+
+      const unsigned int hi   = hash_index(&hash, x_i);
+      const unsigned int *elp       = hash.offset + hash.offset[hi];
+      const unsigned int *const ele = hash.offset + hash.offset[hi+1];
+      *code_i  = CODE_NOT_FOUND;
+      *dist2_i = HUGE_VAL;
+
+      for (; elp!=ele; ++elp)
+      {
+         const unsigned int el = *elp;
+         obbox_t box;
+         int n_box_ents = 3*sDIM + sDIM2;
+
+         for (int idx = 0; idx < sDIM; ++idx)
+         {
+            box.c0[idx] = boxinfo[n_box_ents*el + idx];
+            box.x[idx].min = boxinfo[n_box_ents*el + sDIM + idx];
+            box.x[idx].max = boxinfo[n_box_ents*el + 2*sDIM + idx];
+         }
+         for (int idx = 0; idx < sDIM2; ++idx)
+         {
+            box.A[idx] = boxinfo[n_box_ents*el + 3*sDIM + idx];
+         }
+
+         if (obbox_test(&box, x_i)>=0)
+         {
+            //// findpts_local ////
+            {
+               if (MD1 <= 6)
+               {
+                  MFEM_FOREACH_THREAD(j,x,D1D*sDIM)
+                  {
+                     const int qp = j % D1D;
+                     const int d = j / D1D;
+                     elem_coords[qp + d*D1D] =
+                        xElemCoord[qp + el*D1D + d*p_NEL];
+                  }
+                  MFEM_SYNC_THREAD;
+               }
+
+               const double *elx[sDIM];
+               for (int d=0; d<sDIM; d++)
+               {
+                  elx[d] = MD1<= 6 ? &elem_coords[d*D1D] :
+                           xElemCoord + d*p_NEL + el*D1D;
+               }
+               MFEM_SYNC_THREAD;
+               //// findpts_el ////
+               {
+                  MFEM_FOREACH_THREAD(j,x,1)
+                  {
+                     fpt->dist2 = HUGE_VAL;
+                     fpt->dist2p = 0;
+                     fpt->tr = 1.0;
+                  }
+                  MFEM_FOREACH_THREAD(j,x,sDIM)
+                  {
+                     fpt->x[j] = x_i[j];
+                  }
+                  MFEM_SYNC_THREAD;
+
+                  //// seed ////
+                  {
+                     double *dist2_temp = r_workspace_ptr;
+                     double *r_temp = dist2_temp + D1D;
+                     MFEM_FOREACH_THREAD(j,x,nThreads)
+                     {
+                        seed_j(elx, x_i, gll1D, dist2_temp, r_temp, j, D1D);
+                     }
+                     MFEM_SYNC_THREAD;
+
+                     MFEM_FOREACH_THREAD(j,x,1)
+                     {
+                        fpt->dist2 = HUGE_VAL;
+                        for (int ir=0; ir<D1D; ++ir)
+                        {
+                           if (dist2_temp[ir] < fpt->dist2)
+                           {
+                              fpt->dist2 = dist2_temp[ir];
+                              fpt->r = r_temp[ir];
+                           }
+                        }
+                     }
+                     MFEM_SYNC_THREAD;
+                  } //seed done
+
+                  MFEM_FOREACH_THREAD(j,x,1)
+                  {
+                     tmp->dist2 = HUGE_VAL;
+                     tmp->dist2p = 0;
+                     tmp->tr = 1;
+                     tmp->flags = 0;
+                     tmp->r = fpt->r;
+                  }
+                  MFEM_FOREACH_THREAD(j,x,sDIM)
+                  {
+                     tmp->x[j] = fpt->x[j];
+                  }
+                  MFEM_SYNC_THREAD;
+
+                  for (int step=0; step<50; step++)
+                  {
+                     switch (num_constrained(tmp->flags & FLAG_MASK))
+                     {
+                        case 0:
+                        {
+                           double *wt = r_workspace_ptr;
+                           double *resid = wt + 3*D1D;
+                           double *jac = resid + sDIM;
+                           double *hess = jac + sDIM*rDIM;
+
+                           findptsElementGEdge_t edge;
+                           MFEM_FOREACH_THREAD(j,x,D1D)
+                           {
+                              for (int d=0; d<sDIM; ++d)
+                              {
+                                 edge.x[d] = constraint_workspace + d*D1D;
+                                 edge.x[d][j] = elx[d][j];
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           MFEM_FOREACH_THREAD(j,x,D1D)
+                           {
+                              lag_eval_second_der(wt, tmp->r, j, gll1D,
+                                                  lagcoeff, D1D);
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           MFEM_FOREACH_THREAD(j,x,sDIM)
+                           {
+                              resid[j] = tmp->x[j];
+                              jac[j] = 0.0;
+                              hess[j] = 0.0;
+                              for (int k=0; k<D1D; ++k)
+                              {
+                                 resid[j] -= wt[      k]*edge.x[j][k];
+                                 jac[j]   += wt[D1D+k]*edge.x[j][k];
+                                 hess[j]  += wt[2*D1D+k]*edge.x[j][k];
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+
+                           MFEM_FOREACH_THREAD(j,x,1)
+                           {
+                              hess[3] = resid[0]*hess[0] + resid[1]*hess[1] +
+                                        resid[2]*hess[2];
+                           }
+
+                           MFEM_FOREACH_THREAD(l,x,1)
+                           {
+                              if (!reject_prior_step_q(fpt,resid,tmp,tol))
+                              {
+                                 newton_edge(fpt,jac,hess[3],resid,
+                                             tmp->flags&FLAG_MASK,tmp,tol);
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+                           break;
+                        }
+                        case 1:
+                        {
+                           MFEM_FOREACH_THREAD(j,x,1)
+                           {
+                              const int pi = point_index(tmp->flags &
+                                                         FLAG_MASK);
+                              const double *wt = wtend + pi*3*D1D;
+                              findptsElementGPT_t gpt;
+                              for (int d=0; d<sDIM; ++d)
+                              {
+                                 gpt.x[d] = elx[d][pi*(D1D-1)];
+                                 gpt.jac[d] = 0.0;
+                                 gpt.hes[d] = 0.0;
+                                 for (int k=0; k<D1D; ++k)
+                                 {
+                                    gpt.jac[d] += wt[D1D  +k]*elx[d][k];
+                                    gpt.hes[d] += wt[2*D1D+k]*elx[d][k];
+                                 }
+                              }
+
+                              const double *const pt_x = gpt.x;
+                              const double *const jac = gpt.jac;
+                              const double *const hes = gpt.hes;
+                              double resid[sDIM], steep, sr;
+                              resid[0] = fpt->x[0] - pt_x[0];
+                              resid[1] = fpt->x[1] - pt_x[1];
+                              resid[2] = fpt->x[2] - pt_x[2];
+                              steep = jac[0]*resid[0] + jac[1]*resid[1] +
+                                      jac[2]*resid[2];
+                              sr = steep*tmp->r;
+                              if (!reject_prior_step_q(fpt, resid, tmp, tol))
+                              {
+                                 if (sr<0)
+                                 {
+                                    const double rhess = resid[0]*hes[0] +
+                                                         resid[1]*hes[1] +
+                                                         resid[2]*hes[2];
+                                    newton_edge(fpt, jac, rhess,
+                                                resid, 0, tmp, tol);
+                                 }
+                                 else   // sr==0
+                                 {
+                                    fpt->r = tmp->r;
+                                    fpt->dist2p = 0;
+                                    fpt->flags = tmp->flags | CONVERGED_FLAG;
+                                 }
+                              }
+                           }
+                           MFEM_SYNC_THREAD;
+                           break;
+                        } // case 1
+                     } //switch
+                     if (fpt->flags & CONVERGED_FLAG)
+                     {
+                        break;
+                     }
+                     MFEM_SYNC_THREAD;
+
+                     MFEM_FOREACH_THREAD(j,x,1)
+                     {
+                        *tmp = *fpt;
+                     }
+                     MFEM_SYNC_THREAD;
+                  } // for step<50
+               } // findpts_el
+
+               bool converged_internal =
+                  ((fpt->flags&FLAG_MASK) == CONVERGED_FLAG) &&
+                  (fpt->dist2<dist2tol);
+               if (*code_i==CODE_NOT_FOUND || converged_internal ||
+                   fpt->dist2<*dist2_i)
+               {
+                  MFEM_FOREACH_THREAD(j,x,1)
+                  {
+                     *(el_base+i) = el;
+                     *code_i  = converged_internal?CODE_INTERNAL:CODE_BORDER;
+                     *dist2_i = fpt->dist2;
+                     *(r_base+i) = fpt->r;
+                  }
+                  MFEM_SYNC_THREAD;
+                  if (converged_internal)
+                  {
+                     break;
+                  }
+               }
+            } // findpts_local
+         } // obbox_test
+      } // elp
+   });
+}
+
+void FindPointsGSLIB::FindPointsEdgeLocal3(const Vector &point_pos,
+                                           int point_pos_ordering,
+                                           Array<unsigned int> &code,
+                                           Array<unsigned int> &elem,
+                                           Vector &ref,
+                                           Vector &dist,
+                                           int npt)
+{
+   if (npt == 0)
+   {
+      return;
+   }
+   MFEM_VERIFY(spacedim==3 && dim == 1,"Function for 3D edges only");
+   bool use_dev = point_pos.UseDevice();
+   auto pp = point_pos.Read(use_dev);
+   auto pgslm = gsl_mesh.Read(use_dev);
+   auto pwt = DEV.wtend.Read(use_dev);
+   auto pbb = DEV.bb.Read(use_dev);
+   auto plhm = DEV.lh_min.Read(use_dev);
+   auto plhf = DEV.lh_fac.Read(use_dev);
+   auto plho = DEV.lh_offset.ReadWrite(use_dev);
+   auto pcode = code.Write(use_dev);
+   auto pelem = elem.Write(use_dev);
+   auto pref = ref.Write(use_dev);
+   auto pdist = dist.Write(use_dev);
+   auto pgll1d = DEV.gll1d.ReadWrite(use_dev);
+   auto plc = DEV.lagcoeff.Read(use_dev);
+   double dist2tol = DEV.surf_dist_tol;
+   switch (DEV.dof1d)
+   {
+      case 2:
+         return FindPointsEdgeLocal3D_Kernel<2>(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+      case 3:
+         return FindPointsEdgeLocal3D_Kernel<3>(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+      case 4:
+         return FindPointsEdgeLocal3D_Kernel<4>(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc);
+      default:
+         return FindPointsEdgeLocal3D_Kernel(
+                   npt, DEV.newt_tol, dist2tol, pp, point_pos_ordering, pgslm,
+                   NE_split_total, pwt, pbb, DEV.lh_nx, plhm, plhf,
+                   plho, pcode, pelem, pref, pdist, pgll1d, plc, DEV.dof1d);
+   }
+}
+#undef rDIM2
+#undef sDIM2
+#undef rDIM
+#undef sDIM
+#undef CODE_INTERNAL
+#undef CODE_BORDER
+#undef CODE_NOT_FOUND
+#else
+void FindPointsGSLIB::FindPointsEdgeLocal3( const Vector &point_pos,
+                                            int point_pos_ordering,
+                                            Array<unsigned int> &code,
+                                            Array<unsigned int> &elem,
+                                            Vector &ref,
+                                            Vector &dist,
+                                            int npt ) {} ;
+#endif
+} // namespace mfem
+
+#endif //ifdef MFEM_USE_GSLIB

fem/gslib/interpolate_local_1.cpp

@@ -0,0 +1,157 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "../gslib.hpp"
+#include "../../general/forall.hpp"
+#include "../../linalg/kernels.hpp"
+
+#ifdef MFEM_USE_GSLIB
+
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wunused-function"
+#endif
+#include "gslib.h"
+#ifndef GSLIB_RELEASE_VERSION //gslib v1.0.7
+#define GSLIB_RELEASE_VERSION 10007
+#endif
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#pragma GCC diagnostic pop
+#endif
+namespace mfem
+{
+#if GSLIB_RELEASE_VERSION >= 10009
+#define CODE_INTERNAL 0
+#define CODE_BORDER 1
+#define CODE_NOT_FOUND 2
+
+static MFEM_HOST_DEVICE void lagrange_eval(double *p0, double x,
+                                           int i, int p_Nq,
+                                           double *z, double *lagrangeCoeff)
+{
+   double p_i = (1 << (p_Nq - 1));
+   for (int j=0; j<p_Nq; ++j)
+   {
+      p_i *= j==i ? 1 : x-z[j];
+   }
+   p0[i] = lagrangeCoeff[i] * p_i;
+}
+
+template<int T_D1D = 0>
+static void InterpolateLocal1DKernel(const double *const gf_in,
+                                     int *const el,
+                                     double *const r,
+                                     double *const int_out,
+                                     const int npt,
+                                     const int nfields,
+                                     double *gll1D,
+                                     double *lagcoeff,
+                                     const int pN = 0)
+{
+   const int MD1 = T_D1D ? T_D1D : DofQuadLimits::MAX_D1D;
+   const int D1D = T_D1D ? T_D1D : pN;
+   const int p_Nq = D1D;
+   MFEM_VERIFY(MD1 <= DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(pN<=DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(D1D != 0, "Polynomial order not specified.");
+   // for each point of the npt points, create a thread block of size dof1Dsol
+   mfem::forall_2D(npt, D1D, 1, [=] MFEM_HOST_DEVICE (int i)
+   {
+      MFEM_SHARED double wtr[MD1];
+      MFEM_SHARED double sums[MD1];
+
+      // Evaluate basis functions at the reference space coordinates
+      MFEM_FOREACH_THREAD(j,x,D1D)
+      {
+         lagrange_eval(wtr, r[i], j, p_Nq, gll1D, lagcoeff);
+      }
+      MFEM_SYNC_THREAD;
+
+      for (int fld=0; fld<nfields; ++fld)
+      {
+         // If using GetNodalValues, ordering is NDOFS x NEL x VDIM and the
+         // offset would be `el[i] * p_Nq + fld * gf_offset`.
+         // R->Mult produces element vectors in NDOFS x VDIM x NEL layout.
+         const int elemOffset = el[i]*nfields*p_Nq + fld*p_Nq;
+         MFEM_FOREACH_THREAD(j,x,D1D)
+         {
+            sums[j] = wtr[j] * gf_in[elemOffset + j];
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD(j,x,1)
+         {
+            double sumv = 0.0;
+            // sum the contributions of each lagrange polynomial
+            for (int jj=0; jj<D1D; ++jj)
+            {
+               sumv += sums[jj];
+            }
+            int_out[fld*npt + i] = sumv;
+         }
+         MFEM_SYNC_THREAD;
+      }
+   });
+}
+
+void FindPointsGSLIB::InterpolateLocal1( const Vector &field_in,
+                                         Array<int> &gsl_elem_dev_l,
+                                         Vector &gsl_ref_l,
+                                         Vector &field_out,
+                                         int npt,
+                                         int ncomp,
+                                         int dof1Dsol )
+{
+   MFEM_VERIFY(dim == 1, "Kernel for edges only.");
+   if (npt == 0) { return; }
+   bool use_dev = field_in.UseDevice();
+   auto pfin = field_in.Read(use_dev);
+   auto pgsl = gsl_elem_dev_l.ReadWrite(use_dev);
+   auto pgslr = gsl_ref_l.ReadWrite(use_dev);
+   auto pfout = field_out.Write(use_dev);
+   auto pgll = DEV.gll1d_sol.ReadWrite(use_dev);
+   auto plcf = DEV.lagcoeff_sol.ReadWrite(use_dev);
+   switch (dof1Dsol)
+   {
+      case 2: return InterpolateLocal1DKernel<2>(pfin, pgsl, pgslr, pfout,
+                                                    npt, ncomp,
+                                                    pgll, plcf);
+      case 3: return InterpolateLocal1DKernel<3>(pfin, pgsl, pgslr, pfout,
+                                                    npt, ncomp,
+                                                    pgll, plcf);
+      case 4: return InterpolateLocal1DKernel<4>(pfin, pgsl, pgslr, pfout,
+                                                    npt, ncomp,
+                                                    pgll, plcf);
+      case 5: return InterpolateLocal1DKernel<5>(pfin, pgsl, pgslr, pfout,
+                                                    npt, ncomp,
+                                                    pgll, plcf);
+      default: return InterpolateLocal1DKernel(pfin, pgsl, pgslr, pfout,
+                                                  npt, ncomp,
+                                                  pgll, plcf, dof1Dsol);
+   }
+}
+#undef CODE_INTERNAL
+#undef CODE_BORDER
+#undef CODE_NOT_FOUND
+#else
+void FindPointsGSLIB::InterpolateLocal1(const Vector &field_in,
+                                        Array<int> &gsl_elem_dev_l,
+                                        Vector &gsl_ref_l,
+                                        Vector &field_out,
+                                        int npt, int ncomp,
+                                        int dof1Dsol) {};
+#endif
+
+} // namespace mfem
+
+#endif //ifdef MFEM_USE_GSLIB

fem/gslib/interpolate_local_2.cpp

@@ -52,8 +52,6 @@ static void InterpolateLocal2DKernel(const double *const gf_in,
                                      double *const int_out,
                                      const int npt,
                                      const int ncomp,
-                                     const int nel,
-                                     const int gf_offset,
                                      double *gll1D,
                                      double *lagcoeff,
                                      const int pN = 0)
@@ -64,6 +62,8 @@ static void InterpolateLocal2DKernel(const double *const gf_in,
    const int p_Np = D1D*D1D;
    MFEM_VERIFY(MD1 <= DofQuadLimits::MAX_D1D,
                "Increase Max allowable polynomial order.");
+   MFEM_VERIFY(pN<=DofQuadLimits::MAX_D1D,
+               "Increase Max allowable polynomial order.");
    MFEM_VERIFY(D1D != 0, "Polynomial order not specified.");
    mfem::forall_2D(npt, D1D, D1D, [=] MFEM_HOST_DEVICE (int i)
    {
@@ -82,9 +82,9 @@ static void InterpolateLocal2DKernel(const double *const gf_in,
 
       for (int fld = 0; fld < Nfields; ++fld)
       {
-         // If using GetNodalValues, ordering is NDOFSxNELxVDIM
-         // const int elemOffset = el[i] * p_Np + fld * gf_offset;
-         //if using R->Mult for L -> E-Vec use below: NDOFSxVDIMxNEL
+         // If using GetNodalValues, ordering is NDOFS x NEL x VDIM and the
+         // offset would be `el[i] * p_Np + fld * gf_offset`.
+         // R->Mult produces element vectors in NDOFS x VDIM x NEL layout.
          const int elemOffset = el[i] * p_Np * Nfields + fld * p_Np;
          MFEM_FOREACH_THREAD(j,x,D1D)
          {
@@ -120,32 +120,32 @@ void FindPointsGSLIB::InterpolateLocal2(const Vector &field_in,
                                         Vector &gsl_ref_l,
                                         Vector &field_out,
                                         int npt, int ncomp,
-                                        int nel, int dof1Dsol)
+                                        int dof1Dsol)
 {
    if (npt == 0) { return; }
-   const int gf_offset = field_in.Size()/ncomp;
-   auto pfin = field_in.Read();
-   auto pgsl = gsl_elem_dev_l.ReadWrite();
-   auto pgslr = gsl_ref_l.ReadWrite();
-   auto pfout = field_out.Write();
-   auto pgll = DEV.gll1d_sol.ReadWrite();
-   auto plcf = DEV.lagcoeff_sol.ReadWrite();
+   bool use_dev = field_in.UseDevice();
+   auto pfin = field_in.Read(use_dev);
+   auto pgsl = gsl_elem_dev_l.ReadWrite(use_dev);
+   auto pgslr = gsl_ref_l.ReadWrite(use_dev);
+   auto pfout = field_out.Write(use_dev);
+   auto pgll = DEV.gll1d_sol.ReadWrite(use_dev);
+   auto plcf = DEV.lagcoeff_sol.ReadWrite(use_dev);
    switch (dof1Dsol)
    {
       case 2: return InterpolateLocal2DKernel<2>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       case 3: return InterpolateLocal2DKernel<3>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       case 4: return InterpolateLocal2DKernel<4>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       case 5: return InterpolateLocal2DKernel<5>(pfin, pgsl, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       default: return InterpolateLocal2DKernel(pfin, pgsl, pgslr, pfout,
-                                                  npt, ncomp, nel, gf_offset,
+                                                  npt, ncomp,
                                                   pgll, plcf, dof1Dsol);
    }
 }
@@ -160,7 +160,7 @@ void FindPointsGSLIB::InterpolateLocal2(const Vector &field_in,
                                         Vector &gsl_ref_l,
                                         Vector &field_out,
                                         int npt, int ncomp,
-                                        int nel, int dof1Dsol) {};
+                                        int dof1Dsol) {};
 #endif
 } // namespace mfem
 

fem/gslib/interpolate_local_3.cpp

@@ -52,8 +52,6 @@ static void InterpolateLocal3DKernel(const double *const gf_in,
                                      double *const int_out,
                                      const int npt,
                                      const int ncomp,
-                                     const int nel,
-                                     const int gf_offset,
                                      double *gll1D,
                                      double *lagcoeff,
                                      const int pN = 0)
@@ -84,9 +82,9 @@ static void InterpolateLocal3DKernel(const double *const gf_in,
 
       for (int fld = 0; fld < Nfields; ++fld)
       {
-         // If using GetNodalValues, ordering is NDOFSxNELxVDIM
-         // const int elemOffset = el[i] * p_Np + fld * gf_offset;
-         //if using R->Mult for L -> E-Vec use below.
+         // If using GetNodalValues, ordering is NDOFS x NEL x VDIM and the
+         // offset would be `el[i] * p_Np + fld * gf_offset`.
+         // R->Mult produces element vectors in NDOFS x VDIM x NEL layout.
          const int elemOffset = el[i] * p_Np * Nfields + fld * p_Np;
          MFEM_FOREACH_THREAD(j,x,D1D)
          {
@@ -125,37 +123,38 @@ void FindPointsGSLIB::InterpolateLocal3(const Vector &field_in,
                                         Vector &gsl_ref_l,
                                         Vector &field_out,
                                         int npt, int ncomp,
-                                        int nel, int dof1Dsol)
+                                        int dof1Dsol)
 {
    if (npt == 0) { return; }
-   const int gf_offset = field_in.Size()/ncomp;
-   auto pfin = field_in.Read();
-   auto pgsle = gsl_elem_dev_l.ReadWrite();
-   auto pgslr = gsl_ref_l.ReadWrite();
-   auto pfout = field_out.Write();
-   auto pgll = DEV.gll1d_sol.ReadWrite();
-   auto plcf = DEV.lagcoeff_sol.ReadWrite();
+   bool use_dev = field_in.UseDevice();
+   auto pfin = field_in.Read(use_dev);
+   auto pgsle = gsl_elem_dev_l.ReadWrite(use_dev);
+   auto pgslr = gsl_ref_l.ReadWrite(use_dev);
+   auto pfout = field_out.Write(use_dev);
+   auto pgll = DEV.gll1d_sol.ReadWrite(use_dev);
+   auto plcf = DEV.lagcoeff_sol.ReadWrite(use_dev);
    switch (dof1Dsol)
    {
       case 2: return InterpolateLocal3DKernel<2>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       case 3: return InterpolateLocal3DKernel<3>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       case 4: return InterpolateLocal3DKernel<4>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       case 5: return InterpolateLocal3DKernel<5>(pfin, pgsle, pgslr, pfout,
-                                                    npt, ncomp, nel, gf_offset,
+                                                    npt, ncomp,
                                                     pgll, plcf);
       default: return InterpolateLocal3DKernel(pfin, pgsle, pgslr, pfout,
-                                                  npt, ncomp, nel, gf_offset,
+                                                  npt, ncomp,
                                                   pgll, plcf, dof1Dsol);
    }
 }
 
 
+#undef MAXC
 #undef CODE_INTERNAL
 #undef CODE_BORDER
 #undef CODE_NOT_FOUND
@@ -165,7 +164,7 @@ void FindPointsGSLIB::InterpolateLocal3(const Vector &field_in,
                                         Vector &gsl_ref_l,
                                         Vector &field_out,
                                         int npt, int ncomp,
-                                        int nel, int dof1Dsol) {};
+                                        int dof1Dsol) {};
 #endif
 } // namespace mfem
 

fem/tmop.cpp

@@ -3797,13 +3797,18 @@ void TMOP_Integrator::EnableLimiting(const GridFunction &n0, Coefficient &w0,
 
 void TMOP_Integrator::EnableAdaptiveLimiting(const GridFunction &z0,
                                              Coefficient &coeff,
-                                             AdaptivityEvaluator &ae)
+                                             AdaptivityEvaluator &ae,
+                                             real_t delta_max)
 {
+   MFEM_VERIFY(delta_max > 0.0,
+               "EnableAdaptiveLimiting requires delta_max > 0.0.");
+
    adapt_lim_gf0 = &z0;
    delete adapt_lim_gf;
    adapt_lim_gf   = new GridFunction(z0);
    adapt_lim_coeff = &coeff;
    adapt_lim_eval = &ae;
+   adapt_lim_delta_max = delta_max;
 
    adapt_lim_eval->SetSerialMetaInfo(*z0.FESpace()->GetMesh(),
                                      *z0.FESpace());
@@ -3814,14 +3819,19 @@ void TMOP_Integrator::EnableAdaptiveLimiting(const GridFunction &z0,
 #ifdef MFEM_USE_MPI
 void TMOP_Integrator::EnableAdaptiveLimiting(const ParGridFunction &z0,
                                              Coefficient &coeff,
-                                             AdaptivityEvaluator &ae)
+                                             AdaptivityEvaluator &ae,
+                                             real_t delta_max)
 {
+   MFEM_VERIFY(delta_max > 0.0,
+               "EnableAdaptiveLimiting requires delta_max > 0.0.");
+
    adapt_lim_gf0 = &z0;
    adapt_lim_pgf0 = &z0;
    delete adapt_lim_gf;
    adapt_lim_gf   = new GridFunction(z0);
    adapt_lim_coeff = &coeff;
    adapt_lim_eval = &ae;
+   adapt_lim_delta_max = delta_max;
 
    adapt_lim_eval->SetParMetaInfo(*z0.ParFESpace()->GetParMesh(),
                                   *z0.ParFESpace());
@@ -4297,7 +4307,8 @@ real_t TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
       // Contribution from the adaptive limiting term.
       if (adaptive_limiting)
       {
-         const real_t diff = adapt_lim_gf_q(i) - adapt_lim_gf0_q(i);
+         const real_t diff = (adapt_lim_gf_q(i) - adapt_lim_gf0_q(i)) /
+                             adapt_lim_delta_max;
          val += adapt_lim_coeff->Eval(*Tpr, ip) * lim_normal * diff * diff;
       }
 
@@ -4848,14 +4859,16 @@ void TMOP_Integrator::AssembleElemVecAdaptLim(const FiniteElement &el,
    grad_phys.Mult(adapt_lim_gf_e, grad_ptr);
 
    Vector adapt_lim_gf_grad_q(dim);
-
    for (int q = 0; q < nqp; q++)
    {
       const IntegrationPoint &ip = ir.IntPoint(q);
       el.CalcShape(ip, shape);
+
       adapt_lim_gf_grad_e.MultTranspose(shape, adapt_lim_gf_grad_q);
-      adapt_lim_gf_grad_q *= 2.0 * (adapt_lim_gf_q(q) - adapt_lim_gf0_q(q));
+      adapt_lim_gf_grad_q *= 2.0 * (adapt_lim_gf_q(q) - adapt_lim_gf0_q(q)) /
+                             adapt_lim_delta_max / adapt_lim_delta_max;
       adapt_lim_gf_grad_q *= weights(q) * lim_normal * adapt_lim_coeff->Eval(Tpr, ip);
+
       AddMultVWt(shape, adapt_lim_gf_grad_q, mat);
    }
 }
@@ -4902,7 +4915,11 @@ void TMOP_Integrator::AssembleElemGradAdaptLim(const FiniteElement &el,
       Vector gg_ptr(adapt_lim_gf_hess_q.GetData(), dim*dim);
       adapt_lim_gf_hess_e.MultTranspose(shape, gg_ptr);
 
-      const real_t w = weights(q) * lim_normal * adapt_lim_coeff->Eval(Tpr, ip);
+      const real_t coeff = adapt_lim_coeff->Eval(Tpr, ip);
+      const real_t factor =
+         weights(q) * lim_normal * coeff * 2.0 /
+         (adapt_lim_delta_max * adapt_lim_delta_max);
+
       for (int i = 0; i < dof * dim; i++)
       {
          const int idof = i % dof, idim = i / dof;
@@ -4910,10 +4927,11 @@ void TMOP_Integrator::AssembleElemGradAdaptLim(const FiniteElement &el,
          {
             const int jdof = j % dof, jdim = j / dof;
             const real_t entry =
-               w * ( 2.0 * adapt_lim_gf_grad_q(idim) * shape(idof) *
-                     /* */ adapt_lim_gf_grad_q(jdim) * shape(jdof) +
-                     2.0 * (adapt_lim_gf_q(q) - adapt_lim_gf0_q(q)) *
-                     adapt_lim_gf_hess_q(idim, jdim) * shape(idof) * shape(jdof));
+               factor *
+               (adapt_lim_gf_grad_q(idim) * shape(idof) *
+                adapt_lim_gf_grad_q(jdim) * shape(jdof) +
+                (adapt_lim_gf_q(q) - adapt_lim_gf0_q(q)) *
+                adapt_lim_gf_hess_q(idim, jdim) * shape(idof) * shape(jdof));
             mat(i, j) += entry;
             if (i != j) { mat(j, i) += entry; }
          }
@@ -5671,6 +5689,22 @@ UpdateAfterMeshPositionChange(const Vector &d, const FiniteElementSpace &d_fes)
    if (adapt_lim_gf)
    {
       adapt_lim_eval->ComputeAtNewPosition(x_loc, *adapt_lim_gf, ordering);
+      if (PA.enabled)
+      {
+         PA.AL_grads_assembled = false;
+
+         // Step 1 of PA.ALFmF0 update: subtract the old ALF.
+         PA.ALFmF0 -= PA.ALF;
+
+         // Refresh PA.ALF from the updated adapt_lim_gf.
+         const ElementDofOrdering ord = ElementDofOrdering::LEXICOGRAPHIC;
+         const Operator *alf_R =
+            adapt_lim_gf->FESpace()->GetElementRestriction(ord);
+         alf_R->Mult(*adapt_lim_gf, PA.ALF);
+
+         // Step 2 of PA.ALFmF0 update: add the new ALF.
+         PA.ALFmF0 += PA.ALF;
+      }
    }
 
