Vector::DeleteAt on device using InclusiveScan

# Conflicts:
#	mesh/mesh.cpp

fem/bilinearform.cpp

@@ -1275,6 +1275,22 @@ void BilinearForm::Update(FiniteElementSpace *nfes)
    height = width = fes->GetVSize();
 
    if (ext) { ext->Update(); }
+   for (int k = 0; k < domain_integs.Size(); ++k)
+   {
+      domain_integs[k]->Update();
+   }
+   for (int k = 0; k < boundary_integs.Size(); ++k)
+   {
+      boundary_integs[k]->Update();
+   }
+   for (int k = 0; k < interior_face_integs.Size(); ++k)
+   {
+      interior_face_integs[k]->Update();
+   }
+   for (int k = 0; k < boundary_integs.Size(); ++k)
+   {
+      boundary_face_integs[k]->Update();
+   }
 }
 
 void BilinearForm::SetDiagonalPolicy(DiagonalPolicy policy)
@@ -2337,6 +2353,31 @@ void MixedBilinearForm::Update()
    height = test_fes->GetVSize();
    width = trial_fes->GetVSize();
    if (ext) { ext->Update(); }
+
+   for (int k = 0; k < domain_integs.Size(); ++k)
+   {
+      domain_integs[k]->Update();
+   }
+   for (int k = 0; k < boundary_integs.Size(); ++k)
+   {
+      boundary_integs[k]->Update();
+   }
+   for (int k = 0; k < interior_face_integs.Size(); ++k)
+   {
+      interior_face_integs[k]->Update();
+   }
+   for (int k = 0; k < boundary_integs.Size(); ++k)
+   {
+      boundary_face_integs[k]->Update();
+   }
+   for (int k = 0; k < trace_face_integs.Size(); ++k)
+   {
+      trace_face_integs[k]->Update();
+   }
+   for (int k = 0; k < boundary_trace_face_integs.Size(); ++k)
+   {
+      boundary_trace_face_integs[k]->Update();
+   }
 }
 
 MixedBilinearForm::~MixedBilinearForm()

fem/bilininteg.cpp

@@ -21,6 +21,11 @@ using namespace std;
 namespace mfem
 {
 
+void BilinearFormIntegrator::Update()
+{
+   // default no-op
+}
+
 void BilinearFormIntegrator::AssemblePA(const FiniteElementSpace&)
 {
    MFEM_ABORT("BilinearFormIntegrator::AssemblePA(fes)\n"
@@ -3460,6 +3465,12 @@ real_t ElasticityIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
    return energy;
 }
 
+void DGTraceIntegrator::Update()
+{
+   qspace[0].reset();
+   qspace[1].reset();
+}
+
 void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
                                            const FiniteElement &el2,
                                            FaceElementTransformations &Trans,

fem/bilininteg.hpp

@@ -23,6 +23,8 @@
 
 namespace mfem
 {
+class QuadratureSpace;
+class FaceQuadratureSpace;
 
 /// Abstract base class BilinearFormIntegrator
 class BilinearFormIntegrator : public NonlinearFormIntegrator
@@ -44,6 +46,10 @@ public:
    // make sense for the action of the nonlinear operator (but they all make
    // sense for its Jacobian).
 
+   /// Signal this integrator that something about either the trial or test space has changed.
+   virtual void Update();
+
+
    /// Method defining partial assembly.
    /** The result of the partial assembly is stored internally so that it can be
        used later in the methods AddMultPA() and AddMultTransposePA(). */
@@ -3311,6 +3317,7 @@ protected:
    VectorCoefficient *u;
    real_t alpha, beta;
    // PA extension
+   std::unique_ptr<FaceQuadratureSpace> qspace[2];
    Vector pa_data;
    const DofToQuad *maps;             ///< Not owned
    const FaceGeometricFactors *geom;  ///< Not owned
@@ -3333,6 +3340,8 @@ public:
                      real_t a, real_t b)
    { rho = &rho_; u = &u_; alpha = a; beta = b; }
 
+   void Update() override;
+
    using BilinearFormIntegrator::AssembleFaceMatrix;
    void AssembleFaceMatrix(const FiniteElement &el1,
                            const FiniteElement &el2,

fem/integ/bilininteg_dgtrace_pa.cpp

@@ -139,8 +139,6 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
    const MemoryType mt = (pa_mt == MemoryType::DEFAULT) ?
                          Device::GetDeviceMemoryType() : pa_mt;
 
