Remove unnecessary SetCurvature

Fixed a missing GetRajaResource() for hip

.github/workflows/builds-and-tests.yml

@@ -142,6 +142,10 @@ jobs:
 
     continue-on-error: ${{ matrix.enzyme && true || false }}
 
+    # Enable ccache for all jobs except Windows (would need sccache).
+    env:
+      USE_CCACHE: ${{ matrix.os != 'windows-latest' }}
+
     steps:
       # Fix 'No space left on device' errors for Ubuntu builds.
       - name: Run Actions Cleaner
@@ -290,6 +294,52 @@ jobs:
           echo "OMPI_CC=$LLVM_PREFIX/bin/clang" >> $GITHUB_ENV
           echo "OMPI_CXX=$LLVM_PREFIX/bin/clang++" >> $GITHUB_ENV
 
+      # Restore the compiler cache (ccache). The key embeds the run id, so new
+      # runs save a fresh snapshot; the restore-keys prefix warm-starts from the
+      # most recent prior run (incl. the base branch for PRs).
+      - name: cache ccache
+        if: ${{ env.USE_CCACHE == 'true' }}
+        uses: actions/cache@v5
+        with:
+          path: .ccache
+          key: ccache-${{ matrix.os }}-${{ matrix.build-system }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.hypre-target }}-${{ matrix.precision }}${{ matrix.enzyme && '-enzyme' || '' }}-${{ github.run_id }}
+          restore-keys: |
+            ccache-${{ matrix.os }}-${{ matrix.build-system }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.hypre-target }}-${{ matrix.precision }}${{ matrix.enzyme && '-enzyme' || '' }}-
+
+      # Configure ccache and select how it is injected into the MFEM build:
+      # - make:  set CXX="ccache g++"; for MPI, OMPI_CXX="ccache g++" so mpicxx
+      #          runs ccache around g++ (not ccache around the mpicxx wrapper).
+      # - cmake: set CMAKE_<LANG>_COMPILER_LAUNCHER=ccache.
+      # - enzyme: wrap the brew clang++ via OMPI_CXX.
+      # The chosen options are passed through build-mfem's 'config-options'
+      # input (see the build step below).
+      - name: configure ccache
+        if: ${{ env.USE_CCACHE == 'true' }}
+        run: |
+          command -v ccache >/dev/null 2>&1 || {
+            if [[ "${{ runner.os }}" == "Linux" ]]; then
+              sudo apt-get update && sudo apt-get install -y ccache
+            else
+              brew install ccache
+            fi
+          }
+          echo "CCACHE_DIR=${{ github.workspace }}/.ccache" >> $GITHUB_ENV
+          echo "CCACHE_MAXSIZE=1G" >> $GITHUB_ENV
+          echo "CCACHE_COMPILERCHECK=content" >> $GITHUB_ENV
+          # Ignore header timestamps (restamped by each checkout) so direct mode hits.
+          echo "CCACHE_SLOPPINESS=include_file_mtime,include_file_ctime,time_macros" >> $GITHUB_ENV
+          # Hash absolute paths relative to the workspace.
+          echo "CCACHE_BASEDIR=${{ github.workspace }}" >> $GITHUB_ENV
+          if [[ "${{ matrix.enzyme }}" == "true" ]]; then
+            echo "OMPI_CXX=ccache $LLVM_PREFIX/bin/clang++" >> $GITHUB_ENV
+          elif [[ "${{ matrix.build-system }}" == "cmake" ]]; then
+            echo 'CCACHE_CONFIG_OPTS=-DCMAKE_CXX_COMPILER_LAUNCHER=ccache -DCMAKE_C_COMPILER_LAUNCHER=ccache' >> $GITHUB_ENV
+          else
+            echo "OMPI_CXX=ccache g++" >> $GITHUB_ENV
+            echo 'CCACHE_CONFIG_OPTS=CXX="ccache g++" MPICXX="mpicxx"' >> $GITHUB_ENV
+          fi
+        shell: bash
+
       # MFEM build and test
       - name: build
         uses: mfem/github-actions/build-mfem@v2.7
@@ -305,9 +355,14 @@ jobs:
           metis-dir: ${{ env.METIS_TOP_DIR }}
           mfem-dir: ${{ env.MFEM_TOP_DIR }}
           precision: ${{ matrix.precision }}
-          config-options: ${{ matrix.config-opts }}
+          config-options: ${{ matrix.config-opts }} ${{ env.CCACHE_CONFIG_OPTS }}
           library-only: ${{ matrix.target == 'dbg' && matrix.os != 'ubuntu-latest' }}
 