    // Update surf_fit_gf (and optionally its gradients) if surface
@@ -5931,6 +5965,28 @@ void TMOPComboIntegrator::EnableLimiting(const GridFunction &n0,
    for (int i = 1; i < tmopi.Size(); i++) { tmopi[i]->DisableLimiting(); }
 }
 
+void TMOPComboIntegrator::EnableAdaptiveLimiting(const GridFunction &z0,
+                                                 Coefficient &coeff,
+                                                 AdaptivityEvaluator &ae,
+                                                 real_t delta_max)
+{
+   MFEM_VERIFY(tmopi.Size() > 0, "No TMOP_Integrators were added.");
+
+   tmopi[0]->EnableAdaptiveLimiting(z0, coeff, ae, delta_max);
+}
+
+#ifdef MFEM_USE_MPI
+void TMOPComboIntegrator::EnableAdaptiveLimiting(const ParGridFunction &z0,
+                                                 Coefficient &coeff,
+                                                 AdaptivityEvaluator &ae,
+                                                 real_t delta_max)
+{
+   MFEM_VERIFY(tmopi.Size() > 0, "No TMOP_Integrators were added.");
+
+   tmopi[0]->EnableAdaptiveLimiting(z0, coeff, ae, delta_max);
+}
+#endif
+
 void TMOPComboIntegrator::SetLimitingNodes(const GridFunction &n0)
 {
    MFEM_VERIFY(tmopi.Size() > 0, "No TMOP_Integrators were added.");

fem/tmop.hpp

@@ -1440,6 +1440,7 @@ public:
    void Eval_d2(const Vector &x, const Vector &x0, real_t dist,
                 DenseMatrix &d2) const override
    {
+      MFEM_CONTRACT_VAR(x0);
       MFEM_ASSERT(x.Size() == x0.Size(), "Bad input.");
 
       d2.Diag(1.0 / (dist * dist), x.Size());
@@ -2044,6 +2045,7 @@ protected:
    GridFunction *adapt_lim_gf;           // Owned. Updated by adapt_lim_eval.
    Coefficient *adapt_lim_coeff;         // Not owned.
    AdaptivityEvaluator *adapt_lim_eval;  // Not owned.
+   real_t adapt_lim_delta_max = 1.0;
 
    // Surface fitting.
    const Array<bool> *surf_fit_marker;      // Not owned. Nodes to fit.
@@ -2110,9 +2112,20 @@ protected:
    //     Updated by every call to PANonlinearFormExtension::GetGradient().
    // MC: Q-Vector for the metric Coefficient.
    //     Updated when the mesh nodes change.
+   // ALC:  Q-Vector for spatial weight used for the adaptive limiting term.
+   //       Updated when the mesh nodes change.
+   // ALF: E-Vector constructed using adaptive limiting GF zeta.
+   //      The zeta is remapped when the mesh nodes change.
+   // ALFmF0: E-Vector constructed using adaptive limiting GF zeta.
+   //         It stores difference zeta-zeta0, as all computations use this.
+   // ALFG: Q-Vector for gradient of ALF at quadrature points.
+   //       Updated by every call to PANonlinearFormExtension::GetGradient().
+   // ALFH: Q-Vector for Hessian of ALF at quadrature points.
+   //       Updated by every call to PANonlinearFormExtension::GetGradient().
    //
-   // maps:     Dof2Quad map for fes associated with the nodal coordinates.
-   // maps_lim: Dof2Quad map for fes associated with the limiting dist GridFunc.
+   // maps:       Dof2Quad map for fes associated with the nodal coordinates.
+   // maps_lim:   Dof2Quad map for fes associated with the limiting dist GF.
+   // maps_nodes: like maps, but the quad points are the FE nodes.
    //
    // Jtr_debug_grad
    //     We keep track if Jtr was set by AssembleGradPA() in Jtr_debug_grad: it
@@ -2131,9 +2144,13 @@ protected:
       mutable DenseTensor Jtr;
       mutable bool Jtr_needs_update;
       mutable bool Jtr_debug_grad;
-      mutable Vector E, O, X0, XL, H, C0, LD, H0, MC;
+      mutable Vector E, O, X0, XL, H, C0, LD, H0, MC, ALC,
+              ALF, ALFmF0, ALFG, ALFH;
+      mutable bool AL_grads_assembled;
+      real_t al_delta;
       const DofToQuad *maps;
       const DofToQuad *maps_lim = nullptr;
+      const DofToQuad *maps_nodes = nullptr;
       const GeometricFactors *geom;
       const FiniteElementSpace *fes;
       const IntegrationRule *ir;
@@ -2216,16 +2233,25 @@ protected:
       return EnergyIntegrationRule(el);
    }
 
+   //
    // Auxiliary PA methods
+   //
+
+   // PA quadrature data computation - metric term / limiting / adapt limiting.
    void AssembleGradPA_2D(const Vector&) const;
    void AssembleGradPA_3D(const Vector&) const;
    void AssembleGradPA_C0_2D(const Vector&) const;
    void AssembleGradPA_C0_3D(const Vector&) const;
+   void AssembleGradPA_AdaptLim_2D(const Vector&) const;
+   void AssembleGradPA_AdaptLim_3D(const Vector&) const;
 
+   // PA energy computation - metric term / limiting / adaptive limiting.
    void GetLocalStateEnergyPA_2D(const Vector &x, real_t &energy) const;
-   void GetLocalStateEnergyPA_3D(const Vector&, real_t &energy) const;
+   void GetLocalStateEnergyPA_3D(const Vector &x, real_t &energy) const;
    real_t GetLocalStateEnergyPA_C0_2D(const Vector&) const;
    real_t GetLocalStateEnergyPA_C0_3D(const Vector&) const;
+   real_t GetLocalStateEnergyPA_AdaptLim_2D() const;
+   real_t GetLocalStateEnergyPA_AdaptLim_3D() const;
    void GetLocalNormalizationEnergiesPA_2D(const Vector &x,
                                            real_t &met_energy,
                                            real_t &lim_energy) const;
@@ -2233,22 +2259,35 @@ protected:
                                            real_t &met_energy,
                                            real_t &lim_energy) const;
 
+   // PA gradient computation - metric term / limiting / adaptive limiting.
    void AddMultPA_2D(const Vector&, Vector&) const;
    void AddMultPA_3D(const Vector&, Vector&) const;
    void AddMultPA_C0_2D(const Vector&, Vector&) const;
    void AddMultPA_C0_3D(const Vector&, Vector&) const;
+   void AddMultPA_AdaptLim_2D(const Vector&, Vector&) const;
+   void AddMultPA_AdaptLim_3D(const Vector&, Vector&) const;
 
+   // PA Hessian AddMult - metric term / limiting / adaptive limiting.
    void AddMultGradPA_2D(const Vector&, Vector&) const;
    void AddMultGradPA_3D(const Vector&, Vector&) const;
    void AddMultGradPA_C0_2D(const Vector&, Vector&) const;
    void AddMultGradPA_C0_3D(const Vector&, Vector&) const;
+   void AddMultGradPA_AdaptLim_2D(const Vector&, Vector&) const;
+   void AddMultGradPA_AdaptLim_3D(const Vector&, Vector&) const;
 
+   // PA diagonal assemblies - metric term / limiting / adaptive limiting.
    void AssembleDiagonalPA_2D(Vector&) const;
    void AssembleDiagonalPA_3D(Vector&) const;
    void AssembleDiagonalPA_C0_2D(Vector&) const;
    void AssembleDiagonalPA_C0_3D(Vector&) const;
+   void AssembleDiagonalPA_AdaptLim_2D(Vector&) const;
+   void AssembleDiagonalPA_AdaptLim_3D(Vector&) const;
 
+   // Setup of PA data structures related to the limiting term.
    void AssemblePA_Limiting();
+   // Setup of PA data structures related to the adaptive limiting term.
+   void AssemblePA_AdaptLim();
+   // Compute reference->target Jacobians for all quad points.
    void ComputeAllElementTargets(const Vector &xe = Vector()) const;
    // Updates the Q-vectors for the metric_coeff and lim_coeff, based on the
    // new physical positions of the quadrature points.
@@ -2351,21 +2390,23 @@ public:
 
    /** @brief Restriction of the node positions to certain regions.
 
-       Adds the term $ \int c (z(x) - z_0(x_0))^2 $, where z0(x0) is a given
-       function on the starting mesh, and z(x) is its image on the new mesh.
-       Minimizing this term means that a node at x0 is allowed to move to a
-       position x(x0) only if z(x) ~ z0(x0).
+       Adds the term $ \int c (z(x) - z_0(x_0))^2 / delta_max^2 $, where z0(x0)
+       is a given function on the starting mesh, and z(x) is its image on the
+       new mesh. Minimizing this term means that a node at x0 is allowed to
+       move to a position x(x0) only if z(x) ~ z0(x0).
        Such term can be used for tangential mesh relaxation.
 
        @param[in] z0     Function z0 that controls the adaptive limiting.
        @param[in] coeff  Coefficient c for the above integral.
-       @param[in] ae     AdaptivityEvaluator to compute z(x) from z0(x0). */
+       @param[in] ae     AdaptivityEvaluator to compute z(x) from z0(x0).
+       @param[in] delta_max Controls the allowable deviation from z0.
+                            Smaller values activate the term faster. */
    void EnableAdaptiveLimiting(const GridFunction &z0, Coefficient &coeff,
-                               AdaptivityEvaluator &ae);
+                               AdaptivityEvaluator &ae, real_t delta_max = 1.0);
 #ifdef MFEM_USE_MPI
    /// Parallel support for adaptive limiting.
    void EnableAdaptiveLimiting(const ParGridFunction &z0, Coefficient &coeff,
-                               AdaptivityEvaluator &ae);
+                               AdaptivityEvaluator &ae, real_t delta_max = 1.0);
 #endif
 
    /** @brief Fitting of certain DOFs to the zero level set of a function.
@@ -2588,6 +2629,16 @@ public:
    void EnableLimiting(const GridFunction &n0, Coefficient &w0,
                        TMOP_LimiterFunction *lfunc = NULL);
 
+   /// Adds the adaptive limiting term to the first integrator.
+   void EnableAdaptiveLimiting(const GridFunction &z0, Coefficient &coeff,
+                               AdaptivityEvaluator &ae, real_t delta_max = 1.0);
+#ifdef MFEM_USE_MPI
+   /// Parallel support for adaptive limiting.
+   void EnableAdaptiveLimiting(const ParGridFunction &z0, Coefficient &coeff,
+                               AdaptivityEvaluator &ae, real_t delta_max = 1.0);
+#endif
+
+
    /// Update the original/reference nodes used for limiting.
    void SetLimitingNodes(const GridFunction &n0);
 

fem/tmop/assemble/diag2_limit.cpp

@@ -11,7 +11,9 @@
 
 #include "../pa.hpp"
 #include "../../tmop.hpp"
+#include "../../kernels.hpp"
 #include "../../../general/forall.hpp"
+#include "../../../linalg/kernels.hpp"
 
 namespace mfem
 {
@@ -64,6 +66,93 @@ void TMOP_AssembleDiagPA_C0_2D(const int NE,
    });
 }
 
+// Diagonal assembly for AdaptLim limiting (2D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AssembleDiagPA_AdaptLim_2D(const real_t lim_normal,
+                                     const real_t adapt_lim_delta_max,
+                                     const bool const_coeff,
+                                     const DeviceTensor<3, const real_t> &ALC,
+                                     const int NE,
+                                     const DeviceTensor<5, const real_t> &J,
+                                     const ConstDeviceMatrix &W,
+                                     const real_t *b,
+                                     const DeviceTensor<4, const real_t> &ALF_grad,
+                                     const DeviceTensor<5, const real_t> &ALF_hess,
+                                     const ConstDeviceCube &ALFmF0,
+                                     DeviceTensor<4> &D,
+                                     const int d1d,
+                                     const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const real_t normal_inv_delta_sq =
+      2.0 * lim_normal / (adapt_lim_delta_max * adapt_lim_delta_max);
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t sB[MD1][MQ1];
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // ALF and ALF0 values at quad points.
+      kernels::internal::s_regs2d_t<MQ1> alf_dof, alf_quad;
+      kernels::internal::LoadDofs2d(e, D1D, ALFmF0, alf_dof);
+      kernels::internal::Eval2d(D1D, Q1D, smem, sB, alf_dof, alf_quad);
+
+      MFEM_SHARED real_t qd[MQ1 * MD1];
+      DeviceTensor<2, real_t> QD(qd, MQ1, MD1);
+
+      for (int v = 0; v < 2; v++)
+      {
+         // Contract in y.
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               QD(qx, dy) = 0.0;
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  const real_t By = sB[dy][qy];
+                  const real_t bb = By * By;
+
+                  const real_t *Jtr = &J(0, 0, qx, qy, e);
+                  const real_t detJtr = kernels::Det<2>(Jtr);
+                  const real_t weight = W(qx, qy) * detJtr;
+                  const real_t coeff = const_coeff ? ALC(0, 0, 0) : ALC(qx, qy, e);
+                  const real_t factor = weight * coeff * normal_inv_delta_sq;
+
+                  const real_t diff = alf_quad(qy, qx);
+                  const real_t grad_v = ALF_grad(v, qx, qy, e);
+                  const real_t hess_vv = ALF_hess(v, v, qx, qy, e);
+                  const real_t hdiag = factor * (grad_v * grad_v + diff * hess_vv);
+
+                  QD(qx, dy) += bb * hdiag;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Contract in x.
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+            {
+               real_t d = 0.0;
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  const real_t Bx = sB[dx][qx];
+                  const real_t bb = Bx * Bx;
+                  d += bb * QD(qx, dy);
+               }
+               D(dx, dy, v, e) += d;
+            }
+         }
+         MFEM_SYNC_THREAD;
+      }
+   });
+}
+
 MFEM_TMOP_MDQ_REGISTER(TMOPAssembleDiagCoef2D, TMOP_AssembleDiagPA_C0_2D);
 MFEM_TMOP_MDQ_SPECIALIZE(TMOPAssembleDiagCoef2D);
 
@@ -80,4 +169,34 @@ void TMOP_Integrator::AssembleDiagonalPA_C0_2D(Vector &diagonal) const
    TMOPAssembleDiagCoef2D::Run(d, q, NE, B, H0, D, d, q);
 }
 
+MFEM_TMOP_MDQ_REGISTER(TMOPAssembleDiagAdaptLim2D,
+                       TMOP_AssembleDiagPA_AdaptLim_2D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPAssembleDiagAdaptLim2D);
+
+void TMOP_Integrator::AssembleDiagonalPA_AdaptLim_2D(Vector &diagonal) const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, NE);
+
+   const auto J = Reshape(PA.Jtr.Read(), 2, 2, q, q, NE);
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q);
+   const auto *B = PA.maps->B.Read();
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, NE);
+   const auto ALF_grad = Reshape(PA.ALFG.Read(), 2, q, q, NE);
+   const auto ALF_hess = Reshape(PA.ALFH.Read(), 2, 2, q, q, NE);
+   auto D = Reshape(diagonal.ReadWrite(), d, d, 2, NE);
+
+   TMOPAssembleDiagAdaptLim2D::Run(d, q, ln, delta_max, const_coeff, ALC, NE,
+                                   J, W, B, ALF_grad, ALF_hess, ALFmF0, D, d, q);
+}
+
 } // namespace mfem

fem/tmop/assemble/diag3_limit.cpp

@@ -13,6 +13,7 @@
 #include "../../tmop.hpp"
 #include "../../kernels.hpp"
 #include "../../../general/forall.hpp"
+#include "../../../linalg/kernels.hpp"
 
 namespace mfem
 {
@@ -128,4 +129,162 @@ void TMOP_Integrator::AssembleDiagonalPA_C0_3D(Vector &diagonal) const
    TMOPAssembleDiagCoef3D::Run(d, q, NE, B, H0, D, d, q);
 }
 
+// Diagonal assembly for AdaptLim limiting (3D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AssembleDiagPA_AdaptLim_3D(const real_t lim_normal,
+                                     const real_t adapt_lim_delta_max,
+                                     const bool const_coeff,
+                                     const DeviceTensor<4, const real_t> &ALC,
+                                     const int NE,
+                                     const DeviceTensor<6, const real_t> &J,
+                                     const ConstDeviceCube &W,
+                                     const real_t *b,
+                                     const DeviceTensor<5, const real_t> &ALF_grad,
+                                     const DeviceTensor<6, const real_t> &ALF_hess,
+                                     const DeviceTensor<4, const real_t> &ALFmF0,
+                                     DeviceTensor<5> &D,
+                                     const int d1d,
+                                     const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const real_t normal_inv_delta_sq =
+      2.0 * lim_normal / (adapt_lim_delta_max * adapt_lim_delta_max);
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t sB[MD1][MQ1];
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // ALF and ALF0 values at quad points.
+      kernels::internal::s_regs3d_t<MQ1> alf_dof, alf_quad;
+      kernels::internal::LoadDofs3d(e, D1D, ALFmF0, alf_dof);
+      kernels::internal::Eval3d(D1D, Q1D, smem, sB, alf_dof, alf_quad);
+
+      kernels::internal::s_regs3d_t<MQ1> r0, r1;
+
+      for (int v = 0; v < 3; ++v)
+      {
+         // Contract in z.
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  real_t u = 0.0;
+                  for (int qz = 0; qz < Q1D; ++qz)
+                  {
+                     const real_t Bz = sB[dz][qz];
+                     const real_t bb = Bz * Bz;
+
+                     const real_t *Jtr = &J(0, 0, qx, qy, qz, e);
+                     const real_t detJtr = kernels::Det<3>(Jtr);
+                     const real_t weight = W(qx, qy, qz) * detJtr;
+                     const real_t coeff = const_coeff ? ALC(0, 0, 0, 0) : ALC(qx, qy, qz, e);
+                     const real_t factor = weight * coeff * normal_inv_delta_sq;
+
+                     const real_t diff = alf_quad(qz, qy, qx);
+                     const real_t grad_v = ALF_grad(v, qx, qy, qz, e);
+                     const real_t hess_vv = ALF_hess(v, v, qx, qy, qz, e);
+                     const real_t hdiag = factor * (grad_v * grad_v + diff * hess_vv);
+
+                     u += bb * hdiag;
+                  }
+                  r0[dz][qy][qx] = u;
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+
+         // Contract in y.
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  smem[qy][qx] = r0[dz][qy][qx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  real_t u = 0.0;
+                  for (int qy = 0; qy < Q1D; ++qy)
+                  {
+                     const real_t By = sB[dy][qy];
+                     u += (By * By) * smem[qy][qx];
+                  }
+                  r1[dz][dy][qx] = u;
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+
+         // Contract in x.
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  smem[dy][qx] = r1[dz][dy][qx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  real_t u = 0.0;
+                  for (int qx = 0; qx < Q1D; ++qx)
+                  {
+                     const real_t Bx = sB[dx][qx];
+                     u += (Bx * Bx) * smem[dy][qx];
+                  }
+                  D(dx, dy, dz, v, e) += u;
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+      }
+   });
+}
+
+MFEM_TMOP_MDQ_REGISTER(TMOPAssembleDiagAdaptLim3D,
+                       TMOP_AssembleDiagPA_AdaptLim_3D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPAssembleDiagAdaptLim3D);
+
+void TMOP_Integrator::AssembleDiagonalPA_AdaptLim_3D(Vector &diagonal) const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, q, NE);
+   const auto J = Reshape(PA.Jtr.Read(), 3, 3, q, q, q, NE);
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q, q);
+   const auto *B = PA.maps->B.Read();
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, d, NE);
+   const auto ALF_grad = Reshape(PA.ALFG.Read(), 3, q, q, q, NE);
+   const auto ALF_hess = Reshape(PA.ALFH.Read(), 3, 3, q, q, q, NE);
+   auto D = Reshape(diagonal.ReadWrite(), d, d, d, 3, NE);
+
+   TMOPAssembleDiagAdaptLim3D::Run(d, q, ln, delta_max, const_coeff, ALC, NE,
+                                   J, W, B, ALF_grad, ALF_hess, ALFmF0, D, d, q);
+}
+
 } // namespace mfem

fem/tmop/assemble/grad2_limit.cpp

@@ -113,6 +113,178 @@ void TMOP_AssembleGradPA_C0_2D(const real_t lim_normal,
    });
 }
 
+// Assemble gradient and Hessian of ALF field at quadrature points for AdaptLim (2D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AssembleGradPA_AdaptLim_2D(const int NE,
+                                     const real_t *B_nodes,
+                                     const real_t *G_nodes,
+                                     const real_t *B,
+                                     const DeviceTensor<4, const real_t> &X,
+                                     const ConstDeviceCube &ALF,
+                                     DeviceTensor<4> &ALF_grad,
+                                     DeviceTensor<5> &ALF_hess,
+                                     const int d1d,
+                                     const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      // MD1 x MD1 or MQ1 x MQ1 shared memory block.
+      MFEM_SHARED union { real_t d[MD1][MD1]; real_t q[MQ1][MQ1]; } smem;
+      MFEM_SHARED real_t sB_nodes[MD1][MD1], sG_nodes[MD1][MD1];
+      MFEM_SHARED real_t sB_q[MD1][MQ1];
+
+      kernels::internal::s_regs2d_t<MD1> grad_c;
+      kernels::internal::v_regs2d_t<2, MD1> hess_c;
+
+      // Maps nodes - nodes.
+      kernels::internal::LoadMatrix(D1D, D1D, B_nodes, sB_nodes);
+      kernels::internal::LoadMatrix(D1D, D1D, G_nodes, sG_nodes);
+      // Map nodes - quads.
+      kernels::internal::LoadMatrix(D1D, Q1D, B, sB_q);
+
+      // Compute the physical Jacobian at DOF nodes.
+      kernels::internal::vd_regs2d_t<2, 2, MD1> r_X, r_J;
+      kernels::internal::LoadDofs2d(e, D1D, X, r_X);
+      kernels::internal::Grad2d(D1D, D1D, smem.d, sB_nodes, sG_nodes, r_X, r_J);
+
+      // Compute the reference derivatives of ALF at DOF nodes.
+      kernels::internal::s_regs2d_t<MD1> alf_n, dalf_dx_n, dalf_dy_n;
+      kernels::internal::LoadDofs2d(e, D1D, ALF, alf_n);
+      kernels::internal::Contract2d<false, MD1>(D1D, D1D, smem.d,
+                                                sG_nodes, sB_nodes,
+                                                alf_n, dalf_dx_n);
+      kernels::internal::LoadDofs2d(e, D1D, ALF, alf_n);
+      kernels::internal::Contract2d<false, MD1>(D1D, D1D, smem.d,
+                                                sB_nodes, sG_nodes,
+                                                alf_n, dalf_dy_n);
+
+      // Interpolation workspaces.
+      kernels::internal::s_regs2d_t<MQ1> r0, r1;
+
+      // Precompute the inverse of the physical Jacobian.
+      kernels::internal::vd_regs2d_t<2, 2, MD1> Jpr_inv;
+      MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+         {
+            const real_t Jpr[4] =
+            {
+               r_J[0][0][dy][dx], r_J[1][0][dy][dx],
+               r_J[0][1][dy][dx], r_J[1][1][dy][dx]
+            };
+            real_t Jpri[4];
+            kernels::CalcInverse<2>(Jpr, Jpri);
+            Jpr_inv(0, 0, dx, dy) = Jpri[0];
+            Jpr_inv(1, 0, dx, dy) = Jpri[1];
+            Jpr_inv(0, 1, dx, dy) = Jpri[2];
+            Jpr_inv(1, 1, dx, dy) = Jpri[3];
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      // Compute/interpolate gradient and Hessian one vector component at a time.
+      for (int c = 0; c < 2; c++)
+      {
+         kernels::internal::s_regs2d_t<MD1> rgrad_nodes, ddalf_dx_n, ddalf_dy_n;
+
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+            {
+               grad_c[dy][dx] =
+                  Jpr_inv(0, c, dx, dy) * dalf_dx_n[dy][dx] +
+                  Jpr_inv(1, c, dx, dy) * dalf_dy_n[dy][dx];
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Compute ALF_grad with intermediate workspaces
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+            {
+               r0[dy][dx] = grad_c[dy][dx];
+            }
+         }
+         MFEM_SYNC_THREAD;
+         kernels::internal::Eval2d<MQ1>(D1D, Q1D, smem.q, sB_q, r0, r1);
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+            {
+               ALF_grad(c, qx, qy, e) = r1[qy][qx];
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Compute ddalf_dx_n.
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+            {
+               rgrad_nodes[dy][dx] = grad_c[dy][dx];
+            }
+         }
+         MFEM_SYNC_THREAD;
+         kernels::internal::Contract2d<false, MD1>(D1D, D1D, smem.d,
+                                                   sG_nodes, sB_nodes,
+                                                   rgrad_nodes, ddalf_dx_n);
+         // Compute ddalf_dy_n.
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+            {
+               rgrad_nodes[dy][dx] = grad_c[dy][dx];
+            }
+         }
+         MFEM_SYNC_THREAD;
+         kernels::internal::Contract2d<false, MD1>(D1D, D1D, smem.d,
+                                                   sB_nodes, sG_nodes,
+                                                   rgrad_nodes, ddalf_dy_n);
+         // Compute hess_c with ddalf_[dx, dy]_n.
+         MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+            {
+               const real_t ddalf_dx = ddalf_dx_n[dy][dx];
+               const real_t ddalf_dy = ddalf_dy_n[dy][dx];
+               const real_t ddx = Jpr_inv(0, 0, dy, dx) * ddalf_dx +
+                                  Jpr_inv(1, 0, dy, dx) * ddalf_dy;
+               const real_t ddy = Jpr_inv(0, 1, dy, dx) * ddalf_dx +
+                                  Jpr_inv(1, 1, dy, dx) * ddalf_dy;
+               hess_c[0][dy][dx] = ddx;
+               hess_c[1][dy][dx] = ddy;
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         for (int j = 0; j < 2; j++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  r0[dy][dx] = hess_c[j][dy][dx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+            kernels::internal::Eval2d<MQ1>(D1D, Q1D, smem.q, sB_q, r0, r1);
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  ALF_hess(c, j, qx, qy, e) = r1[qy][qx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+      }
+   });
+}
+
 MFEM_TMOP_MDQ_REGISTER(TMOPAssembleGradCoef2D, TMOP_AssembleGradPA_C0_2D);
 MFEM_TMOP_MDQ_SPECIALIZE(TMOPAssembleGradCoef2D);
 
@@ -142,4 +314,29 @@ void TMOP_Integrator::AssembleGradPA_C0_2D(const Vector &x) const
                                J, W, b, bld, XL, X, H0, exp_lim, d, q);
 }
 
+MFEM_TMOP_MDQ_REGISTER(TMOPAssembleGradAdaptLim2D,
+                       TMOP_AssembleGradPA_AdaptLim_2D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPAssembleGradAdaptLim2D);
+
+void TMOP_Integrator::AssembleGradPA_AdaptLim_2D(const Vector &x) const
+{
+   if (PA.AL_grads_assembled) { return; }
+
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const auto *B_nodes = PA.maps_nodes->B.Read(),
+               *G_nodes = PA.maps_nodes->G.Read();
+   const auto *B = PA.maps->B.Read();
+   const auto X = Reshape(x.Read(), d, d, 2, NE);
+   const auto ALF = Reshape(PA.ALF.Read(), d, d, NE);
+   auto ALF_grad = Reshape(PA.ALFG.Write(), 2, q, q, NE);
+   auto ALF_hess = Reshape(PA.ALFH.Write(), 2, 2, q, q, NE);
+
+   TMOPAssembleGradAdaptLim2D::Run(d, q, NE, B_nodes, G_nodes, B, X, ALF,
+                                   ALF_grad, ALF_hess, d, q);
+   PA.AL_grads_assembled = true;
+}
+
 } // namespace mfem

fem/tmop/assemble/grad3_limit.cpp

@@ -164,4 +164,252 @@ void TMOP_Integrator::AssembleGradPA_C0_3D(const Vector &x) const
                                J, W, b, bld, XL, X, H0, exp_lim, d, q);
 }
 