-   nf = fes.GetNFbyType(type);
-   if (nf==0) { return; }
    // Assumes tensor-product elements
    Mesh *mesh = fes.GetMesh();
    const FiniteElement &el = *fes.GetTypicalTraceElement();
@@ -148,6 +146,17 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
                                IntRule:
                                &GetRule(el.GetGeomType(), el.GetOrder(),
                                         *mesh->GetTypicalElementTransformation());
+
+   if (!qspace[static_cast<int>(type)])
+   {
+      qspace[static_cast<int>(type)].reset(
+         new FaceQuadratureSpace(*mesh, *ir, type));
+   }
+
+   FaceQuadratureSpace& qs = *qspace[static_cast<int>(type)];
+   nf = qs.GetNumFaces();
+   if (nf==0) { return; }
+
    const int symmDims = 4;
    nq = ir->GetNPoints();
    dim = mesh->Dimension();
@@ -159,8 +168,6 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
    dofs1D = maps->ndof;
    quad1D = maps->nqpt;
    pa_data.SetSize(symmDims * nq * nf, Device::GetMemoryType());
-
-   FaceQuadratureSpace qs(*mesh, *ir, type);
    CoefficientVector vel(*u, qs, CoefficientStorage::COMPRESSED);
 
    CoefficientVector r(qs, CoefficientStorage::COMPRESSED);

fem/qspace.cpp

@@ -17,8 +17,9 @@ namespace mfem
 {
 
 QuadratureSpaceBase::QuadratureSpaceBase(Mesh &mesh_, Geometry::Type geom,
-                                         const IntegrationRule &ir)
-   : mesh(mesh_), order(ir.GetOrder())
+                                         const IntegrationRule &ir,
+                                         QSpaceStorage storage)
+   : mesh(mesh_), order(ir.GetOrder()), storage(storage)
 {
    for (int g = 0; g < Geometry::NumGeom; g++)
    {
@@ -96,10 +97,10 @@ void QuadratureSpaceBase::Integrate(VectorCoefficient &coeff,
 
 void QuadratureSpace::ConstructOffsets()
 {
-   const int num_elem = mesh.GetNE();
-   ne = num_elem;
+   const int num_elem = ne;
 
-   if (mesh.GetNumGeometries(mesh.Dimension()) == 1)
+   if (storage == QSpaceStorage::COMPRESSED &&
+       mesh.GetNumGeometries(mesh.Dimension()) == 1)
    {
       Array<Geometry::Type> geoms;
       mesh.GetGeometries(mesh.Dimension(), geoms);
@@ -124,14 +125,9 @@ void QuadratureSpace::ConstructOffsets()
    }
 }
 
-void QuadratureSpace::Construct()
-{
-   ConstructIntRules(mesh.Dimension());
-   ConstructOffsets();
-}
-
-QuadratureSpace::QuadratureSpace(Mesh *mesh_, std::istream &in)
-   : QuadratureSpaceBase(*mesh_)
+QuadratureSpace::QuadratureSpace(Mesh *mesh_, std::istream &in,
+                                 QSpaceStorage storage)
+   : QuadratureSpaceBase(*mesh_, 0, storage)
 {
    const char *msg = "invalid input stream";
    std::string ident;
@@ -150,15 +146,24 @@ QuadratureSpace::QuadratureSpace(Mesh *mesh_, std::istream &in)
       return;
    }
 
-   Construct();
+   ne = mesh.GetNE();
+   ConstructIntRules(mesh.Dimension());
 }
 
-QuadratureSpace::QuadratureSpace(Mesh &mesh_, const IntegrationRule &ir)
-   : QuadratureSpaceBase(mesh_, mesh_.GetTypicalElementGeometry(), ir)
+QuadratureSpace::QuadratureSpace(Mesh *mesh_, int order_, QSpaceStorage storage)
+   : QuadratureSpaceBase(*mesh_, order_, storage)
+{
+   ne = mesh.GetNE();
+   ConstructIntRules(mesh.Dimension());
+}
+
+QuadratureSpace::QuadratureSpace(Mesh &mesh_, const IntegrationRule &ir,
+                                 QSpaceStorage storage)
+   : QuadratureSpaceBase(mesh_, mesh_.GetTypicalElementGeometry(), ir, storage)
 {
    MFEM_VERIFY(mesh.GetNumGeometries(mesh.Dimension()) <= 1,
                "Constructor not valid for mixed meshes");
-   ConstructOffsets();
+   ne = mesh.GetNE();
 }
 
 void QuadratureSpace::Save(std::ostream &os) const
@@ -180,55 +185,53 @@ const Vector &QuadratureSpace::GetGeometricFactorWeights() const
 }
 
 FaceQuadratureSpace::FaceQuadratureSpace(Mesh &mesh_, int order_,
-                                         FaceType face_type_)
-   : QuadratureSpaceBase(mesh_, order_),
-     face_type(face_type_),
-     num_faces(mesh.GetNFbyType(face_type))
+                                         FaceType face_type_,
+                                         QSpaceStorage storage)
+   : QuadratureSpaceBase(mesh_, order_, storage), face_type(face_type_),
+     face_indices(mesh.GetFaceIndices(face_type_)),
+     face_indices_inv(mesh.GetInvFaceIndices(face_type_))
 {
-   Construct();
+   ne = face_indices.Size();
+   ConstructIntRules(mesh.Dimension() - 1);
 }
 