+      - name: ccache stats
+        if: ${{ env.USE_CCACHE == 'true' }}
+        run: ccache -s
+        shell: bash
+
       # Run checks (and only checks) on debug targets
       - name: checks
         if: matrix.build-system == 'make' && matrix.target == 'dbg'

.github/workflows/cleanup-pr-caches.yml

@@ -0,0 +1,42 @@
+# 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.
+---
+# A closed PR's caches can never be restored again, so delete them to free
+# space against the 10 GB per-repo cache limit.
+name: Cleanup PR caches
+
+on:
+  pull_request:
+    types: [closed]
+
+permissions:
+  actions: write
+
+jobs:
+  cleanup:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Delete caches for the closed PR
+        env:
+          GH_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+          GH_REPO: ${{ github.repository }}
+          PR_REF: refs/pull/${{ github.event.pull_request.number }}/merge
+        run: |
+          echo "Deleting caches for $PR_REF"
+          while :; do
+            ids=$(gh cache list --ref "$PR_REF" --limit 100 --json id --jq '.[].id')
+            [ -n "$ids" ] || break
+            echo "$ids" | while read -r id; do
+              [ -n "$id" ] || continue
+              echo "Deleting cache $id"
+              gh cache delete "$id" || echo "  (already gone)"
+            done
+          done

.github/workflows/repo-check.yml

@@ -13,6 +13,7 @@ name: "Checks"
 
 permissions:
   actions: write
+  pull-requests: read
 
 on:
   push:
@@ -29,6 +30,11 @@ concurrency:
 # by checking if the workflow trigger is 'push' ("github.event_name == 'push'")
 # and if we are in a fork ("github.event.pull_request.head.repo.full_name !=
 # github.repository").
+#
+# The logic for the branch-history check is slightly different, since that check
+# also inspects the PR's labels to allow for overriding failures. In this case,
+# we run on all 'pull_request' triggers, but only run for 'push' triggers that
+# do not correspond to any open PRs.
 
 jobs:
   file-headers-check:
@@ -128,10 +134,7 @@ jobs:
 
   branch-history:
     if: |
-      github.ref != 'refs/heads/next' &&
-      github.ref != 'refs/heads/master' &&
-      (github.event_name == 'push' ||
-       github.event.pull_request.head.repo.full_name != github.repository)
+      github.ref != 'refs/heads/next' && github.ref != 'refs/heads/master'
     runs-on: ubuntu-latest
     steps:
       - name: checkout mfem
@@ -139,7 +142,27 @@ jobs:
         with:
           fetch-depth: 0
 
+      - name: check for pull request
+        id: check_pr
+        if: github.event_name == 'push'
+        env:
+          GH_TOKEN: ${{ github.token }}
+        run: |
+          pr_exists=$(gh pr list --repo "$GITHUB_REPOSITORY" \
+            --head "$GITHUB_REF_NAME" \
+            --state open \
+            --json number \
+            --jq 'length > 0')
+          echo "pr_exists=$pr_exists" >> "$GITHUB_OUTPUT"
+
       - name: branch-history
+        id: branch_history
+        if: |
+          (github.event_name == 'pull_request' ||
+           github.event_name == 'workflow_dispatch' ||
+           steps.check_pr.outputs.pr_exists == 'false')
+        continue-on-error: ${{ contains(github.event.pull_request.labels.*.name,
+                                        'branch-history-override') }}
         run: |
           # We override origin to make sure we point to the main repo.
           # This is to have consistent test results on PRs from forks.
@@ -147,3 +170,9 @@ jobs:
           git remote add origin https://github.com/mfem/mfem.git
           git checkout -b gh-actions-branch-history
           ./config/githooks/pre-push --history
+
+      - name: report branch-history override
+        if: steps.branch_history.outcome == 'failure'
+        run: |
+          echo "::warning::branch-history check failed, but the" \
+            "'branch-history-override' label is set."