+// Assemble gradient and Hessian of ALF field at quadrature points for AdaptLim (3D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AssembleGradPA_AdaptLim_3D(const int NE,
+                                     const real_t *B_nodes,
+                                     const real_t *G_nodes,
+                                     const real_t *B,
+                                     const DeviceTensor<5, const real_t> &X,
+                                     const DeviceTensor<4, const real_t> &ALF,
+                                     DeviceTensor<5> &ALF_grad,
+                                     DeviceTensor<6> &ALF_hess,
+                                     const int d1d,
+                                     const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   mfem::forall_2D<T_Q1D*T_Q1D>(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      // MD1 x MD1 or MQ1 x MQ1 shared memory block.
+      MFEM_SHARED union { real_t d[MD1][MD1]; real_t q[MQ1][MQ1]; } smem;
+      MFEM_SHARED real_t sB_nodes[MD1][MD1], sG_nodes[MD1][MD1];
+      MFEM_SHARED real_t sB_q[MD1][MQ1];
+
+      kernels::internal::s_regs3d_t<MD1> grad_c;
+      kernels::internal::v_regs3d_t<3, MD1> hess_c;
+
+      // Maps nodes - nodes.
+      kernels::internal::LoadMatrix(D1D, D1D, B_nodes, sB_nodes);
+      kernels::internal::LoadMatrix(D1D, D1D, G_nodes, sG_nodes);
+      // Map nodes - quads.
+      kernels::internal::LoadMatrix(D1D, Q1D, B, sB_q);
+
+      // Compute the physical Jacobian at DOF nodes.
+      kernels::internal::vd_regs3d_t<3, 3, MD1> r_X, r_J;
+      kernels::internal::LoadDofs3d(e, D1D, X, r_X);
+      kernels::internal::Grad3d(D1D, D1D, smem.d, sB_nodes, sG_nodes, r_X, r_J);
+
+      // Compute the reference derivatives of ALF at DOF nodes.
+      kernels::internal::s_regs3d_t<MD1> alf_n, dalf_dxi_n, dalf_deta_n, dalf_dzeta_n;
+      kernels::internal::LoadDofs3d(e, D1D, ALF, alf_n);
+      kernels::internal::Contract3d<false, MD1>(D1D, D1D, smem.d,
+                                                sG_nodes, sB_nodes, sB_nodes,
+                                                alf_n, dalf_dxi_n);
+      kernels::internal::LoadDofs3d(e, D1D, ALF, alf_n);
+      kernels::internal::Contract3d<false, MD1>(D1D, D1D, smem.d,
+                                                sB_nodes, sG_nodes, sB_nodes,
+                                                alf_n, dalf_deta_n);
+      kernels::internal::LoadDofs3d(e, D1D, ALF, alf_n);
+      kernels::internal::Contract3d<false, MD1>(D1D, D1D, smem.d,
+                                                sB_nodes, sB_nodes, sG_nodes,
+                                                alf_n, dalf_dzeta_n);
+
+      // Interpolation workspaces.
+      kernels::internal::s_regs3d_t<MQ1> r0, r1;
+
+      // Compute/interpolate gradient and Hessian one vector component at a time.
+      for (int c = 0; c < 3; c++)
+      {
+         kernels::internal::s_regs3d_t<MD1> rgrad_nodes, dd_dxi_n, dd_deta_n, dd_dzeta_n;
+
+         // Precompute the inverse of the physical Jacobian.
+         kernels::internal::vd_regs3d_t<3, 3, MD1> Jpr_inv;
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  const real_t Jpr[9] =
+                  {
+                     r_J[0][0][dz][dy][dx], r_J[1][0][dz][dy][dx], r_J[2][0][dz][dy][dx],
+                     r_J[0][1][dz][dy][dx], r_J[1][1][dz][dy][dx], r_J[2][1][dz][dy][dx],
+                     r_J[0][2][dz][dy][dx], r_J[1][2][dz][dy][dx], r_J[2][2][dz][dy][dx]
+                  };
+                  real_t Jpri[9];
+                  kernels::CalcInverse<3>(Jpr, Jpri);
+                  Jpr_inv(0, 0, dx, dy, dz) = Jpri[0];
+                  Jpr_inv(1, 0, dx, dy, dz) = Jpri[1];
+                  Jpr_inv(2, 0, dx, dy, dz) = Jpri[2];
+                  Jpr_inv(0, 1, dx, dy, dz) = Jpri[3];
+                  Jpr_inv(1, 1, dx, dy, dz) = Jpri[4];
+                  Jpr_inv(2, 1, dx, dy, dz) = Jpri[5];
+                  Jpr_inv(0, 2, dx, dy, dz) = Jpri[6];
+                  Jpr_inv(1, 2, dx, dy, dz) = Jpri[7];
+                  Jpr_inv(2, 2, dx, dy, dz) = Jpri[8];
+
+                  grad_c[dz][dy][dx] =
+                     Jpr_inv(0, c, dx, dy, dz) * dalf_dxi_n[dz][dy][dx] +
+                     Jpr_inv(1, c, dx, dy, dz) * dalf_deta_n[dz][dy][dx] +
+                     Jpr_inv(2, c, dx, dy, dz) * dalf_dzeta_n[dz][dy][dx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+
+         // Compute ALF_grad with intermediate workspaces.
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  r0[dz][dy][dx] = grad_c[dz][dy][dx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+         kernels::internal::Eval3d<MQ1>(D1D, Q1D, smem.q, sB_q, r0, r1);
+         for (int qz = 0; qz < Q1D; ++qz)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+               {
+                  ALF_grad(c, qx, qy, qz, e) = r1[qz][qy][qx];
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         // Compute dd_dxi_n.
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  rgrad_nodes[dz][dy][dx] = grad_c[dz][dy][dx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+         kernels::internal::Contract3d<false, MD1>(D1D, D1D, smem.d,
+                                                   sG_nodes, sB_nodes, sB_nodes,
+                                                   rgrad_nodes, dd_dxi_n);
+         // Compute dd_deta_n.
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  rgrad_nodes[dz][dy][dx] = grad_c[dz][dy][dx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+         kernels::internal::Contract3d<false, MD1>(D1D, D1D, smem.d,
+                                                   sB_nodes, sG_nodes, sB_nodes,
+                                                   rgrad_nodes, dd_deta_n);
+         // Compute dd_dzeta_n.
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  rgrad_nodes[dz][dy][dx] = grad_c[dz][dy][dx];
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+         kernels::internal::Contract3d<false, MD1>(D1D, D1D, smem.d,
+                                                   sB_nodes, sB_nodes, sG_nodes,
+                                                   rgrad_nodes, dd_dzeta_n);
+
+         // Compute hess_c with dd_[dxi, deta, dzeta]_n.
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+               {
+                  const real_t dd_dxi   = dd_dxi_n[dz][dy][dx];
+                  const real_t dd_deta  = dd_deta_n[dz][dy][dx];
+                  const real_t dd_dzeta = dd_dzeta_n[dz][dy][dx];
+                  const real_t ddx = Jpr_inv(0, 0, dx, dy, dz) * dd_dxi +
+                                     Jpr_inv(1, 0, dx, dy, dz) * dd_deta +
+                                     Jpr_inv(2, 0, dx, dy, dz) * dd_dzeta;
+                  const real_t ddy = Jpr_inv(0, 1, dx, dy, dz) * dd_dxi +
+                                     Jpr_inv(1, 1, dx, dy, dz) * dd_deta +
+                                     Jpr_inv(2, 1, dx, dy, dz) * dd_dzeta;
+                  const real_t ddz = Jpr_inv(0, 2, dx, dy, dz) * dd_dxi +
+                                     Jpr_inv(1, 2, dx, dy, dz) * dd_deta +
+                                     Jpr_inv(2, 2, dx, dy, dz) * dd_dzeta;
+                  hess_c[0][dz][dy][dx] = ddx;
+                  hess_c[1][dz][dy][dx] = ddy;
+                  hess_c[2][dz][dy][dx] = ddz;
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+
+         for (int j = 0; j < 3; j++)
+         {
+            for (int dz = 0; dz < D1D; dz++)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(dy, y, D1D)
+               {
+                  MFEM_FOREACH_THREAD_DIRECT(dx, x, D1D)
+                  {
+                     r0[dz][dy][dx] = hess_c[j][dz][dy][dx];
+                  }
+               }
+               MFEM_SYNC_THREAD;
+            }
+            kernels::internal::Eval3d<MQ1>(D1D, Q1D, smem.q, sB_q, r0, r1);
+            for (int qz = 0; qz < Q1D; ++qz)
+            {
+               MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+               {
+                  MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+                  {
+                     ALF_hess(c, j, qx, qy, qz, e) = r1[qz][qy][qx];
+                  }
+               }
+            }
+            MFEM_SYNC_THREAD;
+         }
+      }
+   });
+}
+
+MFEM_TMOP_MDQ_REGISTER(TMOPAssembleGradAdaptLim3D,
+                       TMOP_AssembleGradPA_AdaptLim_3D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPAssembleGradAdaptLim3D);
+
+void TMOP_Integrator::AssembleGradPA_AdaptLim_3D(const Vector &x) const
+{
+   if (PA.AL_grads_assembled) { return; }
+
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const auto *B_nodes = PA.maps_nodes->B.Read(),
+               *G_nodes = PA.maps_nodes->G.Read();
+   const auto *B = PA.maps->B.Read();
+   const auto X = Reshape(x.Read(), d, d, d, 3, NE);
+   const auto ALF = Reshape(PA.ALF.Read(), d, d, d, NE);
+   auto ALF_grad = Reshape(PA.ALFG.Write(), 3, q, q, q, NE);
+   auto ALF_hess = Reshape(PA.ALFH.Write(), 3, 3, q, q, q, NE);
+
+   TMOPAssembleGradAdaptLim3D::Run(d, q, NE, B_nodes, G_nodes, B, X, ALF,
+                                   ALF_grad, ALF_hess, d, q);
+   PA.AL_grads_assembled = true;
+}
+
 } // namespace mfem

fem/tmop/mult/grad2_limit.cpp

@@ -67,6 +67,96 @@ void TMOP_AddMultGradPA_C0_2D(const int NE,
    });
 }
 
+// Gradient action for AdaptLim limiting (2D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AddMultGradPA_AdaptLim_2D(const real_t lim_normal,
+                                    const real_t adapt_lim_delta_max,
+                                    const bool const_coeff,
+                                    const DeviceTensor<3, const real_t> &ALC,
+                                    const int NE,
+                                    const DeviceTensor<5, const real_t> &J,
+                                    const ConstDeviceMatrix &W,
+                                    const real_t *b,
+                                    const DeviceTensor<4, const real_t> &R,
+                                    const DeviceTensor<4, const real_t> &ALF_grad,
+                                    const DeviceTensor<5, const real_t> &ALF_hess,
+                                    const ConstDeviceCube &ALFmF0,
+                                    DeviceTensor<4> &Y,
+                                    const int d1d,
+                                    const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const real_t normal_inv_delta_sq =
+      2.0 * lim_normal / (adapt_lim_delta_max * adapt_lim_delta_max);
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t sB[MD1][MQ1];
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // ALF and ALF0 values at quad points.
+      kernels::internal::s_regs2d_t<MQ1> alf_dof, alf_quad;
+      kernels::internal::LoadDofs2d(e, D1D, ALFmF0, alf_dof);
+      kernels::internal::Eval2d(D1D, Q1D, smem, sB, alf_dof, alf_quad);
+
+      // Input vector R at quad points.
+      kernels::internal::v_regs2d_t<2,MQ1> r_R_dof, r_R_quad;
+      kernels::internal::LoadDofs2d(e, D1D, R, r_R_dof);
+      kernels::internal::Eval2d(D1D, Q1D, smem, sB, r_R_dof, r_R_quad);
+
+      kernels::internal::v_regs2d_t<2,MQ1> r00, r01;
+      MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            const real_t *Jtr = &J(0, 0, qx, qy, e);
+            const real_t detJtr = kernels::Det<2>(Jtr);
+            const real_t weight = W(qx, qy) * detJtr;
+            const real_t diff = alf_quad(qy, qx);
+
+            // Load precomputed gradient at this quad point.
+            real_t grad_alf[2] =
+            {
+               ALF_grad(0, qx, qy, e),
+               ALF_grad(1, qx, qy, e)
+            };
+
+            // Load precomputed Hessian at this quad point.
+            real_t hess_alf[2][2];
+            for (int i = 0; i < 2; i++)
+            {
+               for (int j = 0; j < 2; j++)
+               {
+                  hess_alf[i][j] = ALF_hess(i, j, qx, qy, e);
+               }
+            }
+
+            // Get input vector at this quad point.
+            const real_t R_q[2] = { r_R_quad(0, qy, qx), r_R_quad(1, qy, qx) };
+
+            // Hessian action:
+            // H = factor * (grad x grad + (gf - gf0) * hess)
+            const real_t coeff = const_coeff ? ALC(0, 0, 0) : ALC(qx, qy, e);
+            const real_t factor = weight * coeff * normal_inv_delta_sq;
+            const real_t grad_dot_R = grad_alf[0] * R_q[0] + grad_alf[1] * R_q[1];
+            real_t hess_R[2];
+            hess_R[0] = hess_alf[0][0] * R_q[0] + hess_alf[0][1] * R_q[1];
+            hess_R[1] = hess_alf[1][0] * R_q[0] + hess_alf[1][1] * R_q[1];
+
+            r00(0, qy, qx) = factor * (grad_alf[0] * grad_dot_R + diff * hess_R[0]);
+            r00(1, qy, qx) = factor * (grad_alf[1] * grad_dot_R + diff * hess_R[1]);
+         }
+      }
+      MFEM_SYNC_THREAD;
+      kernels::internal::EvalTranspose2d(D1D, Q1D, smem, sB, r00, r01);
+      kernels::internal::WriteDofs2d(e, D1D, r01, Y);
+   });
+}
+
 MFEM_TMOP_MDQ_REGISTER(TMOPMultGradCoefKernels, TMOP_AddMultGradPA_C0_2D);
 MFEM_TMOP_MDQ_SPECIALIZE(TMOPMultGradCoefKernels);
 
@@ -85,4 +175,34 @@ void TMOP_Integrator::AddMultGradPA_C0_2D(const Vector &R, Vector &C) const
    TMOPMultGradCoefKernels::Run(d, q, NE, b, H0, X, Y, d, q);
 }
 
+MFEM_TMOP_MDQ_REGISTER(TMOPMultGradAdaptLim, TMOP_AddMultGradPA_AdaptLim_2D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPMultGradAdaptLim);
+
+void TMOP_Integrator::AddMultGradPA_AdaptLim_2D(const Vector &R,
+                                                Vector &C) const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, NE);
+   const auto J = Reshape(PA.Jtr.Read(), 2, 2, q, q, NE);
+   const auto *B = PA.maps->B.Read();
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q);
+   const auto RR = Reshape(R.Read(), d, d, 2, NE);
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, NE);
+   const auto ALF_grad = Reshape(PA.ALFG.Read(), 2, q, q, NE);
+   const auto ALF_hess = Reshape(PA.ALFH.Read(), 2, 2, q, q, NE);
+   auto Y = Reshape(C.ReadWrite(), d, d, 2, NE);
+
+   TMOPMultGradAdaptLim::Run(d, q, ln, delta_max, const_coeff, ALC, NE, J, W, B,
+                             RR, ALF_grad, ALF_hess, ALFmF0, Y, d, q);
+}
+
 } // namespace mfem

fem/tmop/mult/grad3_limit.cpp

@@ -98,4 +98,135 @@ void TMOP_Integrator::AddMultGradPA_C0_3D(const Vector &R, Vector &C) const
    TMOPMultGradCoefKernels3D::Run(d, q, NE, b, H0, X, Y, d, q);
 }
 
+// Gradient action for AdaptLim limiting (3D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AddMultGradPA_AdaptLim_3D(const real_t lim_normal,
+                                    const real_t adapt_lim_delta_max,
+                                    const bool const_coeff,
+                                    const DeviceTensor<4, const real_t> &ALC,
+                                    const int NE,
+                                    const DeviceTensor<6, const real_t> &J,
+                                    const ConstDeviceCube &W,
+                                    const real_t *b,
+                                    const DeviceTensor<5, const real_t> &R,
+                                    const DeviceTensor<5, const real_t> &ALF_grad,
+                                    const DeviceTensor<6, const real_t> &ALF_hess,
+                                    const DeviceTensor<4, const real_t> &ALFmF0,
+                                    DeviceTensor<5> &Y,
+                                    const int d1d,
+                                    const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const real_t normal_inv_delta_sq =
+      2.0 * lim_normal / (adapt_lim_delta_max * adapt_lim_delta_max);
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t sB[MD1][MQ1];
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // ALF and ALF0 values at quad points.
+      kernels::internal::s_regs3d_t<MQ1> alf_dof, alf_quad;
+      kernels::internal::LoadDofs3d(e, D1D, ALFmF0, alf_dof);
+      kernels::internal::Eval3d(D1D, Q1D, smem, sB, alf_dof, alf_quad);
+
+      // Input vector R at quad points.
+      kernels::internal::v_regs3d_t<3, MQ1> r_R_dof, r_R_quad;
+      kernels::internal::LoadDofs3d(e, D1D, R, r_R_dof);
+      kernels::internal::Eval3d(D1D, Q1D, smem, sB, r_R_dof, r_R_quad);
+
+      kernels::internal::v_regs3d_t<3, MQ1> r00, r01;
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+            {
+               const real_t *Jtr = &J(0, 0, qx, qy, qz, e);
+               const real_t detJtr = kernels::Det<3>(Jtr);
+               const real_t weight = W(qx, qy, qz) * detJtr;
+               const real_t diff = alf_quad(qz, qy, qx);
+
+               // Load precomputed gradient at this quad point.
+               const real_t grad_alf[3] =
+               {
+                  ALF_grad(0, qx, qy, qz, e),
+                  ALF_grad(1, qx, qy, qz, e),
+                  ALF_grad(2, qx, qy, qz, e)
+               };
+
+               // Get input vector at this quad point.
+               const real_t R_q[3] =
+               {
+                  r_R_quad(0, qz, qy, qx),
+                  r_R_quad(1, qz, qy, qx),
+                  r_R_quad(2, qz, qy, qx)
+               };
+
+               // Hessian action:
+               // H = factor * (grad x grad + (gf - gf0) * hess)
+               const real_t coeff = const_coeff ? ALC(0, 0, 0, 0) : ALC(qx, qy, qz, e);
+               const real_t factor = weight * coeff * normal_inv_delta_sq;
+               const real_t grad_dot_R =
+                  grad_alf[0] * R_q[0] + grad_alf[1] * R_q[1] + grad_alf[2] * R_q[2];
+               real_t hess_R[3];
+               hess_R[0] =
+                  ALF_hess(0, 0, qx, qy, qz, e) * R_q[0] +
+                  ALF_hess(0, 1, qx, qy, qz, e) * R_q[1] +
+                  ALF_hess(0, 2, qx, qy, qz, e) * R_q[2];
+               hess_R[1] =
+                  ALF_hess(1, 0, qx, qy, qz, e) * R_q[0] +
+                  ALF_hess(1, 1, qx, qy, qz, e) * R_q[1] +
+                  ALF_hess(1, 2, qx, qy, qz, e) * R_q[2];
+               hess_R[2] =
+                  ALF_hess(2, 0, qx, qy, qz, e) * R_q[0] +
+                  ALF_hess(2, 1, qx, qy, qz, e) * R_q[1] +
+                  ALF_hess(2, 2, qx, qy, qz, e) * R_q[2];
+
+               r00(0, qz, qy, qx) = factor * (grad_alf[0] * grad_dot_R + diff * hess_R[0]);
+               r00(1, qz, qy, qx) = factor * (grad_alf[1] * grad_dot_R + diff * hess_R[1]);
+               r00(2, qz, qy, qx) = factor * (grad_alf[2] * grad_dot_R + diff * hess_R[2]);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      kernels::internal::EvalTranspose3d(D1D, Q1D, smem, sB, r00, r01);
+      kernels::internal::WriteDofs3d(e, D1D, r01, Y);
+   });
+}
+
+MFEM_TMOP_MDQ_REGISTER(TMOPMultGradAdaptLim3D, TMOP_AddMultGradPA_AdaptLim_3D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPMultGradAdaptLim3D);
+
+void TMOP_Integrator::AddMultGradPA_AdaptLim_3D(const Vector &R,
+                                                Vector &C) const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, q, NE);
+   const auto J = Reshape(PA.Jtr.Read(), 3, 3, q, q, q, NE);
+   const auto *B = PA.maps->B.Read();
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q, q);
+   const auto RR = Reshape(R.Read(), d, d, d, 3, NE);
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, d, NE);
+   const auto ALF_grad = Reshape(PA.ALFG.Read(), 3, q, q, q, NE);
+   const auto ALF_hess = Reshape(PA.ALFH.Read(), 3, 3, q, q, q, NE);
+   auto Y = Reshape(C.ReadWrite(), d, d, d, 3, NE);
+
+   TMOPMultGradAdaptLim3D::Run(d, q, ln, delta_max, const_coeff, ALC, NE, J, W, B,
+                               RR, ALF_grad, ALF_hess, ALFmF0, Y, d, q);
+}
+
 } // namespace mfem

fem/tmop/mult/mult2_limit.cpp

@@ -108,6 +108,64 @@ void TMOP_AddMultPA_C0_2D(const real_t lim_normal,
    });
 }
 
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AddMultPA_AdaptLim_2D(const real_t lim_normal,
+                                const real_t adapt_lim_delta_max,
+                                const bool const_coeff,
+                                const DeviceTensor<3, const real_t> &ALC,
+                                const int NE,
+                                const DeviceTensor<5, const real_t> &J,
+                                const ConstDeviceMatrix &W,
+                                const real_t *b,
+                                const DeviceTensor<4, const real_t> &ALF_grad,
+                                const ConstDeviceCube &ALFmF0,
+                                DeviceTensor<4> &Y,
+                                const int d1d,
+                                const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const real_t normal_inv_delta_sq =
+      2.0 * lim_normal / (adapt_lim_delta_max * adapt_lim_delta_max);
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      MFEM_SHARED real_t sB[MD1][MQ1];
+
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // Evaluate ALF and ALF0 at the quad points.
+      kernels::internal::s_regs2d_t<MQ1> alf_dof, alf_quad;
+      kernels::internal::LoadDofs2d(e, D1D, ALFmF0, alf_dof);
+      kernels::internal::Eval2d(D1D, Q1D, smem, sB,
+                                alf_dof, alf_quad);
+
+      kernels::internal::v_regs2d_t<2,MQ1> r00, r01;
+      MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            const real_t *Jtr = &J(0, 0, qx, qy, e);
+            const real_t detJtr = kernels::Det<2>(Jtr);
+            const real_t weight = W(qx, qy) * detJtr;
+
+            const real_t coeff = const_coeff ? ALC(0, 0, 0) : ALC(qx, qy, e);
+            const real_t factor = weight * coeff * normal_inv_delta_sq *
+                                  alf_quad(qy, qx);
+
+            r00(0, qy, qx) = factor * ALF_grad(0, qx, qy, e);
+            r00(1, qy, qx) = factor * ALF_grad(1, qx, qy, e);
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      kernels::internal::EvalTranspose2d(D1D, Q1D, smem, sB, r00, r01);
+      kernels::internal::WriteDofs2d(e, D1D, r01, Y);
+   });
+}
+
 MFEM_TMOP_MDQ_REGISTER(TMOPMultCoefKernels, TMOP_AddMultPA_C0_2D);
 MFEM_TMOP_MDQ_SPECIALIZE(TMOPMultCoefKernels);
 
@@ -140,4 +198,32 @@ void TMOP_Integrator::AddMultPA_C0_2D(const Vector &x, Vector &y) const
                             Y, exp_lim, d, q);
 }
 
+MFEM_TMOP_MDQ_REGISTER(TMOPMultAdaptLim, TMOP_AddMultPA_AdaptLim_2D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPMultAdaptLim);
+
+void TMOP_Integrator::AddMultPA_AdaptLim_2D([[maybe_unused]] const Vector &x,
+                                            Vector &y) const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, NE);
+   const auto J = Reshape(PA.Jtr.Read(), 2, 2, q, q, NE);
+   const auto *B = PA.maps->B.Read();
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q);
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, NE);
+   const auto ALF_grad = Reshape(PA.ALFG.Read(), 2, q, q, NE);
+   auto Y = Reshape(y.ReadWrite(), d, d, 2, NE);
+
+   TMOPMultAdaptLim::Run(d, q, ln, delta_max, const_coeff, ALC, NE, J, W,
+                         B, ALF_grad, ALFmF0, Y, d, q);
+}
+
 } // namespace mfem

fem/tmop/mult/mult3_limit.cpp

@@ -148,4 +148,95 @@ void TMOP_Integrator::AddMultPA_C0_3D(const Vector &x, Vector &y) const
                               X, Y, exp_lim, d, q);
 }
 
+// Residual term for AdaptLim limiting (3D)
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_AddMultPA_AdaptLim_3D(const real_t lim_normal,
+                                const real_t adapt_lim_delta_max,
+                                const bool const_coeff,
+                                const DeviceTensor<4, const real_t> &ALC,
+                                const int NE,
+                                const DeviceTensor<6, const real_t> &J,
+                                const ConstDeviceCube &W,
+                                const real_t *b,
+                                const DeviceTensor<5, const real_t> &ALF_grad,
+                                const DeviceTensor<4, const real_t> &ALFmF0,
+                                DeviceTensor<5> &Y,
+                                const int d1d,
+                                const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const real_t normal_inv_delta_sq =
+      2.0 * lim_normal / (adapt_lim_delta_max * adapt_lim_delta_max);
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t sB[MD1][MQ1];
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // Evaluate ALF and ALF0 at the quad points.
+      kernels::internal::s_regs3d_t<MQ1> alf_dof, alf_quad;
+      kernels::internal::LoadDofs3d(e, D1D, ALFmF0, alf_dof);
+      kernels::internal::Eval3d(D1D, Q1D, smem, sB, alf_dof, alf_quad);
+
+      kernels::internal::v_regs3d_t<3, MQ1> r00, r01;
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+            {
+               const real_t *Jtr = &J(0, 0, qx, qy, qz, e);
+               const real_t detJtr = kernels::Det<3>(Jtr);
+               const real_t weight = W(qx, qy, qz) * detJtr;
+
+               const real_t coeff = const_coeff ? ALC(0, 0, 0, 0) : ALC(qx, qy, qz, e);
+               const real_t factor = weight * coeff * normal_inv_delta_sq *
+                                     alf_quad(qz, qy, qx);
+
+               r00(0, qz, qy, qx) = factor * ALF_grad(0, qx, qy, qz, e);
+               r00(1, qz, qy, qx) = factor * ALF_grad(1, qx, qy, qz, e);
+               r00(2, qz, qy, qx) = factor * ALF_grad(2, qx, qy, qz, e);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      kernels::internal::EvalTranspose3d(D1D, Q1D, smem, sB, r00, r01);
+      kernels::internal::WriteDofs3d(e, D1D, r01, Y);
+   });
+}
+
+MFEM_TMOP_MDQ_REGISTER(TMOPMultAdaptLim3D, TMOP_AddMultPA_AdaptLim_3D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPMultAdaptLim3D);
+
+void TMOP_Integrator::AddMultPA_AdaptLim_3D([[maybe_unused]] const Vector &x,
+                                            Vector &y) const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, q, NE);
+   const auto J = Reshape(PA.Jtr.Read(), 3, 3, q, q, q, NE);
+   const auto *B = PA.maps->B.Read();
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q, q);
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, d, NE);
+   const auto ALF_grad = Reshape(PA.ALFG.Read(), 3, q, q, q, NE);
+   auto Y = Reshape(y.ReadWrite(), d, d, d, 3, NE);
+
+   TMOPMultAdaptLim3D::Run(d, q, ln, delta_max, const_coeff, ALC, NE, J, W,
+                           B, ALF_grad, ALFmF0, Y, d, q);
+}
+
 } // namespace mfem

fem/tmop/pa.cpp

@@ -46,12 +46,14 @@ void TMOP_Integrator::AssembleGradPA(const Vector &de,
    {
       AssembleGradPA_2D(xe);
       if (lim_coeff) { AssembleGradPA_C0_2D(xe); }
+      if (adapt_lim_gf) { AssembleGradPA_AdaptLim_2D(xe); }
    }
 
    if (PA.dim == 3)
    {
       AssembleGradPA_3D(xe);
       if (lim_coeff) { AssembleGradPA_C0_3D(xe); }
+      if (adapt_lim_gf) { AssembleGradPA_AdaptLim_3D(xe); }
    }
 }
 
@@ -197,12 +199,14 @@ void TMOP_Integrator::UpdateCoefficientsPA(const Vector &d_loc)
       add(*x_0, d_loc, x_loc);
    }
 
-   // Both are constant or not specified.
-   if (PA.MC.Size() == 1 && PA.C0.Size() == 1) { return; }
+
+   // All are constant or not specified.
+   if (PA.MC.Size() == 1 && PA.C0.Size() <= 1 && PA.ALC.Size() <= 1) { return; }
 