 FaceQuadratureSpace::FaceQuadratureSpace(Mesh &mesh_, const IntegrationRule &ir,
-                                         FaceType face_type_)
-   : QuadratureSpaceBase(mesh_, mesh_.GetTypicalFaceGeometry(), ir),
-     face_type(face_type_),
-     num_faces(mesh.GetNFbyType(face_type))
+                                         FaceType face_type_,
+                                         QSpaceStorage storage)
+   : QuadratureSpaceBase(mesh_, mesh_.GetTypicalFaceGeometry(), ir, storage),
+     face_type(face_type_), face_indices(mesh.GetFaceIndices(face_type_)),
+     face_indices_inv(mesh.GetInvFaceIndices(face_type_))
 {
    MFEM_VERIFY(mesh.GetNumGeometries(mesh.Dimension() - 1) <= 1,
                "Constructor not valid for mixed meshes");
-   ConstructOffsets();
+   ne = face_indices.Size();
 }
 
 void FaceQuadratureSpace::ConstructOffsets()
 {
-   face_indices.SetSize(num_faces);
-   offsets.SetSize(num_faces + 1);
-   ne = num_faces;
-   int offset = 0;
-   int f_idx = 0;
-   for (int i = 0; i < mesh.GetNumFacesWithGhost(); i++)
+   if (storage == QSpaceStorage::COMPRESSED &&
+       mesh.GetNumGeometries(mesh.Dimension() - 1) == 1)
    {
-      const Mesh::FaceInformation face = mesh.GetFaceInformation(i);
-      if (face.IsNonconformingCoarse() || !face.IsOfFaceType(face_type))
-      {
-         continue;
-      }
-      face_indices[f_idx] = i;
-      face_indices_inv[i] = f_idx;
-      offsets[f_idx] = offset;
-      Geometry::Type geom = mesh.GetFaceGeometry(i);
-      MFEM_ASSERT(int_rule[geom] != NULL, "Missing integration rule");
-      offset += int_rule[geom]->GetNPoints();
-
-      f_idx++;
+      Array<Geometry::Type> geoms;
+      mesh.GetGeometries(mesh.Dimension() - 1, geoms);
+      offsets.SetSize(1);
+      offsets.HostWrite();
+      offsets[0] = int_rule[geoms[0]]->GetNPoints();
+      size = ne * offsets[0];
+   }
+   else
+   {
+      offsets.SetSize(face_indices.Size() + 1);
+      int offset = 0;
+      for (int i = 0; i < mesh.GetNFbyType(face_type); ++i)
+      {
+         offsets[i] = offset;
+         Geometry::Type geom = mesh.GetFaceGeometry(face_indices[i]);
+         MFEM_ASSERT(int_rule[geom] != NULL, "Missing integration rule");
+         offset += int_rule[geom]->GetNPoints();
+      }
+      offsets[face_indices.Size()] = size = offset;
    }
-   offsets[num_faces] = size = offset;
-}
-
-void FaceQuadratureSpace::Construct()
-{
-   ConstructIntRules(mesh.Dimension() - 1);
-   ConstructOffsets();
 }
 
 int FaceQuadratureSpace::GetPermutedIndex(int idx, int iq) const

fem/qspace.hpp

@@ -19,39 +19,49 @@
 namespace mfem
 {
 
+enum class QSpaceStorage
+{
+   FULL,
+   COMPRESSED
+};
+
 /// Abstract base class for QuadratureSpace and FaceQuadratureSpace.
 /** This class represents the storage layout for QuadratureFunction%s, that may
     be defined either on mesh elements or mesh faces. */
 class QuadratureSpaceBase
 {
 protected:
-   friend class QuadratureFunction; // Uses the offsets.
-
    Mesh &mesh; ///< The underlying mesh.
    int order; ///< The order of integration rule.
-   int size; ///< Total number of quadrature points.
+   int size = -1; ///< Total number of quadrature points. -1 indicates
+   ///< offsets/size not computed yet.
    int ne; ///< Actual number of entities
    mutable Vector weights; ///< Integration weights.
    mutable long nodes_sequence = 0; ///< Nodes counter for cache invalidation.
 