config/githooks/README.md

@@ -39,3 +39,8 @@ when a picture was added for documentation.
 If that is the case, make sure the failure is indeed justified, and rerun the
 push command with the `--no-verify` option. This will skip the hooks, allowing
 you to push those changes.
+
+The `branch-history` check is run automatically through GitHub Actions. If a
+branch is known to have a large number of changes that are legitimate, the
+check can be overridden by setting  the label 'branch-history-override' on the
+pull request.

doc/CodeDocumentation.dox

@@ -119,6 +119,8 @@ namespace mfem {
  * - <a class="el" href="ex40p_8cpp_source.html">Example 40p</a>: parallel eikonal equation
  * - <a class="el" href="ex41_8cpp_source.html">Example 41</a>: DG/CG IMEX time-dependent advection-diffusion
  * - <a class="el" href="ex41p_8cpp_source.html">Example 41p</a>: parallel DG/CG IMEX time-dependent advection-diffusion
+ * - <a class="el" href="ex42_8cpp_source.html">Example 42</a>: clamped biharmonic equation
+ * - <a class="el" href="ex42p_8cpp_source.html">Example 42p</a>: parallel clamped biharmonic equation
  *
  * <H4>AmgX Examples</H4>
  * - Variants of Examples

examples/CMakeLists.txt

@@ -47,6 +47,7 @@ list(APPEND ALL_EXE_SRCS
   ex39.cpp
   ex40.cpp
   ex41.cpp
+  ex42.cpp
   )
 
 if (MFEM_USE_MPI)
@@ -91,6 +92,7 @@ if (MFEM_USE_MPI)
     ex39p.cpp
     ex40p.cpp
     ex41p.cpp
+    ex42p.cpp
   )
 endif()
 