    // Coefficients are always evaluated on the CPU for now.
    PA.MC.HostWrite();
    PA.C0.HostWrite();
+   PA.ALC.HostWrite();
 
    const IntegrationRule &ir = *PA.ir;
    auto T = new IsoparametricTransformation;
@@ -226,6 +230,14 @@ void TMOP_Integrator::UpdateCoefficientsPA(const Vector &d_loc)
             PA.C0(q + e * PA.nq) = lim_coeff->Eval(*T, ir.IntPoint(q));
          }
       }
+
+      if (PA.ALC.Size() > 1)
+      {
+         for (int q = 0; q < PA.nq; ++q)
+         {
+            PA.ALC(q + e * PA.nq) = adapt_lim_coeff->Eval(*T, ir.IntPoint(q));
+         }
+      }
    }
 
    delete T;
@@ -321,7 +333,93 @@ void TMOP_Integrator::AssemblePA(const FiniteElementSpace &fes)
    PA.Jtr_debug_grad = false;
 
    // Limiting: lim_coeff -> PA.C0, lim_nodes0 -> PA.XL, lim_dist -> PA.LD, PA.H0
-   if (lim_coeff) { AssemblePA_Limiting(); }
+   if (lim_coeff)    { AssemblePA_Limiting(); }
+   // Adaptive limiting: adapt_lim_coeff -> PA.ALC, adapt_lim_gf -> PA.ALF,
+   //                    adapt_lim_gf0 -> PA.ALF0, adapt_lim_delta_max -> PA.ALD
+   if (adapt_lim_gf) { AssemblePA_AdaptLim(); }
+}
+
+void TMOP_Integrator::AssemblePA_AdaptLim()
+{
+   const FiniteElementSpace *alfes = adapt_lim_gf->FESpace();
+
+   MFEM_VERIFY(strcmp(alfes->FEColl()->Name(), PA.fes->FEColl()->Name()) == 0 &&
+               alfes->FEColl()->GetOrder() == PA.fes->FEColl()->GetOrder(),
+               "The PA code assumes the same FE spaces for mesh and limiting.");
+
+   PA.AL_grads_assembled = false;
+
+   // adapt_lim_coeff -> PA.ALC (Q-vector).
+   PA.ALC.UseDevice(true);
+   if (auto *cQ = dynamic_cast<ConstantCoefficient *>(adapt_lim_coeff))
+   {
+      PA.ALC.SetSize(1, Device::GetMemoryType());
+      PA.ALC.HostWrite();
+      PA.ALC(0) = cQ->constant;
+   }
+   else
+   {
+      PA.ALC.SetSize(PA.nq * PA.ne, Device::GetMemoryType());
+      auto ALC = Reshape(PA.ALC.HostWrite(), PA.nq, PA.ne);
+      for (int e = 0; e < PA.ne; ++e)
+      {
+         ElementTransformation &T = *PA.fes->GetElementTransformation(e);
+         for (int q = 0; q < PA.ir->GetNPoints(); ++q)
+         {
+            ALC(q, e) = adapt_lim_coeff->Eval(T, PA.ir->IntPoint(q));
+         }
+      }
+   }
+
+   const ElementDofOrdering ordering = ElementDofOrdering::LEXICOGRAPHIC;
+
+   const FiniteElement *fe_n = PA.fes->GetTypicalFE();
+   // GetNodes() for tensor H1 elements with H1_DOF_MAP is stored in NATIVE
+   // order (via dof_map), while DofToQuad::TENSOR assumes LEXICOGRAPHIC
+   // ordering of the integration points.
+   const IntegrationRule &nodes = fe_n->GetNodes();
+   const auto *nfe = dynamic_cast<const NodalFiniteElement *>(fe_n);
+   const Array<int> *lex = (nfe && nfe->GetLexicographicOrdering().Size() > 0)
+                           ? &nfe->GetLexicographicOrdering() : nullptr;
+   if (!lex)
+   {
+      PA.maps_nodes = &fe_n->GetDofToQuad(nodes, DofToQuad::TENSOR);
+   }
+   else
+   {
+      IntegrationRule lex_nodes(nodes.GetNPoints());
+      MFEM_VERIFY(lex->Size() == nodes.GetNPoints(), "");
+      for (int i = 0; i < nodes.GetNPoints(); i++)
+      {
+         lex_nodes.IntPoint(i) = nodes.IntPoint((*lex)[i]);
+      }
+      PA.maps_nodes = &fe_n->GetDofToQuad(lex_nodes, DofToQuad::TENSOR);
+   }
+
+   // adapt_lim_gf -> PA.ALF (E-vector, same pattern as LD).
+   const FiniteElement &fe = *alfes->GetTypicalFE();
+   PA.ALF.SetSize(PA.ne * fe.GetDof(), Device::GetMemoryType());
+   PA.ALF.UseDevice(true);
+   const Operator *alf_R = alfes->GetElementRestriction(ordering);
+   alf_R->Mult(*adapt_lim_gf, PA.ALF);
+   // adapt_lim_gf - adapt_lim_gf0 -> PA.ALFmF0
+   PA.ALFmF0.SetSize(PA.ne * fe.GetDof(), Device::GetMemoryType());
+   PA.ALFmF0.UseDevice(true);
+   alf_R->Mult(*adapt_lim_gf0, PA.ALFmF0);
+   PA.ALFmF0 *= -1.0;
+   PA.ALFmF0 += PA.ALF;
+
+   // adapt_lim_delta_max -> PA.al_delta.
+   PA.al_delta = adapt_lim_delta_max;
+
+   // Allocate storage for gradient and Hessian of ALF at quadrature points
+   // These will be filled during AssembleGradPA
+   const int dim = PA.dim;
+   PA.ALFG.UseDevice(true);
+   PA.ALFG.SetSize(dim * PA.nq * PA.ne, Device::GetMemoryType());
+   PA.ALFH.UseDevice(true);
+   PA.ALFH.SetSize(dim * dim * PA.nq * PA.ne, Device::GetMemoryType());
+
 }
 
 void TMOP_Integrator::AssembleGradDiagonalPA(Vector &de) const
@@ -341,12 +439,14 @@ void TMOP_Integrator::AssembleGradDiagonalPA(Vector &de) const
    {
       AssembleDiagonalPA_2D(de);
       if (lim_coeff) { AssembleDiagonalPA_C0_2D(de); }
+      if (adapt_lim_gf) { AssembleDiagonalPA_AdaptLim_2D(de); }
    }
 
    if (PA.dim == 3)
    {
       AssembleDiagonalPA_3D(de);
       if (lim_coeff) { AssembleDiagonalPA_C0_3D(de); }
+      if (adapt_lim_gf) { AssembleDiagonalPA_AdaptLim_3D(de); }
    }
 }
 
@@ -373,12 +473,26 @@ void TMOP_Integrator::AddMultPA(const Vector &de, Vector &ye) const
    {
       AddMultPA_2D(xe, ye);
       if (lim_coeff) { AddMultPA_C0_2D(xe, ye); }
+      if (adapt_lim_gf)
+      {
+         // AddMultPA_AdaptLim_2D uses the precomputed AdaptLim field gradient
+         // at quadrature points (PA.ALFG). Ensure it is up-to-date for the
+         // current mesh configuration.
+         AssembleGradPA_AdaptLim_2D(xe);
+         AddMultPA_AdaptLim_2D(xe, ye);
+      }
+
    }
 
    if (PA.dim == 3)
    {
       AddMultPA_3D(xe, ye);
       if (lim_coeff) { AddMultPA_C0_3D(xe, ye); }
+      if (adapt_lim_gf)
+      {
+         AssembleGradPA_AdaptLim_3D(xe);
+         AddMultPA_AdaptLim_3D(xe, ye);
+      }
    }
 }
 
@@ -399,12 +513,14 @@ void TMOP_Integrator::AddMultGradPA(const Vector &re, Vector &ce) const
    {
       AddMultGradPA_2D(re, ce);
       if (lim_coeff) { AddMultGradPA_C0_2D(re, ce); }
+      if (adapt_lim_gf) { AddMultGradPA_AdaptLim_2D(re, ce); }
    }
 
    if (PA.dim == 3)
    {
       AddMultGradPA_3D(re, ce);
       if (lim_coeff) { AddMultGradPA_C0_3D(re, ce); }
+      if (adapt_lim_gf) { AddMultGradPA_AdaptLim_3D(re, ce); }
    }
 }
 
@@ -433,12 +549,14 @@ real_t TMOP_Integrator::GetLocalStateEnergyPA(const Vector &de) const
    {
       GetLocalStateEnergyPA_2D(xe, energy);
       if (lim_coeff) { energy += GetLocalStateEnergyPA_C0_2D(xe); }
+      if (adapt_lim_gf) { energy += GetLocalStateEnergyPA_AdaptLim_2D(); }
    }
 
    if (PA.dim == 3)
    {
       GetLocalStateEnergyPA_3D(xe, energy);
       if (lim_coeff) { energy += GetLocalStateEnergyPA_C0_3D(xe); }
+      if (adapt_lim_gf) { energy += GetLocalStateEnergyPA_AdaptLim_3D(); }
    }
 
    return energy;

fem/tmop/tools/energy2_limit.cpp

@@ -92,6 +92,55 @@ void TMOP_EnergyPA_C0_2D(const real_t lim_normal,
    });
 }
 
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_EnergyPA_AdaptLim_2D(const real_t lim_normal,
+                               const real_t adapt_lim_delta_max,
+                               const bool const_coeff,
+                               const DeviceTensor<3, const real_t> &ALC,
+                               const int NE,
+                               const DeviceTensor<5, const real_t> &J,
+                               const ConstDeviceMatrix &W,
+                               const real_t *b,
+                               const ConstDeviceCube &ALFmF0,
+                               DeviceTensor<3> &E,
+                               const int d1d,
+                               const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      MFEM_SHARED real_t sB[MD1][MQ1];
+
+      // Load basis functions for ALF/ALF0.
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // Load ALF and ALF0 (scalar pattern).
+      kernels::internal::s_regs2d_t<MQ1> rtmp, ralf;
+      kernels::internal::LoadDofs2d(e, D1D, ALFmF0, rtmp);
+      kernels::internal::Eval2d(D1D, Q1D, smem, sB, rtmp, ralf);
+
+      MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+         {
+            const real_t *Jtr = &J(0, 0, qx, qy, e);
+            const real_t detJtr = kernels::Det<2>(Jtr);
+            const real_t weight = W(qx, qy) * detJtr;
+
+            const real_t diff = ralf(qy, qx)  / adapt_lim_delta_max;
+
+            const real_t coeff = const_coeff ? ALC(0, 0, 0) : ALC(qx, qy, e);
+
+            // Energy: coeff * lim_normal * diff^2
+            E(qx, qy, e) = weight * coeff * lim_normal * diff * diff;
+         }
+      }
+   });
+}
+
 MFEM_TMOP_MDQ_REGISTER(TMOPEnergyCoef2D, TMOP_EnergyPA_C0_2D);
 MFEM_TMOP_MDQ_SPECIALIZE(TMOPEnergyCoef2D);
 
@@ -127,4 +176,32 @@ real_t TMOP_Integrator::GetLocalStateEnergyPA_C0_2D(const Vector &x) const
    return PA.E * PA.O;
 }
 
+MFEM_TMOP_MDQ_REGISTER(TMOPEnergyAdaptLim2D, TMOP_EnergyPA_AdaptLim_2D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPEnergyAdaptLim2D);
+
+real_t TMOP_Integrator::GetLocalStateEnergyPA_AdaptLim_2D() const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, NE);
+   const auto J = Reshape(PA.Jtr.Read(), 2, 2, q, q, NE);
+   const auto *b = PA.maps->B.Read();
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q);
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, NE);
+   auto E = Reshape(PA.E.Write(), q, q, NE);
+
+   TMOPEnergyAdaptLim2D::Run(d, q, ln, delta_max, const_coeff, ALC, NE, J, W, b,
+                             ALFmF0, E, d, q);
+
+   return PA.E * PA.O;
+}
+
 } // namespace mfem

fem/tmop/tools/energy3_limit.cpp

@@ -107,6 +107,56 @@ void TMOP_EnergyPA_C0_3D(const real_t lim_normal,
    });
 }
 
+template <int MD1, int MQ1, int T_D1D = 0, int T_Q1D = 0>
+void TMOP_EnergyPA_AdaptLim_3D(const real_t lim_normal,
+                               const real_t adapt_lim_delta_max,
+                               const bool const_coeff,
+                               const DeviceTensor<4, const real_t> &ALC,
+                               const int NE,
+                               const DeviceTensor<6, const real_t> &J,
+                               const ConstDeviceCube &W,
+                               const real_t *b,
+                               const DeviceTensor<4, const real_t> &ALFmF0,
+                               DeviceTensor<4> &E,
+                               const int d1d,
+                               const int q1d)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   mfem::forall_2D(NE, Q1D, Q1D, [=] MFEM_HOST_DEVICE(int e)
+   {
+      MFEM_SHARED real_t smem[MQ1][MQ1];
+      MFEM_SHARED real_t sB[MD1][MQ1];
+
+      // Load basis functions for ALF/ALF0.
+      kernels::internal::LoadMatrix(D1D, Q1D, b, sB);
+
+      // Load ALF and ALF0 (scalar pattern).
+      kernels::internal::s_regs3d_t<MQ1> rtmp, ralf;
+      kernels::internal::LoadDofs3d(e, D1D, ALFmF0, rtmp);
+      kernels::internal::Eval3d(D1D, Q1D, smem, sB, rtmp, ralf);
+
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         MFEM_FOREACH_THREAD_DIRECT(qy, y, Q1D)
+         {
+            MFEM_FOREACH_THREAD_DIRECT(qx, x, Q1D)
+            {
+               const real_t *Jtr = &J(0, 0, qx, qy, qz, e);
+               const real_t detJtr = kernels::Det<3>(Jtr);
+               const real_t weight = W(qx, qy, qz) * detJtr;
+
+               const real_t diff = ralf(qz, qy, qx) / adapt_lim_delta_max;
+
+               const real_t coeff = const_coeff ? ALC(0, 0, 0, 0) : ALC(qx, qy, qz, e);
+               E(qx, qy, qz, e) = weight * coeff * lim_normal * diff * diff;
+            }
+         }
+      }
+   });
+}
+
 MFEM_TMOP_MDQ_REGISTER(TMOPEnergyPAC03D, TMOP_EnergyPA_C0_3D);
 MFEM_TMOP_MDQ_SPECIALIZE(TMOPEnergyPAC03D);
 
@@ -142,4 +192,32 @@ real_t TMOP_Integrator::GetLocalStateEnergyPA_C0_3D(const Vector &x) const
    return PA.E * PA.O;
 }
 
+MFEM_TMOP_MDQ_REGISTER(TMOPEnergyAdaptLim3D, TMOP_EnergyPA_AdaptLim_3D);
+MFEM_TMOP_MDQ_SPECIALIZE(TMOPEnergyAdaptLim3D);
+
+real_t TMOP_Integrator::GetLocalStateEnergyPA_AdaptLim_3D() const
+{
+   const real_t ln = lim_normal;
+   const real_t delta_max = PA.al_delta;
+   const int NE = PA.ne, d = PA.maps->ndof, q = PA.maps->nqpt;
+
+   MFEM_VERIFY(d <= DeviceDofQuadLimits::Get().MAX_D1D, "");
+   MFEM_VERIFY(q <= DeviceDofQuadLimits::Get().MAX_Q1D, "");
+
+   const bool const_coeff = PA.ALC.Size() == 1;
+   const auto ALC = const_coeff
+                    ? Reshape(PA.ALC.Read(), 1, 1, 1, 1)
+                    : Reshape(PA.ALC.Read(), q, q, q, NE);
+   const auto J = Reshape(PA.Jtr.Read(), 3, 3, q, q, q, NE);
+   const auto *b = PA.maps->B.Read();
+   const auto W = Reshape(PA.ir->GetWeights().Read(), q, q, q);
+   const auto ALFmF0 = Reshape(PA.ALFmF0.Read(), d, d, d, NE);
+   auto E = Reshape(PA.E.Write(), q, q, q, NE);
+
+   TMOPEnergyAdaptLim3D::Run(d, q, ln, delta_max, const_coeff, ALC, NE, J, W, b,
+                             ALFmF0, E, d, q);
+
+   return PA.E * PA.O;
+}
+
 } // namespace mfem

general/array.cpp

@@ -111,6 +111,25 @@ void Array<T>::PartialSum()
    }
 }
 
+template <typename U>
+MFEM_HOST_DEVICE inline U abs_signed(U v) { return (v < U(0)) ? -v : v; }
+
+template <typename U>
+void AbsImpl(std::true_type /*signed*/, U* y, int N, bool useDevice)
+{
+   mfem::forall_switch(useDevice, N, [=] MFEM_HOST_DEVICE (int i)
+   {
+      y[i] = abs_signed(y[i]);
+   });
+}
+
+template <typename U>
+void AbsImpl(std::false_type /*unsigned*/, U* /*y*/, int /*N*/,
+             bool /*useDevice*/)
+{
+   // no-op
+}
+
 template <class T>
 void Array<T>::Abs()
 {
@@ -118,10 +137,7 @@ void Array<T>::Abs()
    const bool useDevice = UseDevice();
    const int N = size;
    auto y = ReadWrite(useDevice);
-   mfem::forall_switch(useDevice, N, [=] MFEM_HOST_DEVICE (int i)
-   {
-      y[i] = std::abs(y[i]);
-   });
+   AbsImpl<T>(std::is_signed<T> {}, y, N, useDevice);
 }
 
 // Sum
@@ -207,6 +223,7 @@ void Array2D<T>::Print(std::ostream &os, int width_)
 template class Array<char>;
 template class Array<int>;
 template class Array<long long>;
+template class Array<unsigned int>;
 template class Array<real_t>;
 template class Array2D<int>;
 template class Array2D<real_t>;

general/binaryio.hpp

@@ -25,6 +25,13 @@ namespace mfem
 namespace bin_io
 {
 
+/// Enum to specify if values should be read in binary or ASCII format.
+enum BinaryOrASCII : bool
+{
+   ASCII = false,
+   BINARY = true
+};
+
 /// Write 'value' to stream.
 template<typename T>
 inline void write(std::ostream& os, T value)
@@ -73,6 +80,38 @@ void DecodeBase64(const char *src, size_t len, std::vector<char> &buf);
 /// This is equal to 4*nbytes/3, rounded up to the nearest multiple of 4.
 size_t NumBase64Chars(size_t nbytes);
 
+/// @brief Read and return a value of type @a T from the input stream, in either
+/// binary or ASCII format, depending on the value of @a binary.
+template <typename T>
+T ReadBinaryOrASCII(std::istream &input, BinaryOrASCII binary)
+{
+   if (binary)
+   {
+      return read<T>(input);
+   }
+   else
+   {
+      T val;
+      input >> val;
+      return val;
+   }
+}
+
+/// @brief Skip @a num values of type @a T from the input stream, in either
+/// binary or ASCII format, depending on the value of @a binary.
+template <typename T>
+void Skip(std::istream &input, int num, BinaryOrASCII binary)
+{
+   if (binary)
+   {
+      input.ignore(sizeof(T) * num);
+   }
+   else
+   {
+      for (int i = 0; i < num; ++i) { ReadBinaryOrASCII<T>(input, ASCII); }
+   }
+}
+
 } // namespace mfem::bin_io
 
 } // namespace mfem

mesh/CMakeLists.txt

@@ -37,13 +37,13 @@ set(SRCS
   submesh/ncsubmesh.cpp
   submesh/submesh_utils.cpp
   submesh/transfermap.cpp
+  bb_grid_map.cpp
   )
 
 set(HDRS
   attribute_sets.hpp
   element.hpp
   face_nbr_geom.hpp
-  gmsh.hpp
   hexahedron.hpp
   mesh.hpp
   mesh_headers.hpp
@@ -68,6 +68,7 @@ set(HDRS
   submesh/submesh_utils.hpp
   submesh/transfer_category.hpp
   submesh/transfermap.hpp
+  bb_grid_map.hpp
   )
 
 if (MFEM_USE_MPI)

mesh/bb_grid_map.cpp

@@ -0,0 +1,414 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+/* The BBoxTensorGridMap class is adapted from similar functionality in the
+gslib library. Below is the gslib license and copyright statement:
+
+Copyright (c) 2008-2024, UCHICAGO ARGONNE, LLC.
+
+The UChicago Argonne, LLC as Operator of Argonne National
+Laboratory holds copyright in the Software. The copyright holder
+reserves all rights except those expressly granted to licensees,
+and U.S. Government license rights.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
+
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the disclaimer below.
+
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the disclaimer (as noted below)
+in the documentation and/or other materials provided with the
+distribution.
+
+3. Neither the name of ANL nor the names of its contributors
+may be used to endorse or promote products derived from this software
+without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
+UCHICAGO ARGONNE, LLC, THE U.S. DEPARTMENT OF
+ENERGY OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
+#include "bb_grid_map.hpp"
+
+#include <limits>
+#include <cmath>
+#include <algorithm>
+
+namespace mfem
+{
+
+using namespace std;
+
+BBoxTensorGridMap::BBoxTensorGridMap(Mesh &mesh, int nx)
+{
+   GridFunction *nodes = mesh.GetNodes();
+   const int nel = mesh.GetNE();
+   sdim = mesh.SpaceDimension();
+   Vector elmin(nel*sdim), elmax(nel*sdim);
+   elmin = numeric_limits<real_t>::max();
+   elmax = -numeric_limits<real_t>::max();
+   if (!nodes)
+   {
+      Array<int> verts;
+      real_t *coord;
+      // create bounding boxes from vertex coordinates
+      for (int e = 0; e < nel; e++)
+      {
+         mesh.GetElementVertices(e, verts);
+         for (int v = 0; v < verts.Size(); v++)
+         {
+            coord = mesh.GetVertex(verts[v]);
+            for (int d = 0; d < sdim; d++)
+            {
+               elmin(d*nel + e) = min(elmin(d*nel + e), coord[d]);
+               elmax(d*nel + e) = max(elmax(d*nel + e), coord[d]);
+            }
+         }
+      }
+   }
+   else
+   {
+      int nref = 3;
+      nodes->GetElementBounds(elmin, elmax, nref);
+   }
+   Array<int> nx_arr(sdim);
+   nx_arr = nx;
+   Setup(elmin, elmax, nel, nx_arr, false);
+}
+
+BBoxTensorGridMap::BBoxTensorGridMap(Vector &elmin,
+                                     Vector &elmax,
+                                     int nel,
+                                     int sdim_,
+                                     int n,
+                                     bool by_max_size)
+{
+   sdim = sdim_;
+   MFEM_VERIFY(0 < sdim && sdim <= 3,
+               "BBoxTensorGridMap only supports spatial dimensions 1, 2, and 3.");
+   if (nel > 0)
+   {
+      MFEM_VERIFY(elmin.Size() == sdim * nel && elmax.Size() == sdim * nel,
+                  "Element bounds size must match dim * nel.");
+   }
+   Array<int> nx_arr(sdim);
+   nx_arr = n;
+   Setup(elmin, elmax, nel, nx_arr, by_max_size);
+}
+
+BBoxTensorGridMap::BBoxTensorGridMap(Vector &elmin, Vector &elmax,
+                                     int nel, int sdim_,
+                                     Array<int> &nx,
+                                     bool by_max_size)
+{
+   sdim = sdim_;
+   Setup(elmin, elmax, nel, nx, by_max_size);
+}
+
+void BBoxTensorGridMap::Setup(Vector &elmin, Vector &elmax,
+                              int nel, Array<int> &nx, bool by_max_size)
+{
+   MFEM_VERIFY(0 < sdim && sdim <= 3,
+               "BBoxTensorGridMap only supports spatial dimensions 1, 2, and 3.");
+   MFEM_VERIFY(nx.Size() == sdim,
+               "BBoxTensorGridMap requires nx to have the same size as the number of dimensions.");
+   if (nel > 0)
+   {
+      MFEM_VERIFY(elmin.Size() == sdim * nel && elmax.Size() == sdim * nel,
+                  "Element bounds size must match dim * nel.");
+   }
+   lmap_bnd_min.SetSize(sdim);
+   lmap_bnd_max.SetSize(sdim);
+   lmap_fac.SetSize(sdim);
+   lmap_nx.SetSize(sdim);
+   lmap_nx = nx;
+
+   if (by_max_size)
+   {
+      MFEM_VERIFY(nx[0] >= 0,
+                  "BBoxTensorGridMap requires a nonnegative max-size hint.");
+   }
+   else
+   {
+      for (int d = 0; d < nx.Size(); d++)
+      {
+         MFEM_VERIFY(nx[d] > 0,
+                     "BBoxTensorGridMap requires positive number of divisions in each dimension.");
+      }
+   }
+   if (nel == 0)
+   {
+      lmap_bnd_min = 0.0;
+      lmap_bnd_max = 1.0;
+      if (by_max_size) { lmap_nx = 1; }
+      SetGridFac(lmap_fac, lmap_nx, lmap_bnd_min, lmap_bnd_max);
+
+      lmap_nxd = lmap_nx[0];
+      for (int d = 1; d < sdim; d++)
+      {
+         lmap_nxd *= lmap_nx[d];
+      }
+
+      lgrid_map.SetSize(lmap_nxd + 1);
+      lgrid_map = lmap_nxd + 1;
+      return;
+   }
+
+   for (int d = 0; d < sdim; d++)
+   {
+      Vector elmind(elmin.GetData() + d*nel, nel);
+      Vector elmaxd(elmax.GetData() + d*nel, nel);
+      lmap_bnd_min[d] = elmind.Min();
+      lmap_bnd_max[d] = elmaxd.Max();
+   }
+
+   Array<int> elmin_h, elmax_h;
+   unsigned int store_size;
+   if (by_max_size)
+   {
+      int nmax = nx[0];
+      int nlow = 1, nhigh = nmax > nel ? ceil(pow(nmax - nel, 1.0 / sdim)) : 1;
+      int size_low = 2 + nel;
+      int size = 0;
+      while (nhigh - nlow > 1)
+      {
+         int nmid = nlow + (nhigh - nlow) / 2;
+         int nmd = nmid;
+         for (int d = 1; d < sdim; d++)
+         {
+            nmd *= nmid;
+         }
+         lmap_nx = nmid;
+         SetGridFac(lmap_fac, lmap_nx, lmap_bnd_min, lmap_bnd_max);
+         size = nmd + 1 + GetGridCountAndRange(lmap_nx, lmap_fac,
+                                               lmap_bnd_min, lmap_bnd_max,
+                                               elmin, elmax,
+                                               elmin_h, elmax_h);
+         if (size <= nmax) { nlow = nmid; size_low = size; }
+         else { nhigh = nmid; }
+      }
+      lmap_nx = nlow;
+      lmap_nxd = nlow;
+      for (int d = 1; d < sdim; d++)
+      {
+         lmap_nxd *= nlow;
+      }
+      store_size = size_low;
+      SetGridFac(lmap_fac, lmap_nx, lmap_bnd_min, lmap_bnd_max);
+      if (size != size_low)
+      {
+         GetGridCountAndRange(lmap_nx, lmap_fac,
+                              lmap_bnd_min, lmap_bnd_max,
+                              elmin, elmax,
+                              elmin_h, elmax_h);
+      }
+   }
+   else
+   {
+      SetGridFac(lmap_fac, lmap_nx, lmap_bnd_min, lmap_bnd_max);
+
+      lmap_nxd = lmap_nx[0];
+      for (int d = 1; d < sdim; d++)
+      {
+         lmap_nxd *= lmap_nx[d];
+      }
+
+      // Grid cell ranges for each element in each direction
+      store_size = lmap_nxd + 1 + GetGridCountAndRange(lmap_nx, lmap_fac,
+                                                       lmap_bnd_min,
+                                                       lmap_bnd_max,
+                                                       elmin, elmax,
+                                                       elmin_h, elmax_h);
+   }
+
+   lgrid_map.SetSize(store_size);
+   lgrid_map[0] = lmap_nxd + 1;
+
+   Array<unsigned int> grid_el_count(lmap_nxd);
+   grid_el_count = 0;
+
+   for (int e = 0; e < nel; e++)
+   {
+      int klim = sdim < 3 ? 1 : (elmax_h[2*nel+e]-elmin_h[2*nel+e]);
+      int jlim = sdim < 2 ? 1 : (elmax_h[1*nel+e]-elmin_h[1*nel+e]);
+      int ilim = (elmax_h[0*nel+e]-elmin_h[0*nel+e]);
+      for (int k = 0; k < klim; k++)
+      {
+         int koff = sdim < 3 ? 0 :
+                    (elmin_h[2*nel + e] + k) * lmap_nx[0] * lmap_nx[1];
+         for (int j = 0; j < jlim; j++)
+         {
+            int joff = sdim < 2 ? 0 : (elmin_h[1*nel + e] + j) * lmap_nx[0];
+            for (int i = 0; i < ilim; i++)
+            {
+               int ioff = elmin_h[e] + i;
+               int idx = ioff + joff + koff;
+               grid_el_count[idx]++;
+            }
+         }
+      }
+   }
+
+   for (unsigned int e = 0; e < lmap_nxd; e++)
+   {
+      lgrid_map[e + 1] = lgrid_map[e] + grid_el_count[e];
+   }
+
+   for (int e = 0; e < nel; e++)
+   {
+      int klim = sdim < 3 ? 1 : (elmax_h[2*nel+e]-elmin_h[2*nel+e]);
+      int jlim = sdim < 2 ? 1 : (elmax_h[1*nel+e]-elmin_h[1*nel+e]);
+      int ilim = (elmax_h[0*nel+e]-elmin_h[0*nel+e]);
+      for (int k = 0; k < klim; k++)
+      {
+         int koff = sdim < 3 ? 0 :
+                    (elmin_h[2*nel+e] + k) * lmap_nx[0] * lmap_nx[1];
+         for (int j = 0; j < jlim; j++)
+         {
+            int joff = sdim < 2 ? 0 : (elmin_h[1*nel + e] + j) * lmap_nx[0];
+            for (int i = 0; i < ilim; i++)
+            {
+               int ioff = elmin_h[e] + i;
+               int idx = ioff + joff + koff;
+               lgrid_map[lgrid_map[idx+1]-grid_el_count[idx]]=e;
+               grid_el_count[idx]--;
+            }
+         }
+      }
+   }
+}
+
+Array<int> BBoxTensorGridMap::GridCellToElements(int i) const
+{
+   MFEM_ASSERT(i >= 0 && (unsigned int)i < lmap_nxd,
+               "Access element " << i << " of local grid with cells = "
+               << lmap_nxd);
+   int start = lgrid_map[i];
+   int end = lgrid_map[i + 1];
+   Array<int> elements(end - start);
+   for (int j = start; j < end; j++)
+   {
+      elements[j - start] = lgrid_map[j];
+   }
+   return elements;
+}
+
+int BBoxTensorGridMap::GetGridCellFromPoint(Vector &xyz) const
+{
+   MFEM_ASSERT(xyz.Size() == sdim,
+               "Point must have the same dimension as the grid.");
+   int sum = 0;
+   for (int d = sdim-1; d >= 0; --d)
+   {
+      if (xyz(d) < lmap_bnd_min(d) || xyz(d) > lmap_bnd_max(d))
+      {
+         return -1; // Point is outside the bounds of the grid
+      }
+      sum *= lmap_nx[d];
+      int i = (int)floor((xyz(d) - lmap_bnd_min(d)) * lmap_fac[d]);
+      sum += i < 0 ? 0 : (lmap_nx[d] - 1 < i ? lmap_nx[d] - 1 : i);
+   }
+   return sum;
+}
+
+Array<int> BBoxTensorGridMap::MapPointToElements(Vector &xyz) const
+{
+   MFEM_ASSERT(xyz.Size() == sdim,
+               "Point must have the same dimension as the grid.");
+   int cell = GetGridCellFromPoint(xyz);
+   if (cell < 0)
+   {
+      return Array<int>(); // Point is outside the bounds of the tensor grid
+   }
+   return GridCellToElements(cell);
+}
+
+void BBoxTensorGridMap::GetGridRange(const int d, const Array<int> &lh_n,
+                                     const Vector &lh_fac,
+                                     const Vector &lh_bnd_min,
+                                     const real_t &xmin, const real_t &xmax,
+                                     int &imin, int &imax)
+{
+   // Use a half-open interval [imin, imax) for the covered grid-cell range.
+   // If xmin is exactly on a grid boundary, use the cell on the right/high
+   // side. If xmax is exactly on a grid boundary, stop before the cell on the
+   // right/high side.
+   int i0 = floor( (xmin - lh_bnd_min[d]) * lh_fac[d] );
+   int i1 = ceil ( (xmax - lh_bnd_min[d]) * lh_fac[d] );
+   imin = i0 < 0 ? 0 : i0;
+   imax = i1 < lh_n[d] ? i1 : lh_n[d];
+   if (imax == imin) { ++imax; }
+}
+
+void BBoxTensorGridMap::SetGridFac(Vector &lh_fac, const Array<int> &nx,
+                                   const Vector &lh_bnd_min,
+                                   const Vector &lh_bnd_max)
+{
+   int dim = lh_bnd_min.Size();
+   for (int d = 0; d < dim; d++)
+   {
+      real_t length = lh_bnd_max[d] - lh_bnd_min[d];
+      if (length > 0.0)
+      {
+         lh_fac[d] = nx[d] / length;
+      }
+      else
+      {
+         lh_fac[d] = 0.0;
+      }
+   }
+}
+
+int BBoxTensorGridMap::GetGridCountAndRange(const Array<int> &lh_n,
+                                            const Vector &lh_fac,
+                                            const Vector &lh_bnd_min,
+                                            const Vector &lh_bnd_max,
+                                            const Vector &elmin,
+                                            const Vector &elmax,
+                                            Array<int> &elmin_h,
+                                            Array<int> &elmax_h)
+{
+   int count = 0;
+   const int dim = lh_bnd_min.Size();
+   const int nel = elmin.Size()/dim;
+   elmin_h.SetSize(dim * nel);
+   elmax_h.SetSize(dim * nel);
+   for (int i = 0; i < nel; i++)
+   {
+      int count_el = 1;
+      for (int d = 0; d < dim; d++)
+      {
+         GetGridRange(d, lh_n, lh_fac, lh_bnd_min,
+                      elmin[d*nel + i], elmax[d*nel + i],
+                      elmin_h[d*nel + i], elmax_h[d*nel + i]);
+         int imax = elmax_h[d*nel + i];
+         int imin = elmin_h[d*nel + i];
+         count_el *= (imax - imin);
+      }
+      count += count_el;
+   }
+   return count;
+}
+
+} // namespace mfem