+   QSpaceStorage storage;
+
    /// @brief Entity quadrature point offset array.
    ///
    /// Supports a constant compression scheme for meshes which have a single
    /// geometry type. When compressed, will have a single value. The true offset
    /// can be computed as i * offsets[0], where i is the entity index. Otherwise
-   /// has size num_entities + 1.
+   /// has size num_entities + 1. Lazily constructed.
    ///
    Array<int> offsets;
    /// The quadrature rules used for each geometry type.
    const IntegrationRule *int_rule[Geometry::NumGeom];
 
    /// Protected constructor. Used by derived classes.
-   QuadratureSpaceBase(Mesh &mesh_, int order_ = 0)
-      : mesh(mesh_), order(order_) { }
+   QuadratureSpaceBase(Mesh &mesh_, int order_ = 0,
+                       QSpaceStorage storage = QSpaceStorage::COMPRESSED)
+      : mesh(mesh_), order(order_), storage(storage)
+   {}
 
    /// Protected constructor. Used by derived classes.
    QuadratureSpaceBase(Mesh &mesh_, Geometry::Type geom,
-                       const IntegrationRule &ir);
+                       const IntegrationRule &ir,
+                       QSpaceStorage storage = QSpaceStorage::COMPRESSED);
 
    /// Fill the @ref int_rule array for each geometry type using @ref order.
    void ConstructIntRules(int dim);
@@ -62,13 +72,21 @@ protected:
    /// Compute the integration weights.
    void ConstructWeights() const;
 
+   virtual void ConstructOffsets() = 0;
+
 public:
+   QSpaceStorage StorageType() const { return storage; }
+
    /// @brief Gets the offset for a given entity @a idx.
    ///
    /// The quadrature point values for entity i are stored in the indices
    /// between Offset(i) and Offset(i+1)
    int Offset(int idx) const
    {
+      if (size < 0)
+      {
+         const_cast<QuadratureSpaceBase *>(this)->ConstructOffsets();
+      }
       return (offsets.Size() == 1) ? (idx * offsets[0]) : offsets[idx];
    }
 
@@ -79,10 +97,24 @@ public:
    /// can be computed as i * offsets[0], where i is the entity index. Otherwise
    /// has size num_entities + 1.
    ///
-   const Array<int> &Offsets() const { return offsets; }
+   const Array<int> &Offsets() const
+   {
+      if (size < 0)
+      {
+         const_cast<QuadratureSpaceBase *>(this)->ConstructOffsets();
+      }
+      return offsets;
+   }
 
    /// Return the total number of quadrature points.
-   int GetSize() const { return size; }
+   int GetSize() const
+   {
+      if (size < 0)
+      {
+         const_cast<QuadratureSpaceBase *>(this)->ConstructOffsets();
+      }
+      return size;
+   }
 
    /// Return the order of the quadrature rule(s) used by all elements.
    int GetOrder() const { return order; }
@@ -142,19 +174,20 @@ class QuadratureSpace : public QuadratureSpaceBase
 {
 protected:
    const Vector &GetGeometricFactorWeights() const override;
-   void ConstructOffsets();
-   void Construct();
+   void ConstructOffsets() override;
 public:
    /// Create a QuadratureSpace based on the global rules from #IntRules.
-   QuadratureSpace(Mesh *mesh_, int order_)
-      : QuadratureSpaceBase(*mesh_, order_) { Construct(); }
+   QuadratureSpace(Mesh *mesh_, int order_,
+                   QSpaceStorage storage = QSpaceStorage::COMPRESSED);
 
    /// @brief Create a QuadratureSpace with an IntegrationRule, valid only when
    /// the mesh has one element type.
-   QuadratureSpace(Mesh &mesh_, const IntegrationRule &ir);
+   QuadratureSpace(Mesh &mesh_, const IntegrationRule &ir,
+                   QSpaceStorage storage = QSpaceStorage::COMPRESSED);
 
    /// Read a QuadratureSpace from the stream @a in.
-   QuadratureSpace(Mesh *mesh_, std::istream &in);
+   QuadratureSpace(Mesh *mesh_, std::istream &in,
+                   QSpaceStorage storage = QSpaceStorage::COMPRESSED);
 
    /// Returns number of elements in the mesh.
    inline int GetNE() const { return mesh.GetNE(); }
@@ -191,29 +224,29 @@ public:
 class FaceQuadratureSpace : public QuadratureSpaceBase
 {
    FaceType face_type; ///< Is the space defined on interior or boundary faces?
-   const int num_faces; ///< Number of faces.
 
    /// Map from boundary or interior face indices to mesh face indices.
-   Array<int> face_indices;
+   const Array<int> &face_indices;
 
    /// Inverse of the map @a face_indices.
-   std::unordered_map<int,int> face_indices_inv;
+   const std::unordered_map<int,int> &face_indices_inv;
 
    const Vector &GetGeometricFactorWeights() const override;
-   void ConstructOffsets();
-   void Construct();
+   void ConstructOffsets() override;
 
 public:
    /// Create a FaceQuadratureSpace based on the global rules from #IntRules.
-   FaceQuadratureSpace(Mesh &mesh_, int order_, FaceType face_type_);
+   FaceQuadratureSpace(Mesh &mesh_, int order_, FaceType face_type_,
+                       QSpaceStorage storage = QSpaceStorage::COMPRESSED);
 