examples/ex42.cpp

@@ -0,0 +1,311 @@
+//                                MFEM Example 42
+//
+// Compile with: make ex42p
+//
+// Sample runs: ex42 -r 3
+//              ex42 -m ../data/hexagon.mesh -r 3 -o 3
+//              ex42 -m ../data/square-mixed.mesh -r 2 -eta 5
+//              ex42 -m ../data/l-shape.mesh -r 3
+//
+// Description: This example solves the clamped biharmonic equation,
+//
+//                      ∇⁴u = f in Ω,  u = 0 and ∇u⋅n = 0 on ∂Ω,
+//
+//              in 2D using just H¹-conforming finite elements by employing the interior penalty
+//              method outlined in [1]. This example demonstrates an approach to solving higher-order
+//              PDEs in MFEM and implementation of custom domain and face integrators to solve the
+//              weak form
+//
+//                      (H(u), H(v))_D - <{{n^T⋅H(u)⋅n}}, [[∇v⋅n]]>_F
+//                                     - <{{n^T⋅H(v)⋅n}}, [[∇u⋅n]]>_F
+//                                     + (η/h_e)<[[∇u⋅n]], [[∇v⋅n]]>_F = (f,v)_D ,
+//
+//               where (⋅,⋅)_D is domain integration, <⋅,⋅>_F is face
+//               integration, and H(⋅) is the Hessian.
+//
+//              [1] Brenner, Susanne & Sung, Li-yeng. (2005). C0 Interior Penalty Methods
+//                  for Fourth Order Elliptic Boundary Value Problems on Polygonal Domains.
+//                  Journal of Scientific Computing. 22-23. 83-118. 10.1007/s10915-004-4135-7.
+
+#include <mfem.hpp>
+
+using namespace mfem;
+using namespace std;
+
+class BiharmonicIntegrator : public BilinearFormIntegrator
+{
+private:
+   Coefficient &D;
+
+   inline static const Vector factors_2D{1.0, 2.0, 1.0};
+   mutable DenseMatrix hessian;
+   mutable Vector factors;
+public:
+   BiharmonicIntegrator(Coefficient &D_) : D(D_) {}
+
+   void AssembleElementMatrix(const FiniteElement &el,
+                              ElementTransformation &Trans, DenseMatrix &elmat) override;
+};
+
+class C0InteriorPenaltyIntegrator : public BilinearFormIntegrator
+{
+private:
+   const double eta;
+
+   mutable Vector normal[2], dnshape[2], nv[2], nd2nshape[2];
+   mutable DenseMatrix dshape[2], hessian[2], blockJ[2][2], blockC[2][2], elmatJ_p,
+           elmatC_p;
+public:
+   C0InteriorPenaltyIntegrator(double eta_) : eta(eta_) {};
+
+   void AssembleFaceMatrix(const FiniteElement &el1, const FiniteElement &el2,
+                           FaceElementTransformations &Trans, DenseMatrix &elmat) override;
+};
+
+int main(int argc, char *argv[])
+{
+   // Parse command line args
+   const char *mesh_file = "../data/star.mesh";
+   int order = 2;
+   int ref_levels = 0;
+   real_t eta = 10;
+   int max_it = 10000;
+   bool visualization = true;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&ref_levels, "-r", "--refs",
+                  "Number of h-refinements.");
+   args.AddOption(&eta, "-eta", "--penalty-coeff",
+                  "Penalty coefficient.");
+   args.AddOption(&max_it, "-mi", "--max-it",
+                  "Maximum number of iterations");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // Read the mesh file
+   Mesh mesh(mesh_file);
+   int dim = mesh.Dimension();
+   MFEM_ASSERT(dim == 2, "This example only supports 2D meshes.");
+
+   // Refine the mesh
+   for (int i = 0; i < ref_levels; i++)
+   {
+      mesh.UniformRefinement();
+   }
+
+   // Initialize the FE collection and FiniteElementSpace
+   H1_FECollection fe_coll(order, dim);
+   FiniteElementSpace fespace(&mesh, &fe_coll, 1);
+
+   // Get the degrees-of-freedom (DOFs) associated with the sides of the panel
+   Array<int> all_bdr_marker(mesh.bdr_attributes.Size());
+   all_bdr_marker = 1; // Mark all sides
+   Array<int> ess_tdof_list;
+   fespace.GetEssentialTrueDofs(all_bdr_marker, ess_tdof_list);
+
+   ConstantCoefficient one(1.0);
+
+   // Initialize the bilinear form
+   BilinearForm a(&fespace);
+   a.AddDomainIntegrator(new BiharmonicIntegrator(one));
+   a.AddInteriorFaceIntegrator(new C0InteriorPenaltyIntegrator(eta));
+   a.AddBdrFaceIntegrator(new C0InteriorPenaltyIntegrator(eta));
+   a.Assemble();
+
+   // Initialize the linear form f=1.0
+   LinearForm b(&fespace);
+   b.AddDomainIntegrator(new DomainLFIntegrator(one));
+   b.Assemble();
+
+   // Form the linear system
+   GridFunction x(&fespace);
+   x = 0.0; // initial guess
+   SparseMatrix A;
+   Vector B, X;
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+
+   // Solve the system using CG with symmetric Gauss-Seidel preconditioner
+   GSSmoother M(A);
+   PCG(A, M, B, X, 1, max_it, 1e-12, 0.0);
+
+   // Recover solution and visualize
+   a.RecoverFEMSolution(X, B, x);