mesh/bb_grid_map.hpp

@@ -0,0 +1,199 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+/* The BBoxTensorGridMap class is adapted from similar functionality in the
+gslib library. Below is the gslib license and copyright statement:
+
+Copyright (c) 2008-2024, UCHICAGO ARGONNE, LLC.
+
+The UChicago Argonne, LLC as Operator of Argonne National
+Laboratory holds copyright in the Software. The copyright holder
+reserves all rights except those expressly granted to licensees,
+and U.S. Government license rights.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
+
+1. Redistributions of source code must retain the above copyright
+notice, this list of conditions and the disclaimer below.
+
+2. Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the disclaimer (as noted below)
+in the documentation and/or other materials provided with the
+distribution.
+
+3. Neither the name of ANL nor the names of its contributors
+may be used to endorse or promote products derived from this software
+without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
+UCHICAGO ARGONNE, LLC, THE U.S. DEPARTMENT OF
+ENERGY OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
+#ifndef MFEM_BB_GRID_MAP
+#define MFEM_BB_GRID_MAP
+
+#include "../config/config.hpp"
+#ifdef MFEM_USE_MPI
+#include "../fem/pgridfunc.hpp"
+#else
+#include "../fem/gridfunc.hpp"
+#endif
+
+namespace mfem
+{
+
+/** \brief Map a point in physical space to candidate elements of a curved mesh.
+ *
+ *  This class builds a Cartesian-aligned tensor grid that covers the domain
+ *  and precomputes, for each grid cell, the set of curved mesh elements whose
+ *  axis-aligned bounding boxes (AABBs) intersect that cell. Given a point (xyz)
+ *  in physical coordinates, the Cartesian grid cell containing the point is
+ *  determined, and the list of candidate element indices whose AABBs are
+ *  intersecting that cell is returned. This yields a fast, conservative
+ *  point-to-element candidate query.
+ *
+ *  The mapping procedure uses a half-open interval convention in each
+ *  dimension. If an element bounding-box minimum lies exactly on a grid-cell
+ *  boundary, it is assigned to the cell on the right/high side of that
+ *  boundary. If an element bounding-box maximum lies exactly on a grid-cell
+ *  boundary, it is assigned to the cell on the left/low side.
+ *
+ *  The map itself is stored as a single array CSR structure where the offsets
+ *  and values are stored in the same array. For a tensor grid with a total of
+ *  N cells, the first N+1 entries store the offsets and the remaining entries
+ *  store the values.
+ *
+ *  The "lgrid_map" looks something like this:
+ *
+ *  Index: 0         1          ...  N             N+1        ...
+ *  Value: [start_0] [start_1]  ... [Length(Map)] [elem_A] [elem_B] [elem_C]...
+ *              |          |                          ^                 ^
+ *              |          |__________________________|_________________|
+ *              |_____________________________________|
+ *
+ *  For grid cell index i, the element indices are stored in
+ *  lgrid_map[j], where lgrid_map[i] <= j < lgrid_map[i+1].
+ *
+ *  If lgrid_map[i] = lgrid_map[i+1], the grid cell i does not intersect any
+ *  elements.
+ *
+ *  See Mittal et al., "General Field Evaluation in High-Order Meshes on GPUs".
+ *  (2025). Computers & Fluids. for technical details.
+ */
+class BBoxTensorGridMap
+{
+private:
+   int sdim; // spatial dimension
+   Array<int> lmap_nx; // grid resolution in each direction
+   Vector lmap_bnd_min, lmap_bnd_max; // min and max extend of grid in x/y/z
+   Vector lmap_fac; // number of cells per unit extent
+   Array<unsigned int> lgrid_map; // actual map from grid cell to mesh elements.
+   unsigned int lmap_nxd; // total number of grid cells
+
+public:
+   /// Constructor for a given mesh and resolution of Cartesian grid.
+   BBoxTensorGridMap(Mesh &mesh, int nx);
+
+   /** @brief Constructor with mesh element bounding boxes and spatial dimension.
+    *
+    *  @details When by_max_size=false, nx gives the Cartesian grid resolution
+    *  in each direction. When by_max_size=true, nx[0] gives the requested
+    *  maximum size of lgrid_map. If nx[0] < 2 + nel, lgrid_map is resized to
+    *  the minimum feasible size 2 + nel.
+    *
+    *  Assumes elmin, elmax Ordering::byNodes:
+    *  elmin -> [x_{0,min},x_{1,min},... ,y_{0,min},y_{1,min},..,z_{nel-1,min}]
+    *  elmax -> [x_{0,max},x_{1,max},... ,y_{0,max},y_{1,max},..,z_{nel-1,max}]
+    *  Note elmin, elmax can be obtained using GridFunction::GetElementBounds()
+   */
+   BBoxTensorGridMap(Vector &elmin, Vector &elmax,
+                     int nel, int sdim, Array<int> &nx,
+                     bool by_max_size=false);
+
+   /** @brief Constructor for given element bounds and spatial dimension.
+    *
+    *  @details The user can either specify the max size of map
+    *  (by_max_size=true) or the number of divisions (by_max_size=false).
+    *
+    *  @details When by_max_size=true, n gives the requested maximum size of
+    *  lgrid_map. If n >= 2 + nel, then lgrid_map.Size() <= n. Otherwise,
+    *  lgrid_map is resized to the minimum feasible size 2 + nel.
+    *
+    *  Assumes elmin, elmax Ordering::byNodes:
+    *  elmin -> [x_{0,min},x_{1,min},... ,y_{0,min},y_{1,min},..,z_{nel-1,min}]
+    *  elmax -> [x_{0,max},x_{1,max},... ,y_{0,max},y_{1,max},..,z_{nel-1,max}]
+    *  Note elmin, elmax can be obtained using GridFunction::GetElementBounds()
+   */
+   BBoxTensorGridMap(Vector &elmin, Vector &elmax,
+                     int nel, int sdim, int n, bool by_max_size=false);
+
+   /// Map a point to possible overlapping elements.
+   Array<int> MapPointToElements(Vector &xyz) const;
+
+   /// Get grid cell index for a given point.
+   int GetGridCellFromPoint(Vector &xyz) const;
+
+   /// Get list of elements corresponding to a grid cell.
+   Array<int> GridCellToElements(int i) const;
+
+   // Some getters
+   const Array<unsigned int> &GetGridMap() const { return lgrid_map; }
+   const Vector &GetGridFac() const { return lmap_fac; }
+   const Vector &GetGridMin() const { return lmap_bnd_min; }
+   const Vector &GetGridMax() const { return lmap_bnd_max; }
+   const Array<int> &GetGridN() const { return lmap_nx; }
+private:
+   /** @brief Setup using the element-wise bounding boxes.
+    *
+    *  @details When by_max_size = false, nx gives number of cells in each
+    *  direction. When by_max_size = true, nx[0] gives the requested maximum
+    *  size of lgrid_map. If nx[0] < 2 + nel, lgrid_map is resized to the
+    *  minimum feasible size 2 + nel. */
+   void Setup(Vector &elmin, Vector &elmax,
+              int nel, Array<int> &nx, bool by_max_size);
+
+public:
+   /** @brief Get local (1D) indices for cells of tensor grid that intersect
+    *  with the given bounding box. */
+   static void GetGridRange(const int d, const Array<int> &lh_n,
+                            const Vector &lh_fac,
+                            const Vector &lh_bnd_min,
+                            const real_t &xmin, const real_t &xmax,
+                            int &imin, int &imax);
+
+   /// Set grid fac - number of grid cells per unit grid extent.
+   static void SetGridFac(Vector &lh_fac, const Array<int> &nx,
+                          const Vector &lh_bnd_min, const Vector &lh_bnd_max);
+
+   /** @brief Get grid count and range - total number of grid cells that
+    *  intersect with all elements of the mesh and get corresponding ranges. */
+   static int GetGridCountAndRange(const Array<int> &lh_n, const Vector &lh_fac,
+                                   const Vector &lh_bnd_min,
+                                   const Vector &lh_bnd_max,
+                                   const Vector &elmin, const Vector &elmax,
+                                   Array<int> &elmin_h, Array<int> &elmax_h);
+};
+
+} // namespace mfem
+
+#endif // MFEM_BB_GRID_MAP

mesh/gmsh.cpp

@@ -9,13 +9,22 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.
 
-#include "gmsh.hpp"
+#include "mesh_headers.hpp"
 #include "vtk.hpp"
+#include "../general/hash_util.hpp"
+
+using namespace std;
+using namespace mfem::bin_io;
 
 namespace mfem
 {
 
-int BarycentricToGmshTet(int *b, int ref)
+namespace gmsh
+{
+
+/// Given barycentric indices @a b of a node in a tetrahedral element of degree
+/// @a ref, return its Gmsh index.
+static int BarycentricToGmshTet(int *b, int ref)
 {
    int i = b[0];
    int j = b[1];
@@ -117,7 +126,9 @@ int BarycentricToGmshTet(int *b, int ref)
    }
 }
 
-int CartesianToGmshQuad(int idx_in[], int ref)
+/// Given the Cartesian indices @a idx_in of a node in a quadrilateral of order
+/// @a ref, return its Gmsh index.
+static int CartesianToGmshQuad(int idx_in[], int ref)
 {
    int i = idx_in[0];
    int j = idx_in[1];
@@ -147,7 +158,9 @@ int CartesianToGmshQuad(int idx_in[], int ref)
    }
 }
 
-int CartesianToGmshHex(int idx_in[], int ref)
+/// Given the Cartesian indices @a idx_in of a node in a hexahedron of order
+/// @a ref, return its Gmsh index.
+static int CartesianToGmshHex(int idx_in[], int ref)
 {
    int i = idx_in[0];
    int j = idx_in[1];
@@ -213,7 +226,9 @@ int CartesianToGmshHex(int idx_in[], int ref)
    }
 }
 
-int WedgeToGmshPri(int idx_in[], int ref)
+/// Given the indices @a idx_in of a node in a prism of order @a ref, return its
+/// Gmsh index.
+static int WedgeToGmshPrism(int idx_in[], int ref)
 {
    int i = idx_in[0];
    int j = idx_in[1];
@@ -308,7 +323,9 @@ int WedgeToGmshPri(int idx_in[], int ref)
    }
 }
 
-int CartesianToGmshPyramid(int idx_in[], int ref)
+/// Given the Cartesian indices @a idx_in of a node in a pyramid of order @a ref
+/// return its Gmsh index.
+static int CartesianToGmshPyramid(int idx_in[], int ref)
 {
    int i = idx_in[0];
    int j = idx_in[1];
@@ -375,7 +392,8 @@ int CartesianToGmshPyramid(int idx_in[], int ref)
    }
 }
 
-void GmshHOSegmentMapping(int order, int *map)
+/// Form the mapping from MFEM to Gmsh segment indices.
+static void HOSegmentMapping(int order, int *map)
 {
    map[0] = 0;
    map[order] = 1;
@@ -385,7 +403,8 @@ void GmshHOSegmentMapping(int order, int *map)
    }
 }
 
-void GmshHOTriangleMapping(int order, int *map)
+/// Form the mapping from MFEM to Gmsh triangle indices.
+static void HOTriangleMapping(int order, int *map)
 {
    int b[3];
    int o = 0;
@@ -400,7 +419,8 @@ void GmshHOTriangleMapping(int order, int *map)
    }
 }
 
-void GmshHOQuadrilateralMapping(int order, int *map)
+/// Form the mapping from MFEM to Gmsh quadrilateral indices.
+static void HOQuadrilateralMapping(int order, int *map)
 {
    int b[2];
    int o = 0;
@@ -414,7 +434,8 @@ void GmshHOQuadrilateralMapping(int order, int *map)
    }
 }
 
-void GmshHOTetrahedronMapping(int order, int *map)
+/// Form the mapping from MFEM to Gmsh tetrahedron indices.
+static void HOTetrahedronMapping(int order, int *map)
 {
    int b[4];
    int o = 0;
@@ -433,7 +454,8 @@ void GmshHOTetrahedronMapping(int order, int *map)
    }
 }
 
-void GmshHOHexahedronMapping(int order, int *map)
+/// Form the mapping from MFEM to Gmsh hexahedron indices.
+static void HOHexahedronMapping(int order, int *map)
 {
    int b[3];
    int o = 0;
@@ -450,7 +472,8 @@ void GmshHOHexahedronMapping(int order, int *map)
    }
 }
 
-void GmshHOWedgeMapping(int order, int *map)
+/// Form the mapping from MFEM to Gmsh prism indices.
+static void HOPrismMapping(int order, int *map)
 {
    int b[3];
    int o = 0;
@@ -460,14 +483,15 @@ void GmshHOWedgeMapping(int order, int *map)
       {
          for (b[0]=0; b[0]<=order - b[1]; b[0]++)
          {
-            map[o] = WedgeToGmshPri(b, order);
+            map[o] = WedgeToGmshPrism(b, order);
             o++;
          }
       }
    }
 }
 
-void GmshHOPyramidMapping(int order, int *map)
+/// Form the mapping from MFEM to Gmsh pyramid indices.
+static void HOPyramidMapping(int order, int *map)
 {
    int b[3];
    int o = 0;
@@ -484,4 +508,805 @@ void GmshHOPyramidMapping(int order, int *map)
    }
 }
 