    /// @brief Create a FaceQuadratureSpace with an IntegrationRule, valid only
    /// when the mesh has one type of face geometry.
    FaceQuadratureSpace(Mesh &mesh_, const IntegrationRule &ir,
-                       FaceType face_type_);
+                       FaceType face_type_,
+                       QSpaceStorage storage = QSpaceStorage::COMPRESSED);
 
    /// Returns number of faces in the mesh.
-   inline int GetNumFaces() const { return num_faces; }
+   inline int GetNumFaces() const { return face_indices.Size(); }
 
    /// Returns the face type (boundary or interior).
    FaceType GetFaceType() const { return face_type; }

general/scan.hpp

@@ -0,0 +1,176 @@
+// 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_SCAN_HPP
+#define MFEM_SCAN_HPP
+
+#ifdef MFEM_USE_CUDA
+#include <cub/device/device_scan.cuh>
+#define MFEM_CUB_NAMESPACE cub
+#elif MFEM_USE_HIP
+#include <hipcub/device/device_scan.hpp>
+#define MFEM_CUB_NAMESPACE hipcub
+#endif
+
+#include <functional>
+#include <numeric>
+
+namespace mfem
+{
+/// Equivalent to InclusiveScan(use_dev, d_in, d_out, num_items, workspace,
+/// std::plus<>{})
+template <class InputIt, class OutputIt>
+void InclusiveScan(bool use_dev, InputIt d_in, OutputIt d_out, size_t num_items,
+                   Array<char> &workspace)
+{
+   // forward to InclusiveSum for potentially faster kernels
+#if defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP)
+   if (use_dev && mfem::Device::Allows(Backend::CUDA_MASK | Backend::HIP_MASK))
+   {
+      size_t bytes = workspace.Size();
+      if (bytes)
+      {
+         auto err = MFEM_CUB_NAMESPACE::DeviceScan::InclusiveSum(
+                       workspace.Write(), bytes, d_in, d_out, num_items);
+#if defined(MFEM_USE_CUDA)
+         if (err == cudaSuccess)
+         {
+            return;
+         }
+#elif defined(MFEM_USE_HIP)
+         if (err == hipSuccess)
+         {
+            return;
+         }
+#endif
+      }
+      // try allocating a larger buffer
+      bytes = 0;
+      MFEM_GPU_CHECK(MFEM_CUB_NAMESPACE::DeviceScan::InclusiveSum(
+                        nullptr, bytes, d_in, d_out, num_items));
+      workspace.SetSize(bytes);
+      MFEM_GPU_CHECK(MFEM_CUB_NAMESPACE::DeviceScan::InclusiveSum(
+                        workspace.Write(), bytes, d_in, d_out, num_items));
+      return;
+   }
+#endif
+   std::inclusive_scan(d_in, d_in + num_items, d_out);
+}
+
+/// Performs an inclusive scan of [d_in, d_in+num_items) -> [d_out,
+/// d_out+num_items). This call is potentially asynchronous on the device.
+/// @a d_in input start.
+/// @a d_out output start. Can perform in-place scans with d_out = d_in
+/// @a workspace temporary workspace used for device scans. TODO: replace with
+/// internal temporary workspace once that's added to the memory manager.
+/// @a scan_op binary scan functor. Must be associative. If only weakly
+/// associative (i.e. floating point addition) results are not deterministic. On
+/// device this must also be commutative.
+template <class InputIt, class OutputIt, class ScanOp>
+void InclusiveScan(bool use_dev, InputIt d_in, OutputIt d_out, size_t num_items,
+                   Array<char> &workspace, ScanOp scan_op)
+{
+#if defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP)
+   if (use_dev && mfem::Device::Allows(Backend::CUDA_MASK | Backend::HIP_MASK))
+   {
+      size_t bytes = workspace.Size();
+      if (bytes)
+      {
+         auto err = MFEM_CUB_NAMESPACE::DeviceScan::InclusiveScan(
+                       workspace.Write(), bytes, d_in, d_out, scan_op, num_items);
+#if defined(MFEM_USE_CUDA)
+         if (err == cudaSuccess)
+         {
+            return;
+         }
+#elif defined(MFEM_USE_HIP)
+         if (err == hipSuccess)
+         {
+            return;
+         }
+#endif
+      }
+      // try allocating a larger buffer
+      bytes = 0;
+      MFEM_GPU_CHECK(MFEM_CUB_NAMESPACE::DeviceScan::InclusiveScan(
+                        nullptr, bytes, d_in, d_out, scan_op, num_items));
+      workspace.SetSize(bytes);
+      MFEM_GPU_CHECK(MFEM_CUB_NAMESPACE::DeviceScan::InclusiveScan(
+                        workspace.Write(), bytes, d_in, d_out, scan_op, num_items));
+      return;
+   }
+#endif
+   std::inclusive_scan(d_in, d_in + num_items, d_out, scan_op);
+}
+
+/// Performs an exclusive scan of [d_in, d_in+num_items) -> [d_out,
+/// d_out+num_items). This call is potentially asynchronous on the device.
+/// @a d_in input start.
+/// @a d_out output start. Can perform in-place scans with d_out = d_in
+/// @a workspace temporary workspace used for device scans. TODO: replace with
+/// internal temporary workspace once that's added to the memory manager.
+/// @a scan_op binary scan functor. Must be associative. If only weakly
+/// associative (i.e. floating point addition) results are not deterministic. On
+/// device this must also be commutative.
+template <class InputIt, class OutputIt, class T, class ScanOp>
+void ExclusiveScan(bool use_dev, InputIt d_in, OutputIt d_out, size_t num_items,
+                   T init_value, Array<char> &workspace, ScanOp scan_op)
+{
+#if defined(MFEM_USE_CUDA) || defined(MFEM_USE_HIP)
+   if (use_dev && mfem::Device::Allows(Backend::CUDA_MASK | Backend::HIP_MASK))
+   {
+      size_t bytes = workspace.Size();
+      if (bytes)
+      {
+         auto err = MFEM_CUB_NAMESPACE::DeviceScan::ExclusiveScan(
+                       workspace.Write(), bytes, d_in, d_out, scan_op, init_value,
+                       num_items);
+#if defined(MFEM_USE_CUDA)
+         if (err == cudaSuccess)
+         {
+            return;
+         }
+#elif defined(MFEM_USE_HIP)
+         if (err == hipSuccess)
+         {
+            return;
+         }
+#endif
+      }
+      // try allocating a larger buffer
+      bytes = 0;
+      MFEM_GPU_CHECK(MFEM_CUB_NAMESPACE::DeviceScan::ExclusiveScan(
+                        nullptr, bytes, d_in, d_out, scan_op, init_value, num_items));
+      workspace.SetSize(bytes);
+      MFEM_GPU_CHECK(MFEM_CUB_NAMESPACE::DeviceScan::ExclusiveScan(
+                        workspace.Write(), bytes, d_in, d_out, scan_op, init_value,
+                        num_items));
+      return;
+   }
+#endif
+   std::exclusive_scan(d_in, d_in + num_items, d_out, init_value, scan_op);
+}
+
+/// Equivalent to ExclusiveScan(use_dev, d_in, d_out, num_items, init_value,
+/// workspace, std::plus<>{})
+template <class InputIt, class OutputIt, class T>
+void ExclusiveScan(bool use_dev, InputIt d_in, OutputIt d_out, size_t num_items,
+                   T init_value, Array<char> &workspace)
+{
+   ExclusiveScan(use_dev, d_in, d_out, num_items, init_value, workspace,
+                 std::plus<> {});
+}
+
+} // namespace mfem
+
+#undef MFEM_CUB_NAMESPACE
+
+#endif