+
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int visport    = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock.precision(8);
+      sol_sock << "solution\n" << mesh << x << flush;
+   }
+
+   return 0;
+}
+
+
+void BiharmonicIntegrator::AssembleElementMatrix(const FiniteElement &el,
+                                                 ElementTransformation &Trans, DenseMatrix &elmat)
+{
+   int ndof = el.GetDof();
+   int dim = el.GetDim();
+
+   MFEM_ASSERT(dim == 2, "Dimension must be 2.");
+
+   hessian.SetSize(ndof, dim * (dim + 1) / 2);
+   elmat.SetSize(ndof);
+   factors.SetSize(dim * (dim + 1) / 2);
+
+   elmat = 0.0;
+
+   const IntegrationRule *ir = GetIntegrationRule(el, Trans);
+   if (ir == NULL)
+   {
+      int order = 2*el.GetOrder();
+      ir = &IntRules.Get(el.GetGeomType(), order);
+   }
+
+   for (int i = 0; i < ir->GetNPoints(); i++)
+   {
+      const mfem::IntegrationPoint &ip = ir->IntPoint(i);
+      Trans.SetIntPoint(&ip);
+
+      el.CalcPhysHessian(Trans, hessian);
+
+      factors = factors_2D;
+      factors *= D.Eval(Trans, ip) * ip.weight * Trans.Weight();
+
+      AddMultADAt(hessian, factors, elmat);
+   }
+}
+
+void C0InteriorPenaltyIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
+                                                     const FiniteElement &el2, FaceElementTransformations &Trans, DenseMatrix &elmat)
+{
+   int dim = el1.GetDim();
+   MFEM_ASSERT(dim == 2, "Dimension must be 2.");
+
+   int ndof[2] = {el1.GetDof(), 0};
+   int num_elems = 1;
+   if (Trans.Elem2No >= 0)
+   {
+      ndof[1] = el2.GetDof();
+      num_elems++;
+   }
+
+   for (int i = 0; i < num_elems; i++)
+   {
+      normal[i].SetSize(dim);
+      dshape[i].SetSize(ndof[i], dim);
+      hessian[i].SetSize(ndof[i], dim * (dim + 1) / 2);
+      nv[i].SetSize(dim * (dim + 1) / 2);
+      dnshape[i].SetSize(ndof[i]);
+      nd2nshape[i].SetSize(ndof[i]);
+   }
+
+   for (int i = 0; i < num_elems; i++)
+   {
+      for (int j = 0; j < num_elems; j++)
+      {
+         blockJ[i][j].SetSize(ndof[i], ndof[j]);
+         blockC[i][j].SetSize(ndof[i], ndof[j]);
+      }
+   }
+
+   elmatJ_p.SetSize(ndof[0] + ndof[1]);
+   elmatC_p.SetSize(ndof[0] + ndof[1]);
+   elmat.SetSize(ndof[0] + ndof[1]);
+   elmat = 0.0;
+
+   const IntegrationRule *ir = IntRule;
+   if (ir == NULL)
+   {
+      int order = 2 * max(el1.GetOrder(), ndof[1] ? el2.GetOrder() : 0);
+      ir = &IntRules.Get(Trans.GetGeometryType(), order);
+   }
+
+   // Compute edge length
+   double h_e  = 0.0;
+   for (int p = 0; p < ir->GetNPoints(); p++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(p);
+      Trans.SetAllIntPoints(&ip);
+      h_e += ip.weight * Trans.Weight();
+   }
+
+   const FiniteElement *els[2] = {&el1, &el2};
+   ElementTransformation *el_trans[2] = {Trans.Elem1, Trans.Elem2};
+
+   for (int p = 0; p < ir->GetNPoints(); p++)
+   {
+      elmatJ_p = 0.0;
+      elmatC_p = 0.0;
+
+      const IntegrationPoint &ip = ir->IntPoint(p);
+
+      // Set the integration point in the face and the neighboring elements
+      Trans.SetAllIntPoints(&ip);
+
+      // Compute normal gradients + Hessians
+      for (int i = 0; i < num_elems; i++)
+      {
+         if (i == 0)
+         {
+            CalcOrtho(Trans.Jacobian(), normal[i]);
+            normal[i] /= normal[i].Norml2();
+         }
+         else
+         {
+            normal[i] = normal[0];
+            normal[i] *= -1;
+         }
+         els[i]->CalcPhysDShape(*el_trans[i], dshape[i]);
+         els[i]->CalcPhysHessian(*el_trans[i], hessian[i]);
+         dshape[i].Mult(normal[i], dnshape[i]);
+         nv[i][0] = normal[i][0]*normal[i][0];
+         nv[i][1] = 2*normal[i][0]*normal[i][1];
+         nv[i][2] = normal[i][1]*normal[i][1];
+         hessian[i].Mult(nv[i], nd2nshape[i]);
+      }
+
+      // Compute blocks
+      for (int i = 0; i < num_elems; i++)
+      {
+         for (int j = 0; j < num_elems; j++)
+         {
+            blockJ[i][j] = 0.0;
+            blockC[i][j] = 0.0;
+            AddMult_a_VWt(-1.0, dnshape[i], nd2nshape[j], blockJ[i][j]);
+            elmatJ_p.SetSubMatrix(i*ndof[0], j*ndof[0], blockJ[i][j]);
+
+            AddMult_a_VWt(eta/h_e, dnshape[i], dnshape[j], blockC[i][j]);
+            elmatC_p.SetSubMatrix(i*ndof[0], j*ndof[0], blockC[i][j]);
+         }
+      }
+
+      // Symmetrize the jump term
+      elmatJ_p.Symmetrize();
+      if (!ndof[1])
+      {
+         elmatJ_p *= 2;
+      }
+
+      // Add penalty term
+      elmatJ_p += elmatC_p;
+      elmatJ_p *= ip.weight * Trans.Weight();
+      elmat += elmatJ_p;
+   }
+}