+/// Number of nodes in an element of type @a geom with order @a order.
+static int NumNodesInElement(Geometry::Type geom, int order)
+{
+   return GlobGeometryRefiner.Refine(geom, order, 1)->RefPts.GetNPoints();
+}
+
+/// @brief Return the space dimension (at least 1) given a 3D bounding box.
+///
+/// If some of the sides of the box have zero (or very small) sides, then that
+/// dimension is not counted.
+static int GetSpaceDimension(double bb_min[3], double bb_max[3])
+{
+   static constexpr double bb_tol = 1e-14;
+   const double bb_size = max(bb_max[0] - bb_min[0],
+                              max(bb_max[1] - bb_min[1],
+                                  bb_max[2] - bb_min[2]));
+   int sd = 1;
+   if (bb_max[1] - bb_min[1] > bb_size * bb_tol)
+   {
+      sd += 1;
+   }
+   if (bb_max[2] - bb_min[2] > bb_size * bb_tol)
+   {
+      sd += 1;
+   }
+   return sd;
+}
+
+/// Skip ahead in the input stream until the next section, which opens on a new
+/// line beginning with $ (but not beginning with $End, which ends the previous
+/// section).
+static string GoToNextSection(istream &input)
+{
+   string line;
+   while (getline(input, line))
+   {
+      filter_dos(line);
+      // Find the next line that starts with '$', but does not start with "$End"
+      if (line.size() >= 1 &&
+          line[0] == '$' &&
+          (line.size() < 4 || line.compare(1, 3, "End") != 0))
+      {
+         return line.substr(1, string::npos);
+      }
+   }
+   return "";
+}
+
+/// Read a double-quoted string from the input stream, and return the result
+/// (without the enclosing quotes).
+static string ReadQuotedString(istream &input)
+{
+   char c;
+   // Find opening quote
+   while (input.get(c))
+   {
+      if (c == '"') { break; }
+   }
+   MFEM_VERIFY(input, "Error reading string.");
+
+   string result;
+   while (input.get(c))
+   {
+      // Find closing quote
+      if (c == '"')
+      {
+         return result;
+      }
+      result.push_back(c);
+   }
+   MFEM_ABORT("Failed to read string.");
+}
+
+void ChompNewline(istream &input)
+{
+   if (input.peek() == '\r') { input.get(); }
+   MFEM_VERIFY(input.get() == '\n', "Inconsistent newlines.");
+};
+
+/// Enum for supported Gmsh mesh file versions.
+enum class GmshVersion { V2_2, V4_1 };
+
+/// @brief Helper class for reading Gmsh meshes.
+///
+/// This is an internal helper class that is not intended for use by the
+/// end-user; see Mesh::ReadGmshMesh for its usage.
+///
+/// This class implements common functionality and state needed to read Gmsh
+/// meshes in version 2.2 and 4.1 format.
+class GmshReader
+{
+   /// List of supported Gmsh element types. types[geom][order-1] contains the
+   /// Gmsh element type number for the element of the given geometry and order.
+   vector<vector<int>> types =
+   {
+      {15}, // point
+      {1, 8, 26, 27, 28, 62, 63, 64, 65, 66}, // segment
+      {2, 9, 21, 23, 25, 42, 43, 44, 45, 46}, // triangle
+      {3, 10, 36, 37, 38, 47, 48, 49, 50, 51}, // quadrilateral
+      {4, 11, 29, 30, 31, 71, 72, 73, 74, 75}, // tetrahedron
+      {5, 12, 92, 93, 94, 95, 96, 97, 98}, // hexahedron
+      {6, 13, 90, 91, 106, 107, 108, 109, 110}, // prism
+      {7, 14, 118, 119, 120, 121, 122, 123, 124} // pyramid
+   };
+   /// Permutations mapping from MFEM lexicographic ordering to Gmsh ordering,
+   /// for a given element type and order. Constructed lazily.
+   unordered_map<pair<Geometry::Type, int>, vector<int>, PairHasher> node_maps;
+
+   bool has_positive_attrs = false;
+   bool has_non_positive_attrs = false;
+
+   istream &input; ///< The input stream to read from.
+
+   BinaryOrASCII is_binary; ///< Is the file in binary or ASCII format?
+   int data_size; ///< Data size in bytes (meaning depends on file format).
+   GmshVersion version; ///< The version of Gmsh format.
+
+   /// A map between a serial number of the vertex and its number in the file
+   /// (there may be gaps in the numbering, and also Gmsh enumerates vertices
+   /// starting from 1, not 0)
+   unordered_map<int, int> vertex_map;
+
+   /// A map containing names of physical curves, surfaces, and volumes. The
+   /// first index is the dimension of the physical manifold, the second index is
+   /// the element attribute number of the set, and the string is the assigned
+   /// name.
+   unordered_map<int,unordered_map<int,string> > phys_names_by_dim;
+
+   /// Gmsh always outputs coordinates in 3D, but MFEM distinguishes between the
+   /// mesh element dimension (Dim) and the dimension of the space in which the
+   /// mesh is embedded (spaceDim). For example, a 2D MFEM mesh has Dim = 2 and
+   /// spaceDim = 2, while a 2D surface mesh in 3D has Dim = 2 but spaceDim = 3.
+   /// We set spaceDim by measuring the mesh bounding box and checking for a
+   /// lower dimensional subspace. The assumption is that the mesh is at least
+   /// 2D if the y-dimension of the box is non-trivial and 3D if the z-dimension
+   /// is non-trivial. Note that with these assumptions a 2D mesh parallel to
+   /// the yz plane will be considered a surface mesh embedded in 3D whereas the
+   /// same 2D mesh parallel to the xy plane will be considered a 2D mesh.
+   ///@{
+   const double inf = numeric_limits<double>::infinity();
+   double bb_min[3] = {inf, inf, inf};
+   double bb_max[3] = {-inf, -inf, -inf};
+   ///@}
+
+   int mesh_order = -1; ///< Mesh order. Variable order meshes are not supported.
+   bool periodic = false; ///< Is the mesh periodic?
+
+   /// Node indices of high-order elements, such that ho_el_nodes[dim][e][i] is
+   /// the i-th node index of the e-th element of dimension dim.
+   vector<vector<vector<int>>> ho_el_nodes{4};
+
+   vector<int> v2v; ///< Periodic vertex mapping (for periodic meshes only).
+
+   /// Get the geometry type and polynomial degree for a given Gmsh element
+   /// type.
+   pair<Geometry::Type, int> GetGeometryAndOrder(int element_type) const
+   {
+      for (int g = Geometry::POINT; g < Geometry::NUM_GEOMETRIES; ++g)
+      {
+         const vector<int> &types_g = types[g];
+         const auto it = lower_bound(types_g.begin(), types_g.end(), element_type);
+         if (it != types_g.end() && *it == element_type)
+         {
+            return {Geometry::Type(g), int(distance(types_g.begin(), it) + 1)};
+         }
+      }
+      MFEM_ABORT("Unknown Gmsh element type.");
+   }
+
+   /// Return node map if it exists, otherwise lazily construct it.
+   const vector<int> &GetNodeMap(Geometry::Type geom, int order)
+   {
+      auto it = node_maps.find(make_pair(geom, order));
+      if (it == node_maps.end())
+      {
+         const int n_nodes = NumNodesInElement(geom, order);
+         auto ret = node_maps.emplace(piecewise_construct,
+                                      forward_as_tuple(geom, order),
+                                      forward_as_tuple(n_nodes));
+         auto &map = ret.first->second;
+         auto data = map.data();
+         switch (geom)
+         {
+            case Geometry::SEGMENT: HOSegmentMapping(order, data); break;
+            case Geometry::TRIANGLE: HOTriangleMapping(order, data); break;
+            case Geometry::SQUARE: HOQuadrilateralMapping(order, data); break;
+            case Geometry::TETRAHEDRON: HOTetrahedronMapping(order, data); break;
+            case Geometry::CUBE: HOHexahedronMapping(order, data); break;
+            case Geometry::PRISM: HOPrismMapping(order, data); break;
+            case Geometry::PYRAMID: HOPyramidMapping(order, data); break;
+            default: MFEM_ABORT("Unsupported element type.");
+         }
+         return map;
+      }
+      else
+      {
+         return it->second;
+      }
+   }
+
+   /// Add the physical names (in @a phys_names_by_dim) to the mesh's attribute
+   /// sets and boundary attribute sets.
+   void AddPhysicalNames(Mesh &mesh)
+   {
+      // Process boundary attribute set names
+      for (auto const &bdr_attr : phys_names_by_dim[mesh.Dimension() - 1])
+      {
+         if (!mesh.bdr_attribute_sets.AttributeSetExists(bdr_attr.second))
+         {
+            mesh.bdr_attribute_sets.CreateAttributeSet(bdr_attr.second);
+         }
+         mesh.bdr_attribute_sets.AddToAttributeSet(bdr_attr.second, bdr_attr.first);
+      }
+
+      // Process element attribute set names
+      for (auto const &attr : phys_names_by_dim[mesh.Dimension()])
+      {
+         if (!mesh.attribute_sets.AttributeSetExists(attr.second))
+         {
+            mesh.attribute_sets.CreateAttributeSet(attr.second);
+         }
+         mesh.attribute_sets.AddToAttributeSet(attr.second, attr.first);
+      }
+   }
+
+   /// In the periodic vertex mapping @a v2v, there may be chains or cycles.
+   /// This will simplify all chains so that they are one link only, and break
+   /// any cycles.
+   void SimplifyPeriodicLinks()
+   {
+      // Follow existing long chains of duplicate->primary in v2v array. Upon
+      // completion of this loop, each v2v[duplicate] will point to a true
+      // primary vertex. This algorithm is useful for periodicity defined in
+      // multiple directions.
+      for (int duplicate = 0; duplicate < int(v2v.size()); duplicate++)
+      {
+         int primary = v2v[duplicate];
+         if (primary != duplicate)
+         {
+            // This loop will end if it finds a circular dependency.
+            while (v2v[primary] != primary && primary != duplicate)
+            {
+               primary = v2v[primary];
+            }
+            if (primary == duplicate)
+            {
+               // If primary and duplicate are the same vertex, circular
+               // dependency exists. We need to fix the problem, we choose
+               // duplicate.
+               v2v[duplicate] = duplicate;
+            }
+            else
+            {
+               // The long chain has ended on the true primary vertex.
+               v2v[duplicate] = primary;
+            }
+         }
+      }
+   }
+
+   /// In the list of Elements @a els, replace periodic vertices using the
+   /// periodic identification map @a v2v.
+   void ReplacePeriodicVertices(Array<Element*> &els) const
+   {
+      for (int i = 0; i < els.Size(); i++)
+      {
+         Element *e = els[i];
+         int *v = e->GetVertices();
+         for (int j = 0; j < e->GetNVertices(); j++)
+         {
+            v[j] = v2v[v[j]];
+         }
+      }
+   }
+
+   /// Set the attribute of element @a e to @a attribute. If the attribute is
+   /// non-positive, set it to 1. Keep track if non-positive or positive
+   /// attributes are encountered to potentially report errors to the user.
+   void SetAttribute(Element *e, int attribute)
+   {
+      if (attribute < 1)
+      {
+         has_non_positive_attrs = true;
+         attribute = 1; // Resetting non-positive attributes to be 1.
+      }
+      else
+      {
+         has_positive_attrs = true;
+      }
+      e->SetAttribute(attribute);
+   }
+
+   /// Create and return a new Element of the given geometry, with specified
+   /// attribute. If the element is higher-order, store the high-order node
+   /// indices.
+   template <typename I>
+   Element *NewElement(Mesh &mesh, Geometry::Type geom, int el_order,
+                       const vector<I> &el_nodes, int attribute)
+   {
+      auto e = mesh.NewElement(geom);
+      int *v = e->GetVertices();
+      for (int i = 0; i < e->GetNVertices(); ++i)
+      {
+         v[i] = vertex_map[el_nodes[i]];
+      }
+      SetAttribute(e, attribute);
+
+      // Store high-order node locations
+      const int dim = Geometry::Dimension[geom];
+      if (el_order > 1)
+      {
+         const int n_elem_nodes = NumNodesInElement(geom, el_order);
+         const vector<int> &map = GetNodeMap(geom, el_order);
+         auto &nodes = ho_el_nodes[dim].emplace_back(n_elem_nodes);
+         for (int i = 0; i < n_elem_nodes; ++i)
+         {
+            nodes[i] = vertex_map[el_nodes[map[i]]];
+         }
+      }
+
+      return e;
+   }
+
+   /// Check that all attributes are positive (or, if none are positive, give a
+   /// warning that they have been replaced by 1).
+   void CheckAttributes() const
+   {
+      if (has_non_positive_attrs)
+      {
+         // If mesh has a mix of positive and non-positive attributes, this is
+         // a user error. All attributes should be positive.
+         MFEM_VERIFY(!has_positive_attrs,
+                     "Non-positive element attribute in Gmsh mesh!\n"
+                     "By default Gmsh sets element tags (attributes)"
+                     " to '0' but MFEM requires that they be"
+                     " positive integers.\n"
+                     "Use \"Physical Curve\", \"Physical Surface\","
+                     " or \"Physical Volume\" to set tags/attributes"
+                     " for all curves, surfaces, or volumes in your"
+                     " Gmsh geometry to values which are >= 1.");
+         // If the mesh has only non-positive attributes, this could be because
+         // Gmsh by default will set zero attributes if no physical entities are
+         // defined. In this case, we warn the user, and set attributes to 1.
+         MFEM_WARNING("Gmsh reader: all element attributes were zero.\n"
+                      "MFEM only supports positive element attributes.\n"
+                      "Setting all element attributes to 1.\n");
+      }
+   }
+
+   /// @brief Read the mesh in Gmsh 4.1 format from the input stream into the
+   /// Mesh @a mesh.
+   void ReadGmsh4Mesh(Mesh &mesh)
+   {
+      MFEM_VERIFY(data_size == sizeof(size_t), "Incompatible Gmsh mesh.");
+
+      const auto b = is_binary;
+      unordered_map<pair<int,int>, int, PairHasher> entity_physical_tag;
+
+      string section;
+      do
+      {
+         section = GoToNextSection(input);
+         if (section == "PhysicalNames")
+         {
+            // $PhysicalNames is always encoded in ASCII
+            const int n_phys_names = ReadBinaryOrASCII<int>(input, ASCII);
+            for (int i = 0; i < n_phys_names; ++i)
+            {
+               const int phys_name_dim = ReadBinaryOrASCII<int>(input, ASCII);
+               const int phys_name_tag = ReadBinaryOrASCII<int>(input, ASCII);
+               const string phys_name = ReadQuotedString(input);
+
+               phys_names_by_dim[phys_name_dim][phys_name_tag] = phys_name;
+            }
+         }
+         else if (section == "Entities")
+         {
+            const size_t n_points = ReadBinaryOrASCII<size_t>(input, b);
+            const size_t n_curves = ReadBinaryOrASCII<size_t>(input, b);
+            const size_t n_surfaces = ReadBinaryOrASCII<size_t>(input, b);
+            const size_t n_volumes = ReadBinaryOrASCII<size_t>(input, b);
+
+            const size_t n_entities[4] = {n_points, n_curves, n_surfaces, n_volumes};
+
+            if (n_volumes > 0) { mesh.Dim = 3; }
+            else if (n_surfaces > 0) { mesh.Dim = 2; }
+            else { mesh.Dim = 1; }
+
+            for (int d = 0; d <= 3; ++d)
+            {
+               for (size_t i = 0; i < n_entities[d]; ++i)
+               {
+                  const int tag = ReadBinaryOrASCII<int>(input, b);
+                  Skip<double>(input, d == 0 ? 3 : 6, b); // Skip X, Y, Z
+                  const size_t n_phys_tags = ReadBinaryOrASCII<size_t>(input, b);
+                  for (size_t iphys = 0; iphys < n_phys_tags; ++iphys)
+                  {
+                     const int phys_tag = ReadBinaryOrASCII<int>(input, b);
+                     // Keep track of codim-0 and codim-1 entities.
+                     if (d == mesh.Dim || d == mesh.Dim - 1)
+                     {
+                        entity_physical_tag[ {d, tag}] = phys_tag;
+                     }
+                  }
+                  if (d > 0)
+                  {
+                     const size_t n_bounding = ReadBinaryOrASCII<size_t>(input, b);
+                     Skip<int>(input, n_bounding, b);
+                  }
+               }
+            }
+         }
+         else if (section == "Nodes")
+         {
+            const size_t n_blocks = ReadBinaryOrASCII<size_t>(input, b);
+            const size_t n_nodes = ReadBinaryOrASCII<size_t>(input, b);
+            Skip<size_t>(input, 2, b); // Skip min and max tags
+
+            mesh.NumOfVertices = n_nodes;
+            mesh.vertices.SetSize(n_nodes);
+            size_t vertex_counter = 0;
+
+            double c[3];
+
+            for (size_t iblock = 0; iblock < n_blocks; ++iblock)
+            {
+               Skip<int>(input, 2, b); // Skip entity dim and ta
+               const int is_parametric = ReadBinaryOrASCII<int>(input, b);
+               const size_t n_nodes_in_block = ReadBinaryOrASCII<size_t>(input, b);
+
+               MFEM_VERIFY(!is_parametric, "Parametric nodes not supported.");
+
+               vector<size_t> node_tags(n_nodes_in_block);
+               for (size_t i = 0; i < n_nodes_in_block; ++i)
+               {
+                  const size_t node_tag = ReadBinaryOrASCII<size_t>(input, b);
+                  node_tags[i] = node_tag;
+               }
+               for (size_t i = 0; i < n_nodes_in_block; ++i)
+               {
+                  for (int d = 0; d < 3; ++d)
+                  {
+                     c[d] = ReadBinaryOrASCII<double>(input, b);
+                     bb_min[d] = min(bb_min[d], c[d]);
+                     bb_max[d] = max(bb_max[d], c[d]);
+                  }
+                  vertex_map[node_tags[i]] = vertex_counter;
+                  mesh.vertices[vertex_counter] = Vertex(c[0], c[1], c[2]);
+                  vertex_counter += 1;
+               }
+            }
+            mesh.spaceDim = GetSpaceDimension(bb_min, bb_max);
+         }
+         else if (section == "Elements")
+         {
+            const size_t n_blocks = ReadBinaryOrASCII<size_t>(input, b);
+            Skip<size_t>(input, 3, b); // Skip n_elements and min/max tags.
+
+            for (size_t iblock = 0; iblock < n_blocks; ++iblock)
+            {
+               const int entity_dim = ReadBinaryOrASCII<int>(input, b);
+               const int entity_tag = ReadBinaryOrASCII<int>(input, b);
+               const int element_type = ReadBinaryOrASCII<int>(input, b);
+               const size_t n_elements = ReadBinaryOrASCII<size_t>(input, b);
+
+               for (size_t ie = 0; ie < n_elements; ++ie)
+               {
+                  Skip<size_t>(input, 1, b); // Skip element tag
+                  const auto [geom, el_order] = GetGeometryAndOrder(element_type);
+
+                  if (mesh_order < 0) { mesh_order = el_order; }
+                  MFEM_VERIFY(mesh_order == el_order,
+                              "Variable order Gmsh meshes are not supported");
+
+                  const int n_elem_nodes = NumNodesInElement(geom, el_order);
+                  vector<size_t> node_tags(n_elem_nodes);
+                  for (int inode = 0; inode < n_elem_nodes; ++inode)
+                  {
+                     node_tags[inode] = ReadBinaryOrASCII<size_t>(input, b);
+                  }
+
+                  // We only add codim-0 and codim-1 elements.
+                  if (entity_dim != mesh.Dim && entity_dim != mesh.Dim - 1) { continue; }
+
+                  const int attribute = entity_physical_tag[ {entity_dim, entity_tag}];
+                  auto e = NewElement(mesh, geom, el_order, node_tags, attribute);
+                  if (entity_dim == mesh.Dim) { mesh.elements.Append(e); }
+                  else if (entity_dim == mesh.Dim - 1) { mesh.boundary.Append(e); }
+               }
+            }
+            mesh.NumOfElements = mesh.elements.Size();
+            mesh.NumOfBdrElements = mesh.boundary.Size();
+         }
+         else if (section == "Periodic")
+         {
+            const size_t n_periodic = ReadBinaryOrASCII<size_t>(input, b);
+            if (n_periodic == 0) { continue; }
+
+            periodic = true;
+            v2v.resize(mesh.NumOfVertices);
+            for (int i = 0; i < mesh.NumOfVertices; i++) { v2v[i] = i; }
+
+            for (size_t i = 0; i < n_periodic; ++i)
+            {
+               Skip<int>(input, 3, b); // Skip entity information
+               const size_t n_affine = ReadBinaryOrASCII<size_t>(input, b);
+               Skip<double>(input, n_affine, b); // Skip affine information
+               const size_t n_nodes = ReadBinaryOrASCII<size_t>(input, b);
+               for (size_t j = 0; j < n_nodes; ++j)
+               {
+                  const size_t node_num = ReadBinaryOrASCII<size_t>(input, b);
+                  const size_t primary_node_num = ReadBinaryOrASCII<size_t>(input, b);
+                  v2v[node_num - 1] = int(primary_node_num - 1);
+               }
+            }
+         }
+      }
+      while (!section.empty());
+   }
+
+   /// @brief Read the mesh in Gmsh 2.2 format from the input stream into the
+   /// Mesh @a mesh.
+   void ReadGmsh2Mesh(Mesh &mesh)
+   {
+      const auto b = is_binary;
+      MFEM_VERIFY(data_size == sizeof(double), "Incompatible data size.");
+
+      string section;
+      do
+      {
+         section = GoToNextSection(input);
+         if (section == "Nodes")
+         {
+            mesh.NumOfVertices = ReadBinaryOrASCII<int>(input, ASCII);
+            ChompNewline(input);
+            mesh.vertices.SetSize(mesh.NumOfVertices);
+            double c[3];
+            for (int v = 0; v < mesh.NumOfVertices; ++v)
+            {
+               const int node_num = ReadBinaryOrASCII<int>(input, b);
+               for (int d = 0; d < 3; ++d)
+               {
+                  c[d] = ReadBinaryOrASCII<double>(input, b);
+                  bb_min[d] = min(bb_min[d], c[d]);
+                  bb_max[d] = max(bb_max[d], c[d]);
+               }
+               mesh.vertices[v] = Vertex(c[0], c[1], c[2]);
+               vertex_map[node_num] = v;
+            }
+            mesh.spaceDim = GetSpaceDimension(bb_min, bb_max);
+            MFEM_VERIFY(vertex_map.size() == size_t(mesh.NumOfVertices),
+                        "Gmsh node indices are not unique.");
+         }
+         else if (section == "Elements")
+         {
+            const int num_elements = ReadBinaryOrASCII<int>(input, ASCII);
+            ChompNewline(input);
+            int num_el_read = 0;
+
+            vector<vector<unique_ptr<Element>>> elems_by_dim(4);
+
+            while (num_el_read < num_elements)
+            {
+               auto add_element = [&](int el_type, int el_phys_tag, Geometry::Type geom,
+                                      int el_order, const vector<int> &el_nodes)
+               {
+                  if (mesh_order < 0) { mesh_order = el_order; }
+                  MFEM_VERIFY(mesh_order == el_order,
+                              "Variable order Gmsh meshes are not supported");
+                  Element *e = NewElement(mesh, geom, el_order, el_nodes, el_phys_tag);
+                  elems_by_dim[Geometry::Dimension[geom]].emplace_back(e);
+               };
+
+               if (b)
+               {
+                  // Header
+                  const int el_type  = ReadBinaryOrASCII<int>(input, BINARY);
+                  const int n_els  = ReadBinaryOrASCII<int>(input, BINARY);
+                  const int n_tags = ReadBinaryOrASCII<int>(input, BINARY);
+                  const auto [geom, el_order] = GetGeometryAndOrder(el_type);
+                  const int n_el_nodes = NumNodesInElement(geom, el_order);
+                  vector<int> el_nodes(n_el_nodes);
+                  // Element blocks
+                  for (int e = 0; e < n_els; ++e)
+                  {
+                     Skip<int>(input, 1, BINARY); // Skip element number
+                     int el_phys_tag = 0;
+                     if (n_tags > 0)
+                     {
+                        el_phys_tag = ReadBinaryOrASCII<int>(input, BINARY);
+                        Skip<int>(input, n_tags - 1, BINARY);
+                     }
+                     for (int i = 0; i < n_el_nodes; ++i)
+                     {
+                        el_nodes[i] = ReadBinaryOrASCII<int>(input, BINARY);
+                     }
+                     add_element(el_type, el_phys_tag, geom, el_order, el_nodes);
+                     num_el_read += 1;
+                  }
+               }
+               else
+               {
+                  Skip<int>(input, 1, ASCII); // Skip element number
+                  const int el_type = ReadBinaryOrASCII<int>(input, ASCII);
+                  const int n_tags = ReadBinaryOrASCII<int>(input, ASCII);
+                  int el_phys_tag = 0;
+                  if (n_tags > 0)
+                  {
+                     el_phys_tag = ReadBinaryOrASCII<int>(input, ASCII);
+                     Skip<int>(input, n_tags - 1, ASCII);
+                  }
+                  const auto [geom, el_order] = GetGeometryAndOrder(el_type);
+                  const int n_el_nodes = NumNodesInElement(geom, el_order);
+                  vector<int> el_nodes(n_el_nodes);
+                  for (int i = 0; i < n_el_nodes; ++i)
+                  {
+                     el_nodes[i] = ReadBinaryOrASCII<int>(input, ASCII);
+                  }
+                  add_element(el_type, el_phys_tag, geom, el_order, el_nodes);
+                  num_el_read += 1;
+               }
+            }
+
+            if (elems_by_dim[3].size() > 0) { mesh.Dim = 3; }
+            else if (elems_by_dim[2].size() > 0) { mesh.Dim = 2; }
+            else { mesh.Dim = 1; }
+
+            mesh.NumOfElements = elems_by_dim[mesh.Dim].size();
+            mesh.elements.SetSize(mesh.NumOfElements);
+            for (int i = 0; i < mesh.NumOfElements; ++i)
+            {
+               mesh.elements[i] = elems_by_dim[mesh.Dim][i].release();
+            }
+            mesh.NumOfBdrElements = elems_by_dim[mesh.Dim - 1].size();
+            mesh.boundary.SetSize(mesh.NumOfBdrElements);
+            for (int i = 0; i < mesh.NumOfBdrElements; ++i)
+            {
+               mesh.boundary[i] = elems_by_dim[mesh.Dim - 1][i].release();
+            }
+         }
+         else if (section == "PhysicalNames")
+         {
+            const int num_names = ReadBinaryOrASCII<int>(input, ASCII);
+            for (int i = 0; i < num_names; ++i)
+            {
+               const int phys_dim = ReadBinaryOrASCII<int>(input, ASCII);
+               const int phys_tag = ReadBinaryOrASCII<int>(input, ASCII);
+               phys_names_by_dim[phys_dim][phys_tag] = ReadQuotedString(input);
+            }
+         }
+         else if (section == "Periodic")
+         {
+            const int n_periodic_entities = ReadBinaryOrASCII<int>(input, ASCII);
+            if (n_periodic_entities == 0) { continue; }
+
+            periodic = true;
+            v2v.resize(mesh.NumOfVertices);
+            for (int i = 0; i < mesh.NumOfVertices; i++) { v2v[i] = i; }
+
+            for (int i = 0; i < n_periodic_entities; i++)
+            {
+               Skip<int>(input, 3, ASCII); // Skip dimension, tag, and master tag
+               ChompNewline(input);
+               // Next section might be "Affine"; if so, skip.
+               if (input.peek() == 'A')
+               {
+                  MFEM_VERIFY(ReadBinaryOrASCII<string>(input, ASCII) == "Affine",
+                              "Cannot find Affine transformation");
+                  string line;
+                  getline(input, line);
+               }
+               const int n_nodes = ReadBinaryOrASCII<int>(input, ASCII);
+               for (int j = 0; j < n_nodes; ++j)
+               {
+                  const int node_num = ReadBinaryOrASCII<int>(input, ASCII);
+                  const int primary_node_num = ReadBinaryOrASCII<int>(input, ASCII);
+                  v2v[node_num - 1] = primary_node_num - 1;
+               }
+            }
+         }
+      }
+      while (section != "");
+   }
+
+public:
+
+   /// @brief Read the mesh from the input stream @a input_ into mesh @a mesh.
+   ///
+   /// Meshes in Gmsh format 2.2 or 4.1 and in either binary or ASCII can be
+   /// read; the format is determined automatically.
+   GmshReader(istream &input_, Mesh &mesh) : input(input_)
+   {
+      const string version_str = ReadBinaryOrASCII<string>(input, ASCII);
+      MFEM_VERIFY(version_str == "2.2" || version_str == "4.1",
+                  "Unsupported Gmsh file version. Supported versions: 2.2 and 4.1");
+      version = version_str == "2.2" ? GmshVersion::V2_2 : GmshVersion::V4_1;
+      is_binary = BinaryOrASCII(ReadBinaryOrASCII<bool>(input, ASCII));
+      data_size = ReadBinaryOrASCII<int>(input, ASCII);
+      ChompNewline(input);
+      if (is_binary)
+      {
+         const int one = ReadBinaryOrASCII<int>(input, BINARY);
+         MFEM_VERIFY(one == 1, "Incompatible endianness.");
+      }
+
+      if (version == GmshVersion::V4_1)
+      {
+         ReadGmsh4Mesh(mesh);
+      }
+      else if (version == GmshVersion::V2_2)
+      {
+         ReadGmsh2Mesh(mesh);
+      }
+
+      // Make sure all element and boundary attributes are positive.
+      CheckAttributes();
+
+      // Merge periodic vertices
+      if (periodic)
+      {
+         // If the mesh is low-order, we need to populate ho_el_nodes before
+         // periodic vertices are identified in order to set the L2 nodes grid
+         // function.
+         if (mesh_order == 1)
+         {
+            ho_el_nodes[mesh.Dim].resize(mesh.NumOfElements);
+            for (int ie = 0; ie < mesh.NumOfElements; ++ie)
+            {
+               const Element *e = mesh.elements[ie];
+               const int nv = e->GetNVertices();
+               const int *v = e->GetVertices();
+               ho_el_nodes[mesh.Dim][ie].resize(nv);
+               const vector<int> &map = GetNodeMap(e->GetGeometryType(), 1);
+               for (int i = 0; i < nv; ++i)
+               {
+                  ho_el_nodes[mesh.Dim][ie][i] = v[map[i]];
+               }
+            }
+         }
+         SimplifyPeriodicLinks();
+         ReplacePeriodicVertices(mesh.elements);
+         ReplacePeriodicVertices(mesh.boundary);
+      }
+
+      // If the elements are high-order, keep a copy of the nodes before removing
+      // unused vertices.
+      Array<Vertex> ho_vertices;
+      if (mesh_order > 1 || periodic) { ho_vertices = mesh.vertices; }
+
+      AddPhysicalNames(mesh);
+      mesh.RemoveUnusedVertices();
+      mesh.FinalizeTopology();
+
+      // Now that the mesh topology has been fully created, set the high-order
+      // nodal information (if needed). For periodic meshes, we need to set the
+      // L2 grid function.
+      if (mesh_order > 1 || periodic)
+      {
+         // Gmsh uses uniform nodal points
+         const int bt = BasisType::ClosedUniform;
+         FiniteElementCollection *fec;
+         if (periodic) { fec = new L2_FECollection(mesh_order, mesh.Dim, bt); }
+         else { fec = new H1_FECollection(mesh_order, mesh.Dim, bt); }
+         FiniteElementSpace *fes = new FiniteElementSpace(
+            &mesh, fec, mesh.spaceDim, Ordering::byVDIM);
+         GridFunction *nodes_gf = new GridFunction(fes);
+         // The nodal grid function, owned by mesh, will own fec and fec
+         nodes_gf->MakeOwner(fec);
+         mesh.SetNodalGridFunction(nodes_gf, true);
+         Array<int> vdofs;
+         for (int e = 0; e < mesh.NumOfElements; ++e)
+         {
+            const FiniteElement *fe = fes->GetFE(e);
+            auto *nfe = dynamic_cast<const NodalFiniteElement*>(fe);
+            MFEM_ASSERT(nfe, "Invalid FE");
+            const Array<int> &lex = nfe->GetLexicographicOrdering();
+            fes->GetElementVDofs(e, vdofs);
+            const int n = vdofs.Size() / mesh.spaceDim;
+            for (int i = 0; i < n; ++i)
+            {
+               const int ii = lex.IsEmpty() ? i : lex[i];
+               Vertex v = ho_vertices[ho_el_nodes[mesh.Dim][e][i]];
+               for (int d = 0; d < mesh.spaceDim; ++d)
+               {
+                  (*nodes_gf)[vdofs[ii + d*n]] = v(d);
+               }
+            }
+         }
+         // Set curvature to use Gauss-Lobatto instead of uniform basis
+         mesh.SetCurvature(mesh_order, periodic, mesh.spaceDim, Ordering::byVDIM);
+      }
+   }
+};
+
+} // namespace gmsh
+
+void Mesh::ReadGmshMesh(istream &input)
+{
+   gmsh::GmshReader(input, *this);
+}
+
 } // namespace mfem

mesh/gmsh.hpp

@@ -1,55 +0,0 @@
-// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#ifndef MFEM_GMSH
-#define MFEM_GMSH
-
-namespace mfem
-{
-
-// Helpers for reading high order elements in Gmsh format
-
-/** @name Gmsh High-Order Vertex Mappings
-
-    These functions generate the mappings needed to translate the order of
-    Gmsh's high-order vertices into MFEM's L2 degree of freedom ordering. The
-    mapping is defined so that MFEM_DoF[i] = Gmsh_Vert[map[i]]. The @a map
-    array must already be allocated with the proper number of entries for the
-    element type at the given element @a order.
-*/
-///@{
-
-/// @brief Generate Gmsh vertex mapping for a Segment
-void GmshHOSegmentMapping(int order, int *map);
-
-/// @brief Generate Gmsh vertex mapping for a Triangle
-void GmshHOTriangleMapping(int order, int *map);
-
-/// @brief Generate Gmsh vertex mapping for a Quadrilateral
-void GmshHOQuadrilateralMapping(int order, int *map);
-
-/// @brief Generate Gmsh vertex mapping for a Tetrahedron
-void GmshHOTetrahedronMapping(int order, int *map);
-
-/// @brief Generate Gmsh vertex mapping for a Hexahedron
-void GmshHOHexahedronMapping(int order, int *map);
-
-/// @brief Generate Gmsh vertex mapping for a Wedge
-void GmshHOWedgeMapping(int order, int *map);
-
-/// @brief Generate Gmsh vertex mapping for a Pyramid
-void GmshHOPyramidMapping(int order, int *map);
-
-///@}
-
-} // namespace mfem
-
-#endif

mesh/mesh.cpp

@@ -5069,7 +5069,10 @@ void Mesh::Loader(std::istream &input, int generate_edges,
    }
    else if (mesh_type == "$MeshFormat") // Gmsh
    {
-      ReadGmshMesh(input, curved, read_gf);
+      ReadGmshMesh(input);
+      finalize_topo = false; // Gmsh mesh reader already finalizes the topology
+      curved = Nodes != nullptr;
+      read_gf = false;
    }
    else if
    ((mesh_type.size() > 2 &&
@@ -7033,7 +7036,7 @@ void Mesh::EnsureNodes()
    }
    else // First order H1 mesh
    {
-      SetCurvature(1, false, -1, Ordering::byVDIM);
+      SetCurvature(1, false, -1, Ordering::byNODES);//VDIM);
    }
 }
 
@@ -11332,6 +11335,8 @@ void Mesh::Swap(Mesh& other, bool non_geometry)
 
    mfem::Swap(attributes, other.attributes);
    mfem::Swap(bdr_attributes, other.bdr_attributes);
+   mfem::Swap(attribute_sets.attr_sets, other.attribute_sets.attr_sets);
+   mfem::Swap(bdr_attribute_sets.attr_sets, other.bdr_attribute_sets.attr_sets);
 
    mfem::Swap(geom_factors, other.geom_factors);
    mfem::Swap(face_geom_factors, other.face_geom_factors);

mesh/mesh.hpp

@@ -60,12 +60,15 @@ class CubitBlock;
 }
 #endif
 
+namespace gmsh { class GmshReader; }
+
 /// Mesh data type
 class Mesh
 {
    friend class NCMesh;
    friend class NURBSExtension;
    friend class NCNURBSExtension;
+   friend class gmsh::GmshReader;
 #ifdef MFEM_USE_MPI
    friend class ParMesh;
    friend class ParNCMesh;
@@ -362,7 +365,7 @@ protected:
    void ReadNURBSMesh(std::istream &input, int &curved, int &read_gf,
                       bool spacing=false, bool nc=false);
    void ReadInlineMesh(std::istream &input, bool generate_edges = false);
-   void ReadGmshMesh(std::istream &input, int &curved, int &read_gf);
+   void ReadGmshMesh(std::istream &input);
 
    /* Note NetCDF (optional library) is used for reading cubit files */
 #ifdef MFEM_USE_NETCDF

mesh/mesh_headers.hpp

@@ -33,6 +33,7 @@
 #include "nurbs.hpp"
 #include "wedge.hpp"
 #include "pyramid.hpp"
+#include "bb_grid_map.hpp"
 
 #ifdef MFEM_USE_MPI
 #include "pncmesh.hpp"

miniapps/gslib/findpts.cpp

@@ -45,6 +45,10 @@
 //    findpts -m ../../data/fichera-mixed.mesh -o 3 -mo 2
 //    findpts -m ../../data/inline-pyramid.mesh -o 1 -mo 1
 //    findpts -m ../../data/tinyzoo-3d.mesh -o 1 -mo 1
+// Surface meshes:
+//    findpts -m ../../data/ref-square.mesh -o 2 -mo 1 -random 1 -surf
+//    findpts -m ../../data/ref-cube.mesh -o 2 -mo 1 -random 1 -surf
+//    findpts -m ../../data/square-disc-p2.mesh -o 4 -mo 2 -random 1 -surf
 
 #include "mfem.hpp"
 #include "../common/mfem-common.hpp"
@@ -102,6 +106,9 @@ int main (int argc, char *argv[])
    int point_ordering    = 0;
    int gf_ordering       = 0;
    bool mesh_prefinement = false;
+   int randomization     = 0;
+   int npt               = 100;
+   bool surface          = false;
 
    // Parse command-line options.
    OptionsParser args(argc, argv);
@@ -135,6 +142,14 @@ int main (int argc, char *argv[])
    args.AddOption(&mesh_prefinement, "-mpr", "--mesh-p-refinement", "-no-mpr",
                   "--no-mesh-p-refinement",
                   "Do random p refinements to mesh Nodes.");
+   args.AddOption(&randomization, "-random", "--random",
+                  "0: generate points randomly in the bounding box of domain, "
+                  "1: generate points randomly inside each element in mesh.");
+   args.AddOption(&npt, "-npt", "--npt",
+                  "Number of points per element when -random 1 is used.");
+   args.AddOption(&surface, "-surf", "--surface", "-no-surf",
+                  "--no-surface",
+                  "Extract surface mesh from volume mesh.");
 
    args.Parse();
    if (!args.Good())
@@ -146,49 +161,72 @@ int main (int argc, char *argv[])
 
    func_order = std::min(order, 2);
 
-   // Initialize and refine the starting mesh.
-   Mesh mesh(mesh_file, 1, 1, false);
-   for (int lev = 0; lev < rs_levels; lev++) { mesh.UniformRefinement(); }
-   const int dim = mesh.Dimension();
+   // Initialize and optionally extract the surface mesh.
+   Mesh input_mesh(mesh_file, 1, 1, false);
+   Mesh *mesh = surface ? nullptr : &input_mesh;
+   if (surface)
+   {
+      MFEM_VERIFY(input_mesh.bdr_attributes.Size() > 0,
+                  "--surface requires a mesh with boundary attributes.");
+      mesh = new Mesh(SubMesh::CreateFromBoundary(input_mesh,
+                                                  input_mesh.bdr_attributes));
+   }
+
+   MFEM_VERIFY(!(surface && prefinement),
+               "Surface interpolation does not support variable-order "
+               "solution spaces; use -no-pr with --surface.");
+
+   for (int lev = 0; lev < rs_levels; lev++) { mesh->UniformRefinement(); }
+   const int dim = mesh->Dimension(),
+             sdim = mesh->SpaceDimension();
    cout << "Mesh curvature of the original mesh: ";
-   if (mesh.GetNodes()) { cout << mesh.GetNodes()->OwnFEC()->Name(); }
+   if (mesh->GetNodes()) { cout << mesh->GetNodes()->OwnFEC()->Name(); }
    else { cout << "(NONE)"; }
    cout << endl;
 