linalg/vector.cpp

@@ -14,6 +14,7 @@
 #include "../general/forall.hpp"
 #include "../general/reducers.hpp"
 #include "../general/hash.hpp"
+#include "../general/scan.hpp"
 #include "vector.hpp"
 
 #ifdef MFEM_USE_OPENMP
@@ -1252,4 +1253,44 @@ real_t Vector::Sum() const
    return res;
 }
 
+void Vector::DeleteAt(const Array<int> &indices)
+{
+   const bool use_dev = UseDevice();
+
+   Array<int> flag(size);
+   const auto d_flag = flag.Write(use_dev);
+   mfem::forall_switch(use_dev, size, [=] MFEM_HOST_DEVICE (int i)
+   {
+      d_flag[i] = true;
+   });
+   const auto d_indices = indices.Read(use_dev);
+   mfem::forall_switch(use_dev, indices.Size(), [=] MFEM_HOST_DEVICE (int i)
+   {
+      d_flag[d_indices[i]] = false;
+   });
+
+   Array<int> out_idx(size);
+   auto d_out_idx = out_idx.Write(use_dev);
+   Array<char> workspace;
+   // Perform inclusive scan so that the last entry is the new size.
+   InclusiveScan(use_dev, d_flag, d_out_idx, size, workspace);
+
+   Vector copy(*this);
+   auto d_in = copy.Read(use_dev);
+   auto d_out = Write(use_dev);
+   mfem::forall_switch(use_dev, size, [=] MFEM_HOST_DEVICE (int i)
+   {
+      if (d_flag[i])
+      {
+         // Transform inclusive scan to exclusive by shifting.
+         const int j = (i > 0) ? d_out_idx[i - 1] : 0;
+         d_out[j] = d_in[i];
+      }
+   });
+
+   // Get the new size of the vector. Copy only the last entry.
+   Memory<int> submem(out_idx.GetMemory(), out_idx.Size() - 1, 1);
+   size = submem.Read(MemoryClass::HOST, 1)[0];
+}
+
 } // namespace mfem