examples/ex42p.cpp

@@ -0,0 +1,331 @@
+//                       MFEM Example 42 - Parallel Version
+//
+// Compile with: make ex42p
+//
+// Sample runs: mpirun -np 4 ex42p -r 3
+//              mpirun -np 4 ex42p -m ../data/hexagon.mesh -r 3 -o 3
+//              mpirun -np 4 ex42p -m ../data/square-mixed.mesh -r 2 -eta 5
+//              mpirun -np 4 ex42p -m ../data/l-shape.mesh -r 3
+//
+// Description: This example solves the clamped biharmonic equation,
+//
+//                      ∇⁴u = f in Ω,  u = 0 and ∇u⋅n = 0 on ∂Ω,
+//
+//              in 2D using just H¹-conforming finite elements by employing the interior penalty
+//              method outlined in [1]. This example demonstrates an approach to solving higher-order
+//              PDEs in MFEM and implementation of custom domain and face integrators to solve the
+//              weak form
+//
+//                      (H(u), H(v))_D - <{{n^T⋅H(u)⋅n}}, [[∇v⋅n]]>_F
+//                                     - <{{n^T⋅H(v)⋅n}}, [[∇u⋅n]]>_F
+//                                     + (η/h_e)<[[∇u⋅n]], [[∇v⋅n]]>_F = (f,v)_D ,
+//
+//               where (⋅,⋅)_D is domain integration, <⋅,⋅>_F is face
+//               integration, and H(⋅) is the Hessian.
+//
+//              [1] Brenner, Susanne & Sung, Li-yeng. (2005). C0 Interior Penalty Methods
+//                  for Fourth Order Elliptic Boundary Value Problems on Polygonal Domains.
+//                  Journal of Scientific Computing. 22-23. 83-118. 10.1007/s10915-004-4135-7.
+
+#include <mfem.hpp>
+
+using namespace mfem;
+using namespace std;
+
+class BiharmonicIntegrator : public BilinearFormIntegrator
+{
+private:
+   Coefficient &D;
+
+   inline static const Vector factors_2D{1.0, 2.0, 1.0};
+   mutable DenseMatrix hessian;
+   mutable Vector factors;
+public:
+   BiharmonicIntegrator(Coefficient &D_) : D(D_) {}
+
+   void AssembleElementMatrix(const FiniteElement &el,
+                              ElementTransformation &Trans, DenseMatrix &elmat) override;
+};
+
+class C0InteriorPenaltyIntegrator : public BilinearFormIntegrator
+{
+private:
+   const double eta;
+
+   mutable Vector normal[2], dnshape[2], nv[2], nd2nshape[2];
+   mutable DenseMatrix dshape[2], hessian[2], blockJ[2][2], blockC[2][2], elmatJ_p,
+           elmatC_p;
+public:
+   C0InteriorPenaltyIntegrator(double eta_) : eta(eta_) {};
+
+   void AssembleFaceMatrix(const FiniteElement &el1, const FiniteElement &el2,
+                           FaceElementTransformations &Trans, DenseMatrix &elmat) override;
+};
+
+int main(int argc, char *argv[])
+{
+   // Initialize MPI and HYPRE.
+   Mpi::Init(argc, argv);
+   int size = Mpi::WorldSize();
+   int rank = Mpi::WorldRank();
+   Hypre::Init();
+
+   // Parse command line args
+   const char *mesh_file = "../data/star.mesh";
+   int order = 2;
+   int ref_levels = 0;
+   real_t eta = 10;
+   int max_it = 10000;
+   bool visualization = true;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&ref_levels, "-r", "--refs",
+                  "Number of h-refinements.");
+   args.AddOption(&eta, "-eta", "--penalty-coeff",
+                  "Penalty coefficient.");
+   args.AddOption(&max_it, "-mi", "--max-it",
+                  "Maximum number of iterations");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   if (rank == 0)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // Read the mesh file