    // Mesh bounding box.
    Vector pos_min, pos_max;
    MFEM_VERIFY(mesh_poly_deg > 0, "The order of the mesh must be positive.");
-   mesh.GetBoundingBox(pos_min, pos_max, mesh_poly_deg);
-   if (hrefinement || prefinement || mesh_prefinement) { mesh.EnsureNCMesh(true); }
-   cout << "--- Generating equidistant point for:\n"
-        << "x in [" << pos_min(0) << ", " << pos_max(0) << "]\n"
-        << "y in [" << pos_min(1) << ", " << pos_max(1) << "]\n";
-   if (dim == 3)
+   mesh->GetBoundingBox(pos_min, pos_max, mesh_poly_deg);
+   if (hrefinement || prefinement || mesh_prefinement)
+   {
+      mesh->EnsureNCMesh(true);
+   }
+
+   cout << "--- Generating points for:\n"
+        << "x in [" << pos_min(0) << ", " << pos_max(0) << "]\n";
+   if (sdim >= 2)
+   {
+      cout << "y in [" << pos_min(1) << ", " << pos_max(1) << "]" << std::endl;
+   }
+   if (sdim == 3)
    {
       cout << "z in [" << pos_min(2) << ", " << pos_max(2) << "]\n";
    }
 
    // Random h-refinements to mesh
-   if (hrefinement) { mesh.RandomRefinement(0.5); }
+   if (hrefinement) { mesh->RandomRefinement(0.5); }
 
    // Curve the mesh based on the chosen polynomial degree.
    H1_FECollection fecm(mesh_poly_deg, dim);
-   FiniteElementSpace fespace(&mesh, &fecm, dim);
-   mesh.SetNodalFESpace(&fespace);
+   FiniteElementSpace fespace(mesh, &fecm, sdim);
+   mesh->SetNodalFESpace(&fespace);
    GridFunction Nodes(&fespace);
-   mesh.SetNodalGridFunction(&Nodes);
+   mesh->SetNodalGridFunction(&Nodes);
    cout << "Mesh curvature of the curved mesh: " << fecm.Name() << endl;
 
    if (mesh_prefinement)
    {
       Array<pRefinement> refs;
-      for (int e = 0; e < mesh.GetNE(); e++)
+      for (int e = 0; e < mesh->GetNE(); e++)
       {
          if ((double) rand() / RAND_MAX < 0.2)
          {
             refs.Append(pRefinement(e,1));
          }
       }
+      std::cout << refs.Size() << " elements will be p-refined for the mesh." <<
+                std::endl;
       fespace.PRefineAndUpdate(refs);
       Nodes.Update();
    }
@@ -210,28 +248,28 @@ int main (int argc, char *argv[])
    {
       fec = new RT_FECollection(order, dim);
       ncomp = 1;
-      vec_dim = dim;
+      vec_dim = sdim;
       cout << "H(div)-GridFunction\n";
    }
    else if (fieldtype == 3)
    {
       fec = new ND_FECollection(order, dim);
       ncomp = 1;
-      vec_dim = dim;
+      vec_dim = sdim;
       cout << "H(curl)-GridFunction\n";
    }
    else
    {
       MFEM_ABORT("Invalid field type.");
    }
-   FiniteElementSpace sc_fes(&mesh, fec, ncomp, gf_ordering);
+   FiniteElementSpace sc_fes(mesh, fec, ncomp, gf_ordering);
    GridFunction field_vals(&sc_fes);
 
    // Random p-refinements to the solution field
    if (prefinement)
    {
       Array<pRefinement> refs;
-      for (int e = 0; e < mesh.GetNE(); e++)
+      for (int e = 0; e < mesh->GetNE(); e++)
       {
          if ((double) rand() / RAND_MAX < 0.5)
          {
@@ -249,16 +287,16 @@ int main (int argc, char *argv[])
 
    if (mesh_prefinement && visualization)
    {
-      mesh.SetNodalGridFunction(mesh_nodes_pref);
+      mesh->SetNodalGridFunction(mesh_nodes_pref);
       VisualizeFESpacePolynomialOrder(fespace, "Mesh Polynomial Order", 400);
-      mesh.SetNodalGridFunction(&Nodes);
+      mesh->SetNodalGridFunction(&Nodes);
    }
 
    if (prefinement && visualization)
    {
-      mesh.SetNodalGridFunction(mesh_nodes_pref);
+      mesh->SetNodalGridFunction(mesh_nodes_pref);
       VisualizeFESpacePolynomialOrder(sc_fes, "Solution Polynomial Order", 800);
-      mesh.SetNodalGridFunction(&Nodes);
+      mesh->SetNodalGridFunction(&Nodes);
    }
 
    // Project the GridFunction using VectorFunctionCoefficient.
@@ -273,64 +311,81 @@ int main (int argc, char *argv[])
    // Display the mesh and the field through glvis.
    if (visualization)
    {
-      if (mesh_prefinement) { mesh.SetNodalGridFunction(mesh_nodes_pref); }
+      if (mesh_prefinement) { mesh->SetNodalGridFunction(mesh_nodes_pref); }
       socketstream vis1;
       common::VisualizeField(vis1, "localhost", 19916, *field_vals_pref,
                              "Solution",
                              0, 0, 400, 400, "RmjA*****");
-      if (mesh_prefinement) { mesh.SetNodalGridFunction(&Nodes); }
+      if (mesh_prefinement) { mesh->SetNodalGridFunction(&Nodes); }
    }
 
-   // Generate equidistant points in physical coordinates over the whole mesh.
-   // Note that some points might be outside, if the mesh is not a box. Note
-   // also that all tasks search the same points (not mandatory).
-   const int pts_cnt_1D = 25;
-   int pts_cnt = pow(pts_cnt_1D, dim);
-   Vector vxyz(pts_cnt * dim);
-   if (dim == 2)
+   // Generate random points in physical coordinates over the whole mesh.
+   // Note that some points might be outside if the mesh is not a box.
+   int pts_cnt = npt;
+   Vector vxyz;
+   int npt_face_per_elem = 4; // number of pts on faces when randomization != 0
+   int npt_total_face = 0;
+   if (randomization == 0)
    {
-      L2_QuadrilateralElement el(pts_cnt_1D - 1, BasisType::ClosedUniform);
-      const IntegrationRule &ir = el.GetNodes();
-      for (int i = 0; i < ir.GetNPoints(); i++)
+      vxyz.SetSize(pts_cnt * sdim);
+      vxyz.Randomize(1);
+
+      // Scale based on min/max dimensions
+      for (int i = 0; i < pts_cnt; i++)
       {
-         const IntegrationPoint &ip = ir.IntPoint(i);
-         if (point_ordering == Ordering::byNODES)
+         for (int d = 0; d < sdim; d++)
          {
-            vxyz(i)           = pos_min(0) + ip.x * (pos_max(0)-pos_min(0));
-            vxyz(pts_cnt + i) = pos_min(1) + ip.y * (pos_max(1)-pos_min(1));
-         }
-         else
-         {
-            vxyz(i*dim + 0) = pos_min(0) + ip.x * (pos_max(0)-pos_min(0));
-            vxyz(i*dim + 1) = pos_min(1) + ip.y * (pos_max(1)-pos_min(1));
+            if (point_ordering == Ordering::byNODES)
+            {
+               vxyz(i + d*pts_cnt) =
+                  pos_min(d) + vxyz(i + d*pts_cnt) * (pos_max(d) - pos_min(d));
+            }
+            else
+            {
+               vxyz(i*sdim + d) =
+                  pos_min(d) + vxyz(i*sdim + d) * (pos_max(d) - pos_min(d));
+            }
          }
       }
    }
-   else
+   else // randomization == 1
    {
-      L2_HexahedronElement el(pts_cnt_1D - 1, BasisType::ClosedUniform);
-      const IntegrationRule &ir = el.GetNodes();
-      for (int i = 0; i < ir.GetNPoints(); i++)
+      pts_cnt = npt * mesh->GetNE();
+      vxyz.SetSize(pts_cnt * sdim);
+      for (int i = 0; i < mesh->GetNE(); i++)
       {
-         const IntegrationPoint &ip = ir.IntPoint(i);
-         if (point_ordering == Ordering::byNODES)
+         ElementTransformation *transf = mesh->GetElementTransformation(i);
+         const Geometry::Type geom = mesh->GetElementGeometry(i);
+         for (int j = 0; j < npt; j++)
          {
-            vxyz(i)             = pos_min(0) + ip.x * (pos_max(0)-pos_min(0));
-            vxyz(pts_cnt + i)   = pos_min(1) + ip.y * (pos_max(1)-pos_min(1));
-            vxyz(2*pts_cnt + i) = pos_min(2) + ip.z * (pos_max(2)-pos_min(2));
-         }
-         else
-         {
-            vxyz(i*dim + 0) = pos_min(0) + ip.x * (pos_max(0)-pos_min(0));
-            vxyz(i*dim + 1) = pos_min(1) + ip.y * (pos_max(1)-pos_min(1));
-            vxyz(i*dim + 2) = pos_min(2) + ip.z * (pos_max(2)-pos_min(2));
+            IntegrationPoint ip;
+            Geometry::GetRandomPoint(geom, ip);
+            if (j < npt_face_per_elem)
+            {
+               ip.x = 0.0; // force point to be on the face
+               npt_total_face++;
+            }
+            Vector pos_i(sdim);
+            transf->Transform(ip, pos_i);
+            for (int d = 0; d < sdim; d++)
+            {
+               if (point_ordering == Ordering::byNODES)
+               {
+                  vxyz(j + npt*i + d*pts_cnt) = pos_i(d);
+               }
+               else
+               {
+                  vxyz((j + npt*i)*sdim + d) = pos_i(d);
+               }
+            }
          }
       }
    }
 
    // Find and Interpolate FE function values on the desired points.
    Vector interp_vals(pts_cnt*vec_dim);
-   FindPointsGSLIB finder(mesh);
+   FindPointsGSLIB finder(*mesh);
+   finder.SetDistanceToleranceForPointsFoundOnBoundary(10);
    finder.SetL2AvgType(FindPointsGSLIB::NONE);
    finder.Interpolate(vxyz, field_vals, interp_vals, point_ordering);
    Array<unsigned int> code_out    = finder.GetCode();
@@ -338,7 +393,7 @@ int main (int argc, char *argv[])
 
    int face_pts = 0, not_found = 0, found = 0;
    double error = 0.0, max_err = 0.0, max_dist = 0.0;
-   Vector pos(dim);
+   Vector pos(sdim);
    for (int j = 0; j < vec_dim; j++)
    {
       for (int i = 0; i < pts_cnt; i++)
@@ -346,11 +401,11 @@ int main (int argc, char *argv[])
          if (code_out[i] < 2)
          {
             if (j == 0) { found++; }
-            for (int d = 0; d < dim; d++)
+            for (int d = 0; d < sdim; d++)
             {
                pos(d) = point_ordering == Ordering::byNODES ?
                         vxyz(d*pts_cnt + i) :
-                        vxyz(i*dim + d);
+                        vxyz(i*sdim + d);
             }
             Vector exact_val(vec_dim);
             F_exact(pos, exact_val);
@@ -370,10 +425,19 @@ int main (int argc, char *argv[])
         << "\nFound points:        " << found
         << "\nMax interp error:    " << max_err
         << "\nMax dist (of found): " << max_dist
-        << "\nPoints not found:    " << not_found
-        << "\nPoints on faces:     " << face_pts << endl;
+        << "\nPoints not found:    " << not_found;
+   if (randomization == 1)
+   {
+      cout << "\nPoints on faces:     " << face_pts << " out of "
+           << npt_total_face << endl;
+   }
+   else
+   {
+      cout << "\nPoints on faces:     " << face_pts << endl;
+   }
 
    delete fec;
+   if (surface) { delete mesh; }
 
    return 0;
 }

miniapps/gslib/pfindpts.cpp

@@ -49,7 +49,10 @@
 //    mpirun -np 2 pfindpts -m ../../data/inline-quad.mesh -o 3 -mo 2 -random 1 -d debug
 //    mpirun -np 2 pfindpts -m ../../data/amr-quad.mesh -rs 1 -o 4 -mo 2 -random 1 -npt 100 -d debug
 //    mpirun -np 2 pfindpts -m ../../data/inline-hex.mesh -o 3 -mo 2 -random 1 -d debug
-
+// Surface meshes:
+//    mpirun -np 4 pfindpts -m ../../data/square-disc-p2.mesh -o 4 -mo 2 -vis -random 1 -surf
+//    mpirun -np 4 pfindpts -m ../../data/star-q3.mesh -o 6 -mo 3 -vis -random 1 -surf
+//    mpirun -np 4 pfindpts -m ../../data/fichera-q2.mesh -o 6 -mo 3 -vis -random 1 -surf
 
 #include "mfem.hpp"
 #include "../common/mfem-common.hpp"
@@ -98,7 +101,7 @@ int main (int argc, char *argv[])
    const char *devopt    = "cpu";
    int randomization     = 0;
    int npt               = 100; //points per proc
-   int visport           = 19916;
+   bool surface          = false;
 
    // Parse command-line options.
    OptionsParser args(argc, argv);
@@ -139,7 +142,9 @@ int main (int argc, char *argv[])
                   "1: generate points randomly inside each element in mesh.");
    args.AddOption(&npt, "-npt", "--npt",
                   "# points / rank initialized on entire mesh (random = 0) or every element (random = 1).");
-   args.AddOption(&visport, "-p", "--send-port", "Socket for GLVis.");
+   args.AddOption(&surface, "-surf", "--surface", "-no-surf",
+                  "--no-surface",
+                  "Extract surface mesh from volume mesh.");
 
    args.Parse();
    if (!args.Good())
@@ -155,17 +160,19 @@ int main (int argc, char *argv[])
 
    func_order = std::min(order, 2);
 
-   // Initialize and refine the starting mesh.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1, false);
-   for (int lev = 0; lev < rs_levels; lev++) { mesh->UniformRefinement(); }
-   const int dim = mesh->Dimension();
-
-   if (mesh->GetNumGeometries(dim) != 1 ||
-       (mesh->GetElementType(0)!=Element::QUADRILATERAL &&
-        mesh->GetElementType(0) != Element::HEXAHEDRON))
+   // Initialize and extract surface mesh if requested.
+   Mesh *input_mesh = new Mesh(mesh_file, 1, 1, false);
+   Mesh *mesh = surface ? nullptr : input_mesh;
+   if (surface)
    {
-      randomization = 0;
+      MFEM_VERIFY(input_mesh->bdr_attributes.Size() > 0,
+                  "--surface requires a mesh with boundary attributes.");
+      mesh = new Mesh(SubMesh::CreateFromBoundary(*input_mesh,
+                                                  input_mesh->bdr_attributes));
    }
+   for (int lev = 0; lev < rs_levels; lev++) { mesh->UniformRefinement(); }
+   const int dim = mesh->Dimension(),
+             sdim = mesh->SpaceDimension();
 
    if (myid == 0)
    {
@@ -182,9 +189,12 @@ int main (int argc, char *argv[])
    if (myid == 0)
    {
       cout << "--- Generating points for:\n"
-           << "x in [" << pos_min(0) << ", " << pos_max(0) << "]\n"
-           << "y in [" << pos_min(1) << ", " << pos_max(1) << "]" << std::endl;
-      if (dim == 3)
+           << "x in [" << pos_min(0) << ", " << pos_max(0) << "]\n";
+      if (sdim >= 2)
+      {
+         cout << "y in [" << pos_min(1) << ", " << pos_max(1) << "]" << std::endl;
+      }
+      if (sdim == 3)
       {
          cout << "z in [" << pos_min(2) << ", " << pos_max(2) << "]" << std::endl;
       }
@@ -192,8 +202,13 @@ int main (int argc, char *argv[])
 
    // Distribute the mesh.
    if (hrefinement) { mesh->EnsureNCMesh(); }
-   ParMesh pmesh(MPI_COMM_WORLD, *mesh);
-   if (randomization == 0) { delete mesh; }
+   ParMesh pmesh(MPI_COMM_WORLD, *mesh, nullptr,
+                 (dim == 1 && sdim == 3) ? 0 : 1);
+   if (randomization == 0)
+   {
+      delete mesh;
+      if (surface) { delete input_mesh; }
+   }
    else
    {
       // we will need mesh nodal space later
@@ -206,7 +221,7 @@ int main (int argc, char *argv[])
 
    // Curve the mesh based on the chosen polynomial degree.
    H1_FECollection fecm(mesh_poly_deg, dim);
-   ParFiniteElementSpace pfespace(&pmesh, &fecm, dim);
+   ParFiniteElementSpace pfespace(&pmesh, &fecm, sdim);
    pmesh.SetNodalFESpace(&pfespace);
    ParGridFunction x(&pfespace);
    pmesh.SetNodalGridFunction(&x);
@@ -234,14 +249,14 @@ int main (int argc, char *argv[])
    {
       fec = new RT_FECollection(order, dim);
       ncomp = 1;
-      vec_dim = dim;
+      vec_dim = sdim;
       if (myid == 0) { cout << "H(div)-GridFunction" << std::endl; }
    }
    else if (fieldtype == 3)
    {
       fec = new ND_FECollection(order, dim);
       ncomp = 1;
-      vec_dim = dim;
+      vec_dim = sdim;
       if (myid == 0) { cout << "H(curl)-GridFunction" << std::endl; }
    }
    else
@@ -260,13 +275,13 @@ int main (int argc, char *argv[])
    {
       char vishost[] = "localhost";
       socketstream sout;
-      sout.open(vishost, visport);
+      sout.open(vishost, 19916);
       if (!sout)
       {
          if (myid == 0)
          {
             cout << "Unable to connect to GLVis server at "
-                 << vishost << ':' << visport << endl;
+                 << vishost << ':' << 19916 << endl;
          }
       }
       else
@@ -274,8 +289,11 @@ int main (int argc, char *argv[])
          sout << "parallel " << num_procs << " " << myid << "\n";
          sout.precision(8);
          sout << "solution\n" << pmesh << field_vals;
-         if (dim == 2) { sout << "keys RmjA*****\n"; }
-         if (dim == 3) { sout << "keys mA\n"; }
+         if (sdim == 2) { sout << "keys RmjA*****\n"; }
+         if (sdim == 3) { sout << "keys mA\n"; }
+         sout << "window_title 'Solution'\n"
+              << "window_geometry "
+              << 0 << " " << 0 << " " << 400 << " " << 400 << "\n";
          sout << flush;
       }
    }
@@ -285,16 +303,17 @@ int main (int argc, char *argv[])
    int pts_cnt = npt;
    Vector vxyz;
    vxyz.UseDevice(!cpu_mode);
-   int npt_face_per_elem = 4; // number of pts on el faces for randomization != 0
+   int npt_face_per_elem = 4; // number of pts on faces when randomization != 0
+   int npt_total_face = 0;
    if (randomization == 0)
    {
-      vxyz.SetSize(pts_cnt * dim);
+      vxyz.SetSize(pts_cnt * sdim);
       vxyz.Randomize(myid+1);
 
       // Scale based on min/max dimensions
       for (int i = 0; i < pts_cnt; i++)
       {
-         for (int d = 0; d < dim; d++)
+         for (int d = 0; d < sdim; d++)
          {
             if (point_ordering == Ordering::byNODES)
             {
@@ -303,8 +322,8 @@ int main (int argc, char *argv[])
             }
             else
             {
-               vxyz(i*dim + d) =
-                  pos_min(d) + vxyz(i*dim + d) * (pos_max(d) - pos_min(d));
+               vxyz(i*sdim + d) =
+                  pos_min(d) + vxyz(i*sdim + d) * (pos_max(d) - pos_min(d));
             }
          }
       }
@@ -312,30 +331,24 @@ int main (int argc, char *argv[])
    else // randomization == 1
    {
       pts_cnt = npt*nelemglob;
-      vxyz.SetSize(pts_cnt * dim);
+      vxyz.SetSize(pts_cnt * sdim);
       for (int i=0; i<mesh->GetNE(); i++)
       {
          const FiniteElementSpace *s_fespace = mesh->GetNodalFESpace();
          ElementTransformation *transf = s_fespace->GetElementTransformation(i);
-
-         Vector pos_ref1(npt*dim);
-         pos_ref1.Randomize((myid+1)*17.0);
+         const Geometry::Type geom = mesh->GetElementGeometry(i);
          for (int j=0; j<npt; j++)
          {
             IntegrationPoint ip;
-            ip.x = pos_ref1(j*dim + 0);
-            ip.y = pos_ref1(j*dim + 1);
-            if (dim == 3)
-            {
-               ip.z = pos_ref1(j*dim + 2);
-            }
+            Geometry::GetRandomPoint(geom, ip);
             if (j < npt_face_per_elem)
             {
                ip.x = 0.0; // force point to be on the face
+               npt_total_face++;
             }
-            Vector pos_i(dim);
+            Vector pos_i(sdim);
             transf->Transform(ip, pos_i);
-            for (int d=0; d<dim; d++)
+            for (int d=0; d<sdim; d++)
             {
                if (point_ordering == Ordering::byNODES)
                {
@@ -343,18 +356,20 @@ int main (int argc, char *argv[])
                }
                else
                {
-                  vxyz((j + npt*i)*dim + d) = pos_i(d);
+                  vxyz((j + npt*i)*sdim + d) = pos_i(d);
                }
             }
          }
       }
    }
-
    if ( (myid != 0) && (search_on_rank_0) )
    {
       pts_cnt = 0;
       vxyz.Destroy();
+      npt_total_face = 0;
    }
+   MPI_Allreduce(MPI_IN_PLACE, &npt_total_face, 1, MPI_INT, MPI_SUM,
+                 pmesh.GetComm());
 
    // Find and Interpolate FE function values on the desired points.
    Vector interp_vals(pts_cnt*vec_dim);
@@ -375,28 +390,31 @@ int main (int argc, char *argv[])
    Array<unsigned int> code_out    = finder.GetCode();
    Array<unsigned int> task_id_out = finder.GetProc();
    Vector dist_p_out = finder.GetDist();
-   Vector rst = finder.GetReferencePosition();
+
+   auto h_code_out = code_out.HostRead();
+   auto h_task_id_out = task_id_out.HostRead();
+   auto h_dist_p_out = dist_p_out.HostRead();
 
    int face_pts = 0, not_found = 0, found_loc = 0, found_away = 0;
    double error = 0.0, max_error = 0.0, max_dist = 0.0;
 
-   Vector pos(dim);
+   Vector pos(sdim);
    for (int j = 0; j < vec_dim; j++)
    {
       for (int i = 0; i < pts_cnt; i++)
       {
          if (j == 0)
          {
-            (task_id_out[i] == (unsigned)myid) ? found_loc++ : found_away++;
+            (h_task_id_out[i] == (unsigned)myid) ? found_loc++ : found_away++;
          }
 
-         if (code_out[i] < 2)
+         if (h_code_out[i] < 2)
          {
-            for (int d = 0; d < dim; d++)
+            for (int d = 0; d < sdim; d++)
             {
                pos(d) = point_ordering == Ordering::byNODES ?
                         vxyz(d*pts_cnt + i) :
-                        vxyz(i*dim + d);
+                        vxyz(i*sdim + d);
             }
             Vector exact_val(vec_dim);
             F_exact(pos, exact_val);
@@ -404,8 +422,8 @@ int main (int argc, char *argv[])
                     fabs(exact_val(j) - interp_vals[i + j*pts_cnt]) :
                     fabs(exact_val(j) - interp_vals[i*vec_dim + j]);
             max_error  = std::max(max_error, error);
-            max_dist = std::max(max_dist, dist_p_out(i));
-            if (code_out[i] == 1 && j == 0) { face_pts++; }
+            max_dist = std::max(max_dist, h_dist_p_out[i]);
+            if (h_code_out[i] == 1 && j == 0) { face_pts++; }
          }
          else { if (j == 0) { not_found++; } }
       }
@@ -435,14 +453,20 @@ int main (int argc, char *argv[])
            << "\nFound locally on ranks:  " << found_loc
            << "\nFound on other tasks: " << found_away
            << "\nPoints not found:     " << not_found
-           << "\nPoints on faces:      " << face_pts
+           << "\nPoints on faces:      " << face_pts << " out of "
+           << npt_total_face
            << "\nMax interp error:     " << max_error
            << "\nMax dist (of found):  " << max_dist
            << endl;
    }
 
    delete fec;
-   if (randomization != 0) { delete mesh; }
+
+   if (randomization != 0)
+   {
+      delete mesh;
+      if (surface) { delete input_mesh; }
+   }
 
    return 0;
 }

miniapps/hooke/hooke.cpp

@@ -62,6 +62,7 @@ int main(int argc, char *argv[])
    Mpi::Init(argc, argv);
    int num_procs = Mpi::WorldSize();
    int myid = Mpi::WorldRank();
+   Hypre::Init();
 
    int order = 1;
    const char *device_config = "cpu";

miniapps/meshing/CMakeLists.txt

@@ -19,6 +19,7 @@ set(MESH_FILES
   square01.mesh
   square01-tri.mesh
   stretched2D.mesh
+  stretched3D.mesh
 )
 
 # Add a target to copy the mesh files from the source directory; used by sample

miniapps/meshing/fit-node-position.cpp

@@ -36,6 +36,7 @@ int main (int argc, char *argv[])
    // Initialize MPI.
    Mpi::Init();
    int myid = Mpi::WorldRank();
+   Hypre::Init();
 
    const char *mesh_file = "square01.mesh";
    int rs_levels     = 2;

miniapps/meshing/makefile

@@ -58,7 +58,7 @@ lib-common:
 # building out-of-source:
 ifneq ($(SRC),)
 MESH_FILES = amr-quad-q2.mesh blade.mesh cube.mesh cube-tet.mesh icf.mesh\
-jagged.mesh square01.mesh square01-tri.mesh stretched2D.mesh
+jagged.mesh square01.mesh square01-tri.mesh stretched2D.mesh stretched3D.mesh
 $(MESH_FILES): %: $(SRC)%
 	ln -sf $(<) .
 mesh-optimizer pmesh-optimizer pmesh-fitting fit-node-position: | $(MESH_FILES)

miniapps/meshing/mesh-optimizer.cpp

@@ -73,7 +73,8 @@
 //   * mesh-optimizer -m ../../../data/periodic/per-amr-square.mesh -o 2 -mid 94 -tid 5 -ni 50 -qo 4 -nor -pa
 //
 //   Adaptive limiting:
-//     mesh-optimizer -m stretched2D.mesh -o 2 -mid 2 -tid 1 -ni 50 -qo 5 -nor -vl 1 -alc 0.5
+//     mesh-optimizer -m stretched2D.mesh -rs 1 -o 2 -mid 2 -tid 1 -ni 50 -qo 5 -nor -vl 1 -alc 1.0
+//     mesh-optimizer -m stretched3D.mesh -rs 2 -o 2 -mid 302 -tid 1 -ni 50 -qo 5 -nor -vl 1 -alc 2.0 -pa
 //   Adaptive limiting through the L-BFGS solver:
 //     mesh-optimizer -m stretched2D.mesh -o 2 -mid 2 -tid 1 -ni 400 -qo 5 -nor -vl 1 -alc 0.5 -st 1 -rtol 1e-8
 //
@@ -876,8 +877,6 @@ int main(int argc, char *argv[])
    AdaptivityEvaluator *adapt_lim_eval = NULL;
    if (adapt_lim_const > 0.0)
    {
-      MFEM_VERIFY(pa == false, "PA is not implemented for adaptive limiting");
-
       FunctionCoefficient adapt_lim_gf0_coeff(adapt_lim_fun);
       adapt_lim_gf0.ProjectCoefficient(adapt_lim_gf0_coeff);
 
@@ -893,12 +892,12 @@ int main(int argc, char *argv[])
       else { MFEM_ABORT("Bad interpolation option."); }
 
       tmop_integ->EnableAdaptiveLimiting(adapt_lim_gf0, adapt_lim_coeff,
-                                         *adapt_lim_eval);
+                                         *adapt_lim_eval, 1.0);
       if (visualization)
       {
          socketstream vis1;
-         common::VisualizeField(vis1, "localhost", 19916, adapt_lim_gf0, "Zeta 0",
-                                300, 600, 300, 300);
+         common::VisualizeField(vis1, "localhost", 19916, adapt_lim_gf0,
+                                "Zeta 0 - initial mesh", 300, 600, 300, 300);
       }
    }
 
@@ -1223,8 +1222,8 @@ int main(int argc, char *argv[])
    if (adapt_lim_const > 0.0 && visualization)
    {
       socketstream vis0;
-      common::VisualizeField(vis0, "localhost", 19916, adapt_lim_gf0, "Xi 0",
-                             600, 600, 300, 300);
+      common::VisualizeField(vis0, "localhost", 19916, adapt_lim_gf0,
+                             "Zeta 0 - final mesh", 600, 600, 300, 300);
    }
 
    // Visualize the mesh displacement.