linalg/vector.hpp

@@ -639,29 +639,6 @@ inline void Vector::Reserve(int res)
    }
 }
 
-inline void Vector::DeleteAt(const Array<int> &indices)
-{
-   // Make copy of the indices, sorted.
-   Array<int> sorted_indices(indices);
-   sorted_indices.Sort();
-
-   int rm_count = 0;
-   for (int i = 0; i < size; i++)
-   {
-      if (rm_count < sorted_indices.Size() && i == sorted_indices[rm_count])
-      {
-         rm_count++;
-      }
-      else
-      {
-         data[i-rm_count] = data[i]; // shift data rm_count
-      }
-   }
-
-   // Resize to remove tail
-   size -= rm_count;
-}
-
 inline void Vector::NewMemoryAndSize(const Memory<real_t> &mem, int s,
                                      bool own_mem)
 {

mesh/mesh.cpp

@@ -979,6 +979,46 @@ const Array<int>& Mesh::GetElementAttributes() const
    return elem_attrs_cache;
 }
 
+void Mesh::ComputeFaceInfo(FaceType ftype) const
+{
+   auto &fidcs = face_indices[static_cast<int>(ftype)];
+   auto &ifidcs = inv_face_indices[static_cast<int>(ftype)];
+   fidcs.SetSize(GetNFbyType(ftype));
+   fidcs.HostWrite();
+   ifidcs.reserve(fidcs.Size());
+   int f_idx = 0;
+   for (int i = 0; i < GetNumFacesWithGhost(); ++i)
+   {
+      const FaceInformation face = GetFaceInformation(i);
+      if (face.IsNonconformingCoarse() || !face.IsOfFaceType(ftype))
+      {
+         continue;
+      }
+      fidcs[f_idx] = i;
+      ifidcs[i] = f_idx;
+      ++f_idx;
+   }
+}
+
+const Array<int> &Mesh::GetFaceIndices(FaceType ftype) const
+{
+   if (face_indices[static_cast<int>(ftype)].Size() == 0)
+   {
+      ComputeFaceInfo(ftype);
+   }
+   return face_indices[static_cast<int>(ftype)];
+}
+
+const std::unordered_map<int, int> &
+Mesh::GetInvFaceIndices(FaceType ftype) const
+{
+   if (inv_face_indices[static_cast<int>(ftype)].empty())
+   {
+      ComputeFaceInfo(ftype);
+   }
+   return inv_face_indices[static_cast<int>(ftype)];
+}
+
 void Mesh::DeleteGeometricFactors()
 {
    for (int i = 0; i < geom_factors.Size(); i++)
@@ -1866,6 +1906,11 @@ void Mesh::Destroy()
    bdr_face_attrs_cache.DeleteAll();
    attributes.DeleteAll();
    bdr_attributes.DeleteAll();
+
+   face_indices[0].DeleteAll();
+   face_indices[1].DeleteAll();
+   inv_face_indices[0] = std::unordered_map<int, int>();
+   inv_face_indices[1] = std::unordered_map<int, int>();
 }
 
 void Mesh::ResetLazyData()
@@ -8137,6 +8182,12 @@ void Mesh::GenerateFaces()
       FreeElement(f);
    }
 
+   // delete caches
+   face_indices[0].SetSize(0);
+   face_indices[1].SetSize(0);
+   inv_face_indices[0].clear();
+   inv_face_indices[1].clear();
+
    // (re)generate the interior faces and the info for them
    faces.SetSize(nfaces);
    faces_info.SetSize(nfaces);
@@ -10936,6 +10987,11 @@ void Mesh::Swap(Mesh& other, bool non_geometry)
    // copy attribute caches
    mfem::Swap(elem_attrs_cache, other.elem_attrs_cache);
    mfem::Swap(bdr_face_attrs_cache, other.bdr_face_attrs_cache);
+
+   mfem::Swap(face_indices[0], other.face_indices[0]);
+   mfem::Swap(face_indices[1], other.face_indices[1]);
+   inv_face_indices[0].swap(other.inv_face_indices[0]);
+   inv_face_indices[1].swap(other.inv_face_indices[1]);
 }
 
 void Mesh::GetElementData(const Array<Element*> &elem_array, int geom,

mesh/mesh.hpp

@@ -278,6 +278,13 @@ protected:
 
    // used during NC mesh initialization only
    Array<Triple<int, int, int> > tmp_vertex_parents;
+   /// cache for FaceIndices(ftype)
+   mutable Array<int> face_indices[2];
+   /// cache for FaceIndices(ftype)
+   mutable std::unordered_map<int, int> inv_face_indices[2];
+
+   /// compute face_indices[ftype] and inv_face_indices[type]
+   void ComputeFaceInfo(FaceType ftype) const;
 
 public:
    typedef Geometry::Constants<Geometry::SEGMENT>     seg_t;
@@ -312,6 +319,11 @@ public:
    // (true) is set in mesh_readers.cpp.
    static bool remove_unused_vertices;
 