miniapps/meshing/mesh-optimizer.hpp

@@ -436,11 +436,20 @@ real_t weight_fun(const Vector &x)
 // Used for the adaptive limiting examples.
 real_t adapt_lim_fun(const Vector &x)
 {
-   const real_t xc = x(0) - 0.1, yc = x(1) - 0.2;
-   const real_t r = sqrt(xc*xc + yc*yc);
-   real_t r1 = 0.45; real_t r2 = 0.55; real_t sf=30.0;
-   real_t val = 0.5*(1+std::tanh(sf*(r-r1))) - 0.5*(1+std::tanh(sf*(r-r2)));
+   // Bump between these rad values, with sf sharpness.
+   real_t r1 = 0.45, r2 = 0.55, sf=30.0, r;
+   if (x.Size() == 2)
+   {
+      const real_t xc = x(0) - 0.1, yc = x(1) - 0.2;
+      r = sqrt(xc*xc + yc*yc);
+   }
+   else
+   {
+      const real_t xc = x(0) - 0.9, yc = x(1) - 0.2, zc = x(2) - 0.0;
+      r = sqrt(xc*xc + yc*yc + zc*zc);
+   }
 
+   real_t val = 0.5*(1+std::tanh(sf*(r-r1))) - 0.5*(1+std::tanh(sf*(r-r2)));
    val = std::max((real_t) 0.,val);
    val = std::min((real_t) 1.,val);
    return val;

miniapps/meshing/pmesh-optimizer.cpp

@@ -75,9 +75,10 @@
 //   * mpirun -np 4 pmesh-optimizer -m ../../../data/periodic/per-amr-square.mesh -o 2 -mid 94 -tid 5 -ni 50 -qo 4 -nor -pa
 //
 //   Adaptive limiting:
-//     mpirun -np 4 pmesh-optimizer -m stretched2D.mesh -o 2 -mid 2 -tid 1 -ni 50 -qo 5 -nor -vl 1 -alc 0.5
+//     mpirun -np 4 pmesh-optimizer -m stretched2D.mesh -rs 1 -o 2 -mid 2 -tid 1 -ni 50 -qo 5 -nor -vl 1 -alc 1.0
+//     mpirun -np 8 pmesh-optimizer -m stretched3D.mesh -rs 2 -o 2 -mid 302 -tid 1 -ni 50 -qo 5 -nor -vl 1 -alc 2.0 -pa
 //   Adaptive limiting through the L-BFGS solver:
-//     mpirun -np 4 pmesh-optimizer -m stretched2D.mesh -o 2 -mid 2 -tid 1 -ni 400 -qo 5 -nor -vl 1 -alc 0.5 -st 1 -rtol 1e-8
+//     mpirun -np 4 pmesh-optimizer -m stretched2D.mesh -o 2 -mid 2 -tid 1 -ni 400 -qo 5 -nor -vl 1 -alc 1.0 -st 1 -rtol 1e-8
 //
 //   Blade shape:
 //     mpirun -np 4 pmesh-optimizer -m blade.mesh -o 4 -mid 2 -tid 1 -ni 30 -ls 3 -art 1 -bnd -qt 1 -qo 8
@@ -913,8 +914,6 @@ int main (int argc, char *argv[])
    AdaptivityEvaluator *adapt_lim_eval = NULL;
    if (adapt_lim_const > 0.0)
    {
-      MFEM_VERIFY(pa == false, "PA is not implemented for adaptive limiting");
-
       FunctionCoefficient adapt_lim_gf0_coeff(adapt_lim_fun);
       adapt_lim_gf0.ProjectCoefficient(adapt_lim_gf0_coeff);
 
@@ -930,12 +929,12 @@ int main (int argc, char *argv[])
       else { MFEM_ABORT("Bad interpolation option."); }
 
       tmop_integ->EnableAdaptiveLimiting(adapt_lim_gf0, adapt_lim_coeff,
-                                         *adapt_lim_eval);
+                                         *adapt_lim_eval, 1.0);
       if (visualization)
       {
          socketstream vis1;
-         common::VisualizeField(vis1, "localhost", 19916, adapt_lim_gf0, "Zeta 0",
-                                300, 600, 300, 300);
+         common::VisualizeField(vis1, "localhost", 19916, adapt_lim_gf0,
+                                "Zeta 0 - initial mesh", 300, 600, 300, 300);
       }
    }
 
@@ -1275,8 +1274,8 @@ int main (int argc, char *argv[])
    if (adapt_lim_const > 0.0 && visualization)
    {
       socketstream vis0;
-      common::VisualizeField(vis0, "localhost", 19916, adapt_lim_gf0, "Xi 0",
-                             600, 600, 300, 300);
+      common::VisualizeField(vis0, "localhost", 19916, adapt_lim_gf0,
+                             "Zeta 0 - final mesh", 600, 600, 300, 300);
    }
 
    // Visualize the mesh displacement.

miniapps/meshing/stretched3D.mesh

@@ -0,0 +1,568 @@
+MFEM mesh v1.0
+
+#
+# MFEM Geometry Types (see fem/geom.hpp):
+#
+# POINT       = 0
+# SEGMENT     = 1
+# TRIANGLE    = 2
+# SQUARE      = 3
+# TETRAHEDRON = 4
+# CUBE        = 5
+# PRISM       = 6
+# PYRAMID     = 7
+#
+
+dimension
+3
+
+elements
+64
+1 5 0 27 81 30 35 82 117 85
+1 5 27 1 28 81 82 36 83 117
+1 5 81 28 4 29 117 83 37 84
+1 5 30 81 29 3 85 117 84 38
+1 5 35 82 117 85 9 31 86 34
+1 5 82 36 83 117 31 10 32 86
+1 5 117 83 37 84 86 32 13 33
+1 5 85 117 84 38 34 86 33 12
+1 5 3 29 87 41 38 84 118 90
+1 5 29 4 39 87 84 37 88 118
+1 5 87 39 7 40 118 88 45 89
+1 5 41 87 40 6 90 118 89 46
+1 5 38 84 118 90 12 33 91 44
+1 5 84 37 88 118 33 13 42 91
+1 5 118 88 45 89 91 42 16 43
+1 5 90 118 89 46 44 91 43 15
+1 5 12 33 91 44 51 92 119 95
+1 5 33 13 42 91 92 52 93 119
+1 5 91 42 16 43 119 93 53 94
+1 5 44 91 43 15 95 119 94 54
+1 5 51 92 119 95 21 47 96 50
+1 5 92 52 93 119 47 22 48 96
+1 5 119 93 53 94 96 48 25 49
+1 5 95 119 94 54 50 96 49 24
+1 5 9 31 86 34 58 97 120 99
+1 5 31 10 32 86 97 59 98 120
+1 5 86 32 13 33 120 98 52 92
+1 5 34 86 33 12 99 120 92 51
+1 5 58 97 120 99 18 55 100 57
+1 5 97 59 98 120 55 19 56 100
+1 5 120 98 52 92 100 56 22 47
+1 5 99 120 92 51 57 100 47 21
+1 5 10 60 101 32 59 102 121 98
+1 5 60 11 61 101 102 66 103 121
+1 5 101 61 14 62 121 103 67 104
+1 5 32 101 62 13 98 121 104 52
+1 5 59 102 121 98 19 63 105 56
+1 5 102 66 103 121 63 20 64 105
+1 5 121 103 67 104 105 64 23 65
+1 5 98 121 104 52 56 105 65 22
+1 5 13 62 106 42 52 104 122 93
+1 5 62 14 68 106 104 67 107 122
+1 5 106 68 17 69 122 107 72 108
+1 5 42 106 69 16 93 122 108 53
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tests/unit/CMakeLists.txt

@@ -77,6 +77,7 @@ set(UNIT_TESTS_SRCS
   mesh/mesh_test_utils.cpp
   mesh/test_exodus_reader.cpp
   mesh/test_mfem_mesh_reader.cpp
+  mesh/test_bb_grid_map.cpp
   mesh/test_exodus_writer.cpp
   mesh/test_face_orientations.cpp
   mesh/test_fms.cpp

tests/unit/mesh/test_bb_grid_map.cpp

@@ -0,0 +1,164 @@
+// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "mfem.hpp"
+#include "unit_tests.hpp"
+
+using namespace mfem;
+
+TEST_CASE("BBoxTensorGridMap nD", "[BBoxTensorGridMap]")
+{
+   // Create a Cartesian mesh on [0,1]^D.
+   int dim  = GENERATE(1, 2, 3);
+   CAPTURE(dim);
+   Mesh mesh;
+   if (dim == 1)
+   {
+      mesh = Mesh::MakeCartesian1D(2);
+   }
+   else if (dim == 2)
+   {
+      mesh = Mesh::MakeCartesian2D(2, 2, Element::QUADRILATERAL);
+   }
+   else if (dim == 3)
+   {
+      mesh = Mesh::MakeCartesian3D(2, 2, 2, Element::HEXAHEDRON);
+   }
+
+   // Create map with a 4^dim tensor grid.
+   int nx = 4;
+   BBoxTensorGridMap map(mesh, nx);
+
+   // Test each element's center
+   Vector center(dim);
+   for (int e = 0; e < mesh.GetNE(); e++)
+   {
+      mesh.GetElementCenter(e, center);
+      Array<int> elems = map.MapPointToElements(center);
+      REQUIRE(elems.Size() > 0);
+      REQUIRE(elems.Find(e) >= 0);
+   }
+
+   // Test point outside
+   Vector pt(dim);
+   pt = 0.0;
+   pt(0) = 1.5;
+   Array<int> elems = map.MapPointToElements(pt);
+   REQUIRE(elems.Size() == 0);
+}
+
+TEST_CASE("BBoxTensorGridMap Boundary", "[BBoxTensorGridMap]")
+{
+   // Create a 1x1 quad mesh on [0,1]x[0,1]
+   Mesh mesh = Mesh::MakeCartesian2D(2, 2, Element::QUADRILATERAL);
+
+   // Create map with 2x2 grid
+   int nx = 2;
+   BBoxTensorGridMap map(mesh, nx);
+
+   // Point exactly on the boundary of all 4 tensor grid cells
+   Vector pt(2);
+   pt(0) = 0.5; pt(1) = 0.5;
+   int grid_cell = map.GetGridCellFromPoint(pt);
+   REQUIRE(grid_cell == 3); // cell index should be 3 (top-right)
+
+   // This should include mesh element 2 (top-right) in the candidate list.
+   Array<int> elems = map.MapPointToElements(pt);
+   REQUIRE(elems.Size() > 0);
+   REQUIRE(elems.Find(2) >= 0);
+}
+
+TEST_CASE("BBoxTensorGridMap Empty", "[BBoxTensorGridMap]")
+{
+   int dim = GENERATE(1, 2, 3);
+   bool by_max_size = GENERATE(false, true);
+   CAPTURE(dim);
+   CAPTURE(by_max_size);
+
+   Vector elmin, elmax;
+   Array<int> nx(dim);
+   nx = 4;
+   const int n = 4;
+
+   BBoxTensorGridMap map_array(elmin, elmax, 0, dim, nx, by_max_size);
+   BBoxTensorGridMap map_scalar(elmin, elmax, 0, dim, n, by_max_size);
+
+   Vector pt(dim);
+   pt = 0.5;
+   Array<int> elems = map_array.MapPointToElements(pt);
+   REQUIRE(elems.Size() == 0);
+
+   elems = map_scalar.MapPointToElements(pt);
+   REQUIRE(elems.Size() == 0);
+}
+
+#if defined(MFEM_USE_MPI) && defined(MFEM_USE_GSLIB)
+TEST_CASE("GlobalBBoxTensorGridMap Parallel",
+          "[GlobalBBoxTensorGridMap][Parallel]")
+{
+   int num_procs;
+   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
+   int myid;
+   MPI_Comm_rank(MPI_COMM_WORLD, &myid);
+
+   // Create a mesh on [0,1]^D
+   int dim  = GENERATE(2, 3);
+   CAPTURE(dim);
+   Mesh mesh;
+   if (dim == 2)
+   {
+      mesh = Mesh::MakeCartesian2D(4, 4, Element::QUADRILATERAL);
+   }
+   else if (dim == 3)
+   {
+      mesh = Mesh::MakeCartesian3D(4, 4, 4, Element::HEXAHEDRON);
+   }
+
+   int nel = mesh.GetNE();
+   Array<int> partitioning(mesh.GetNE());
+   for (int e = 0; e < mesh.GetNE(); e++)
+   {
+      partitioning[e] = e % num_procs;
+   }
+   ParMesh pmesh(MPI_COMM_WORLD, mesh, partitioning.GetData());
+
+   // Setup a list of points to find - center of each element, plus one point
+   // outside the global bounding box.
+   Vector centers((nel + 1)*dim);
+   for (int e = 0; e < nel; e++)
+   {
+      Vector center_el(centers.GetData() + e*dim, dim);
+      mesh.GetElementCenter(e, center_el);
+   }
+   for (int d = 0; d < dim; d++)
+   {
+      centers(nel*dim + d) = 2.0;
+   }
+
+   // Create map with 4x4x4 global grid
+   int nx = 4;
+   GlobalBBoxTensorGridMap map(pmesh, nx);
+
+   // Test MapPointsToProcs - each point should map to the processor owning the
+   // element, and outside points should have an empty candidate list.
+   std::map<int, std::vector<int>> pt_to_procs;
+   map.MapPointsToProcs(centers, 1, pt_to_procs);
+
+   REQUIRE(pt_to_procs.size() == nel + 1);
+   for (int i = 0; i < nel; i++)
+   {
+      std::vector<int> procs = pt_to_procs[i];
+      REQUIRE(procs.size() > 0);
+      REQUIRE(procs[0] == i % num_procs);
+   }
+   REQUIRE(pt_to_procs[nel].empty());
+}
+#endif

tests/unit/mesh/test_mesh.cpp

@@ -478,3 +478,42 @@ TEST_CASE("NURBS 1D curve in 2D from patches", "[Mesh]")
       }
    }
 }
+
+TEST_CASE("Mesh::Swap preserves named attribute sets", "[Mesh]")
+{
+   // Regression test for a bug where Mesh::Swap swapped attributes and
+   // bdr_attributes but omitted the attr_sets maps, silently losing all named
+   // element/boundary sets on any move or swap of an mfem::Mesh.
+
+   Mesh a = Mesh::MakeCartesian2D(2, 2, Element::QUADRILATERAL);
+   Mesh b = Mesh::MakeCartesian2D(3, 3, Element::QUADRILATERAL);
+
+   Array<int> a_elem_attrs({1});
+   Array<int> b_elem_attrs({1});
+   Array<int> a_bdr_attrs({1, 2});
+   Array<int> b_bdr_attrs({3, 4});
+
+   a.attribute_sets.SetAttributeSet("elem_set_a", a_elem_attrs);
+   a.bdr_attribute_sets.SetAttributeSet("bdr_set_a", a_bdr_attrs);
+   b.attribute_sets.SetAttributeSet("elem_set_b", b_elem_attrs);
+   b.bdr_attribute_sets.SetAttributeSet("bdr_set_b", b_bdr_attrs);
+
+   a.Swap(b, true);
+
+   // After swap, a should hold b's sets and b should hold a's sets.
+   REQUIRE(a.attribute_sets.AttributeSetExists("elem_set_b"));
+   REQUIRE(!a.attribute_sets.AttributeSetExists("elem_set_a"));
+   REQUIRE(a.bdr_attribute_sets.AttributeSetExists("bdr_set_b"));
+   REQUIRE(!a.bdr_attribute_sets.AttributeSetExists("bdr_set_a"));
+
+   REQUIRE(b.attribute_sets.AttributeSetExists("elem_set_a"));
+   REQUIRE(!b.attribute_sets.AttributeSetExists("elem_set_b"));
+   REQUIRE(b.bdr_attribute_sets.AttributeSetExists("bdr_set_a"));
+   REQUIRE(!b.bdr_attribute_sets.AttributeSetExists("bdr_set_b"));
+
+   // Verify set contents survived the swap.
+   Array<int> a_bdr_result = a.bdr_attribute_sets.GetAttributeSet("bdr_set_b");
+   Array<int> b_bdr_result = b.bdr_attribute_sets.GetAttributeSet("bdr_set_a");
+   REQUIRE(a_bdr_result == b_bdr_attrs);
+   REQUIRE(b_bdr_result == a_bdr_attrs);
+}

tests/unit/miniapps/test_tmop_pa.cpp

@@ -84,6 +84,7 @@ int tmop(int id, Req &res, int argc, char *argv[])
    int lin_solver = 2;
    int max_lin_iter = 100;
    real_t lim_const = 0.0;
+   real_t adapt_lim_const = 0.0;
    int lim_type = 0;
    bool normalization = false;
    real_t jitter = 0.0;
@@ -117,6 +118,7 @@ int tmop(int id, Req &res, int argc, char *argv[])
    args.AddOption(&lin_solver, "-ls", "--lin-solver", "");
    args.AddOption(&max_lin_iter, "-li", "--lin-iter", "");
    args.AddOption(&lim_const, "-lc", "--limit-const", "");
+   args.AddOption(&adapt_lim_const, "-alc", "--adapt-limit-const", "");
    args.AddOption(&lim_type, "-lt", "--limit-type", "");
    args.AddOption(&normalization, "-nor", "--normalization",
                   "-no-nor", "--no-normalization", "");
@@ -394,6 +396,22 @@ int tmop(int id, Req &res, int argc, char *argv[])
       }
    }
 
+   // Adaptive limiting.
+   std::unique_ptr<AdaptivityEvaluator> adapt_lim_eval = nullptr;
+   std::unique_ptr<Coefficient> adapt_lim_coeff = nullptr;
+   std::unique_ptr<ParGridFunction> adapt_lim_gf0 = nullptr;
+   if (adapt_lim_const > 0.0)
+   {
+      adapt_lim_gf0.reset(new ParGridFunction(&ind_fes));
+      FunctionCoefficient adapt_lim_gf0_coeff(adapt_lim_fun);
+      adapt_lim_gf0->ProjectCoefficient(adapt_lim_gf0_coeff);
+
+      adapt_lim_coeff.reset(new ConstantCoefficient(adapt_lim_const));
+      adapt_lim_eval.reset(new AdvectorCG(al));
+      tmop_integ->EnableAdaptiveLimiting(*adapt_lim_gf0, *adapt_lim_coeff,
+                                         *adapt_lim_eval, 1.0);
+   }
+
    // Setup the NonlinearForm which defines the integral of interest.
    ParNonlinearForm a(&fes_h1);
    a.SetAssemblyLevel(pa ? AssemblyLevel::PARTIAL : AssemblyLevel::LEGACY);
@@ -495,6 +513,9 @@ int tmop(int id, Req &res, int argc, char *argv[])
       if (pa) { a.GetGradient(xt).AssembleDiagonal(d); }
       else
       {
+         std::unique_ptr<AdaptivityEvaluator> adapt_lim_eval_diag = nullptr;
+         std::unique_ptr<Coefficient> adapt_lim_coeff_diag = nullptr;
+
          ParNonlinearForm nlf_fa(&fes_h1);
          auto *nlfi_fa = new TMOP_Integrator(metric.get(), target_c.get());
          nlfi_fa->SetIntegrationRules(*irules, quad_order);
@@ -508,6 +529,13 @@ int tmop(int id, Req &res, int argc, char *argv[])
                                        new TMOP_ExponentialLimiter);
             }
          }
+         if (adapt_lim_const > 0.0)
+         {
+            adapt_lim_eval_diag.reset(new AdvectorCG(al));
+            adapt_lim_coeff_diag.reset(new ConstantCoefficient(adapt_lim_const));
+            nlfi_fa->EnableAdaptiveLimiting(*adapt_lim_gf0, *adapt_lim_coeff_diag,
+                                            *adapt_lim_eval_diag, 1.0);
+         }
          nlf_fa.AddDomainIntegrator(nlfi_fa);
          nlf_fa.SetEssentialBC(ess_bdr);
          dynamic_cast<GradientClass &>(nlf_fa.GetGradient(xt)).GetDiag(d);
@@ -612,6 +640,15 @@ int tmop(int id, Req &res, int argc, char *argv[])
          }
       }
 
+      // Adaptive limiting evolves adapt_lim_gf as the mesh moves. When running
+      // repeated solves from the same initial mesh (newton_loop > 1), reset the
+      // adaptive limiting state so each solve is comparable.
+      if (adapt_lim_const > 0.0)
+      {
+         tmop_integ->EnableAdaptiveLimiting(*adapt_lim_gf0, *adapt_lim_coeff,
+                                            *adapt_lim_eval, 1.0);
+      }
+
       a.Setup();
 
       if (normalization) { tmop_integ->ParEnableNormalization(x); }
@@ -660,40 +697,48 @@ static inline void req_tmop(int id, const char *args[], Req &res)
 #define DEFAULT_ARGS const char *args[] = { "tmop_pa_tests", "-pa", "-m", "mesh", \
    "-o", "0", "-rs", "0", "-mid", "0", "-tid", "0", "-qt", "1", "-qo", "0", \
    "-ni", "10", "-nl", "1", "-nrtol", "1e-8", "-lrtol", "1e-12", "-ls", "2", "-li", "100", "-lc", "0", \
-   "-lt", "0", "-no-nor", "-ji", "0", "-diag", "-cmb",  "0", "-no-bec", "-no-per", nullptr }
+   "-alc", "0", "-lt", "0", "-no-nor", "-ji", "0", "-diag", "-cmb",  "0", "-no-bec", "-no-per", nullptr }
 
 constexpr int ALV = 1, MSH = 3, POR = 5, RS = 7, MID = 9, TID = 11, QTY = 13,
               QOR = 15, NI = 17, NL = 19, NRTOL = 21, LRTOL = 23, LS = 25, LI = 27, LC = 29,
-              LT = 31, NOR = 32, JI = 34, DIAG = 35, CMB = 37, BEC = 38, PER = 39;
+              ALC = 31, LT = 33, NOR = 34, JI = 36, DIAG = 37, CMB = 39, BEC = 40, PER = 41;
 
 static inline void dump_args(int id, const char *args[])
 {
    if (id != 0) { return; }
    const char *format =
       "tmop_pa_tests %6.6s -m %s -o %s -rs %s -mid %s -tid %s -qt %s -qo %s "
-      "-ni %s -nl %s -nrtol %s -lrtol %s -ls %s -li %s -lc %s -lt %s %s -ji %s "
+      "-ni %s -nl %s -nrtol %s -lrtol %s -ls %s -li %s -lc %s -alc %s -lt %s %s -ji %s "
       "%s -cmb %s %s %s\n";
-   printf(format, args[ALV], args[MSH], args[POR], args[RS], args[MID], args[TID],
-          args[QTY], args[QOR], args[NI], args[NL], args[NRTOL], args[LRTOL],
-          args[LS], args[LI], args[LC], args[LT], args[NOR], args[JI], args[DIAG],
-          args[CMB], args[BEC], args[PER]);
+   printf(format, args[ALV], args[MSH], args[POR], args[RS], args[MID],
+          args[TID], args[QTY], args[QOR], args[NI], args[NL], args[NRTOL],
+          args[LRTOL], args[LS], args[LI], args[LC], args[ALC], args[LT],
+          args[NOR], args[JI], args[DIAG], args[CMB], args[BEC], args[PER]);
    fflush(nullptr);
 }
 
 static inline void tmop_require(int id, const char *args[])
 {
+   real_t tol_fe = 4e-12;
+
+   const bool has_adapt_lim = std::atof(args[ALC]) > 0.0;
+   if (has_adapt_lim) { tol_fe = 1e-7; }
+
    Req res[2];
-   constexpr real_t eps = 4e-12;
    (args[ALV] = "-pa", dump_args(id, args), req_tmop(id, args, res[0]));
    (args[ALV] = "-no-pa", dump_args(id, args), req_tmop(id, args, res[1]));
-   REQUIRE(res[0].dot == MFEM_Approx(res[1].dot));
-   REQUIRE(res[0].diag == MFEM_Approx(res[1].diag));
-   REQUIRE(res[0].min_detJ == MFEM_Approx(res[1].min_detJ));
-   REQUIRE(res[0].met_normal == MFEM_Approx(res[1].met_normal));
-   REQUIRE(res[0].lim_normal == MFEM_Approx(res[1].lim_normal));
-   REQUIRE(res[0].bal_weights == MFEM_Approx(res[1].bal_weights));
-   REQUIRE(res[0].init_energy == MFEM_Approx(res[1].init_energy));
-   REQUIRE(res[0].final_energy == MFEM_Approx(res[1].final_energy, eps));
+
+   if (has_adapt_lim == false)
+   {
+      REQUIRE(res[0].dot       == MFEM_Approx(res[1].dot));
+   }
+   REQUIRE(res[0].diag         == MFEM_Approx(res[1].diag));
+   REQUIRE(res[0].min_detJ     == MFEM_Approx(res[1].min_detJ));
+   REQUIRE(res[0].met_normal   == MFEM_Approx(res[1].met_normal));
+   REQUIRE(res[0].lim_normal   == MFEM_Approx(res[1].lim_normal));
+   REQUIRE(res[0].bal_weights  == MFEM_Approx(res[1].bal_weights));
+   REQUIRE(res[0].init_energy  == MFEM_Approx(res[1].init_energy));
+   REQUIRE(res[0].final_energy == MFEM_Approx(res[1].final_energy, tol_fe));
 }
 
 static constexpr int SZ = 32;
@@ -737,6 +782,7 @@ public:
       bool normalization = false;
       bool periodic = false;
       real_t lim_const = 0.0;
+      real_t adapt_lim_const = 0.0;
       int lim_type = 0;
       real_t jitter = 0.0;
       list_t order = { 1, 2, 3, 4 };
@@ -764,6 +810,7 @@ public:
       Args &NEWTON_RTOLERANCE(const real_t arg) { newton_rtol = arg; return *this; }
       Args &LINSOL_RTOLERANCE(const real_t arg) { linsol_rtol = arg; return *this; }
       Args &LIMITING(const real_t arg) { lim_const = arg; return *this; }
+      Args &ADAPT_LIMITING(const real_t arg) { adapt_lim_const = arg; return *this; }
       Args &JI(const real_t arg) { jitter = arg; return *this; }
       // lists
       Args &POR(list_t arg) { order = arg; return *this; }
@@ -776,7 +823,7 @@ public:
    const char *name, *mesh;
    int NEWTON_ITERATIONS, LINSOL_ITERATIONS, REFINE, COMBO, LIMIT_TYPE;
    bool NORMALIZATION, DIAGONAL, BAL_EXPL_COMBO, PERIODIC;
-   real_t NEWTON_RTOLERANCE, LINSOL_RTOLERANCE, LIMITING, JITTER;
+   real_t NEWTON_RTOLERANCE, LINSOL_RTOLERANCE, LIMITING, ADAPT_LIMITING, JITTER;
    list_t P_ORDERS, TARGET_IDS, METRIC_IDS, Q_ORDERS, LINEAR_SOLVERS, NEWTON_LOOPS;
 
 public:
@@ -795,6 +842,7 @@ public:
       NEWTON_RTOLERANCE(a.newton_rtol),
       LINSOL_RTOLERANCE(a.linsol_rtol),
       LIMITING(a.lim_const),
+      ADAPT_LIMITING(a.adapt_lim_const),
       JITTER(a.jitter),
       // lists
       P_ORDERS(a.order),
@@ -809,7 +857,7 @@ public:
       if ((id == 0) && name) { mfem::out << "[" << name << "]" << std::endl; }
       DEFAULT_ARGS;
       char ni[SZ] {}, nrtol[SZ] {}, lrtol[SZ] {}, rs[SZ] {}, li[SZ] {},
-           lc[SZ] {}, lt[SZ] {}, ji[SZ] {}, cmb[SZ] {};
+           lc[SZ] {}, alc[SZ] {}, lt[SZ] {}, ji[SZ] {}, cmb[SZ] {};
       args[MSH] = mesh;
       // int
       args[NI] = itoa(NEWTON_ITERATIONS, ni);
@@ -826,6 +874,7 @@ public:
       args[NRTOL] = dtoa(NEWTON_RTOLERANCE, nrtol);
       args[LRTOL] = dtoa(LINSOL_RTOLERANCE, lrtol);
       args[LC] = dtoa(LIMITING, lc);
+      args[ALC] = dtoa(ADAPT_LIMITING, alc);
       args[JI] = dtoa(JITTER, ji);
 
       for (int p : P_ORDERS)
@@ -926,6 +975,39 @@ static void tmop_tests(int id = 0, bool all = false)
 
    const real_t jitter = 1. / (M_PI * M_PI);
 
+   Launch(Launch::Args("2D + adaptive limiting")
+          .MESH("../../miniapps/meshing/stretched2D.mesh")
+          .REFINE(0)
+          .NORMALIZATION()
+          .MID({ 2 })
+          .TID({ 1 })
+          .LS({ 3 })
+          .POR({ 1 })
+          .QOR({ 5 })
+          .NEWTON_ITERATIONS(50)
+          .NEWTON_RTOLERANCE(1e-6)
+          .LINSOL_RTOLERANCE(1e-10)
+          .LINSOL_ITERATIONS(100)
+          .ADAPT_LIMITING(1.0)
+          .DIAGONAL(true))
+   .Run(id, all);
+
+   Launch(Launch::Args("3D + adaptive limiting")
+          .MESH("../../miniapps/meshing/stretched3D.mesh")
+          .REFINE(0)
+          .NORMALIZATION()
+          .MID({ 302 })
+          .TID({ 1 })
+          .LS({ 3 })
+          .POR({ 1 })
+          .QOR({ 5 })
+          .NEWTON_ITERATIONS(50)
+          .NEWTON_RTOLERANCE(1e-6)
+          .LINSOL_RTOLERANCE(1e-10)
+          .ADAPT_LIMITING(1.0)
+          .DIAGONAL(true))
+   .Run(id, all);
+
    Launch(Launch::Args("2D Periodic + adapted discrete size")
           .MESH("../../data/periodic-square.mesh")
           .PERIODIC()