+   /// Map from boundary or interior face indices to mesh face indices.
+   const Array<int>& GetFaceIndices(FaceType ftype) const;
+   /// Inverse of the map FaceIndices(ftype)
+   const std::unordered_map<int, int>& GetInvFaceIndices(FaceType ftype) const;
+
 protected:
    Operation last_operation;
 

tests/unit/CMakeLists.txt

@@ -22,6 +22,7 @@ set(UNIT_TESTS_SRCS
   dfem/test_mass.cpp
   general/test_array.cpp
   general/test_reduction.cpp
+  general/test_scan.cpp
   general/test_arrays_by_name.cpp
   general/test_error.cpp
   general/test_mem.cpp

tests/unit/general/test_scan.cpp

@@ -0,0 +1,102 @@
+// 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 <algorithm>
+#include <limits>
+
+#include "mfem.hpp"
+#include "unit_tests.hpp"
+
+// must be included after mfem.hpp
+#include "general/scan.hpp"
+
+using namespace mfem;
+
+TEST_CASE("Inclusive Scan", "[Scan],[GPU]")
+{
+   Array<char> workspace;
+   Array<int> a(10);
+
+   for (int use_dev = 0; use_dev < 2; ++use_dev)
+   {
+      CAPTURE(use_dev);
+      a.HostReadWrite();
+      for (int i = 0; i < a.Size(); ++i)
+      {
+         a[i] = i;
+      }
+      auto dptr = a.ReadWrite(use_dev);
+      InclusiveScan(use_dev, dptr, dptr, a.Size(), workspace);
+      a.HostRead();
+      for (int i = 0; i < a.Size(); ++i)
+      {
+         int expected = (i + 1) * i / 2;
+         CAPTURE(i);
+         REQUIRE(a[i] == expected);
+      }
+      a.HostReadWrite();
+      for (int i = 0; i < a.Size(); ++i)
+      {
+         a[i] = i + 1;
+      }
+      a.ReadWrite(use_dev);
+      InclusiveScan(use_dev, dptr, dptr, a.Size(), workspace, std::multiplies<> {});
+      a.HostRead();
+      int expected = 1;
+      for (int i = 0; i < a.Size(); ++i)
+      {
+         expected *= i + 1;
+         CAPTURE(i);
+         REQUIRE(a[i] == expected);
+      }
+   }
+}
+
+TEST_CASE("Exclusive Scan", "[Scan],[GPU]")
+{
+   Array<char> workspace;
+   Array<int> a(10);
+
+   for (int use_dev = 0; use_dev < 2; ++use_dev)
+   {
+      CAPTURE(use_dev);
+      a.HostReadWrite();
+      for (int i = 0; i < a.Size(); ++i)
+      {
+         a[i] = i;
+      }
+      auto dptr = a.ReadWrite(use_dev);
+      ExclusiveScan(use_dev, dptr, dptr, a.Size(), 5, workspace);
+      a.HostRead();
+      for (int i = 0; i < a.Size(); ++i)
+      {
+         int expected = (i + 1) * i / 2 - i + 5;
+         CAPTURE(i);
+         REQUIRE(a[i] == expected);
+      }
+      a.HostReadWrite();
+      for (int i = 0; i < a.Size(); ++i)
+      {
+         a[i] = i + 1;
+      }
+      a.ReadWrite(use_dev);
+      ExclusiveScan(use_dev, dptr, dptr, a.Size(), 5, workspace,
+                    std::multiplies<> {});
+      a.HostRead();
+      int expected = 5;
+      for (int i = 0; i < a.Size(); ++i)
+      {
+         CAPTURE(i);
+         REQUIRE(a[i] == expected);
+         expected *= i + 1;
+      }
+   }
+}

tests/unit/linalg/test_vector.cpp

@@ -248,16 +248,18 @@ TEST_CASE("Vector Sum", "[Vector],[GPU]")
    REQUIRE(sum_1 == MFEM_Approx(sum_2));
 }
 
-TEST_CASE("Vector delete at indices", "[Vector]")
+TEST_CASE("Vector delete at indices", "[Vector][GPU]")
 {
    Vector           test({0,1,2,3,4,5,6,7,8});
    Array<int> rm_indices({0,    3,4,  6,  8});
    Vector         result({  1,2,    5,  7  });
 
+   test.UseDevice(true);
    test.DeleteAt(rm_indices);
 
    REQUIRE(test.Size() == result.Size());
 
+   test.HostReadWrite();
    for (int i = 0; i < test.Size(); i++)
    {
       CHECK(test[i] == result[i]);