+   Mesh mesh(mesh_file);
+   int dim = mesh.Dimension();
+   MFEM_ASSERT(dim == 2, "This example only supports 2D meshes.");
+
+   // Refine the mesh
+   for (int i = 0; i < ref_levels; i++)
+   {
+      mesh.UniformRefinement();
+   }
+
+   // Partition the mesh
+   ParMesh pmesh(MPI_COMM_WORLD, mesh);
+   mesh.Clear();
+
+   // Initialize the FE collection and FiniteElementSpace
+   H1_FECollection fe_coll(order, dim);
+   ParFiniteElementSpace fespace(&pmesh, &fe_coll, 1);
+
+   // Get the degrees-of-freedom (DOFs) associated with the sides of the panel
+   Array<int> all_bdr_marker(pmesh.bdr_attributes.Size());
+   all_bdr_marker = 1; // Mark all sides
+   Array<int> ess_tdof_list;
+   fespace.GetEssentialTrueDofs(all_bdr_marker, ess_tdof_list);
+
+   ConstantCoefficient one(1.0);
+
+   // Initialize the bilinear form
+   ParBilinearForm a(&fespace);
+   a.AddDomainIntegrator(new BiharmonicIntegrator(one));
+   a.AddInteriorFaceIntegrator(new C0InteriorPenaltyIntegrator(eta));
+   a.AddBdrFaceIntegrator(new C0InteriorPenaltyIntegrator(eta));
+   a.Assemble();
+
+   // Initialize the linear form f=1.0
+   ParLinearForm b(&fespace);
+   b.AddDomainIntegrator(new DomainLFIntegrator(one));
+   b.Assemble();
+
+   // Form the linear system
+   ParGridFunction x(&fespace);
+   x = 0.0; // initial guess
+   HypreParMatrix A;
+   Vector B, X;
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+
+   // Solve the system using CG with hypre's BoomerAMG preconditioner
+   HypreBoomerAMG amg(A);
+   CGSolver cg(MPI_COMM_WORLD);
+   cg.SetRelTol(1e-12);
+   cg.SetMaxIter(max_it);
+   cg.SetPrintLevel(1);
+   cg.SetPreconditioner(amg);
+   cg.SetOperator(A);
+   cg.Mult(B, X);
+
+   // Recover solution and visualize
+   a.RecoverFEMSolution(X, B, x);
+
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int visport    = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock << "parallel " << size << " " << rank << "\n";
+      sol_sock.precision(8);
+      sol_sock << "solution\n" << pmesh << x << flush;
+   }
+
+   return 0;
+}
+
+
+void BiharmonicIntegrator::AssembleElementMatrix(const FiniteElement &el,
+                                                 ElementTransformation &Trans, DenseMatrix &elmat)
+{
+   int ndof = el.GetDof();
+   int dim = el.GetDim();
+
+   MFEM_ASSERT(dim == 2, "Dimension must be 2.");
+
+   hessian.SetSize(ndof, dim * (dim + 1) / 2);
+   elmat.SetSize(ndof);
+   factors.SetSize(dim * (dim + 1) / 2);
+
+   elmat = 0.0;
+
+   const IntegrationRule *ir = GetIntegrationRule(el, Trans);
+   if (ir == NULL)
+   {
+      int order = 2*el.GetOrder();
+      ir = &IntRules.Get(el.GetGeomType(), order);
+   }
+
+   for (int i = 0; i < ir->GetNPoints(); i++)
+   {
+      const mfem::IntegrationPoint &ip = ir->IntPoint(i);
+      Trans.SetIntPoint(&ip);
+
+      el.CalcPhysHessian(Trans, hessian);
+
+      factors = factors_2D;
+      factors *= D.Eval(Trans, ip) * ip.weight * Trans.Weight();
+
+      AddMultADAt(hessian, factors, elmat);
+   }
+}
+
+void C0InteriorPenaltyIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
+                                                     const FiniteElement &el2, FaceElementTransformations &Trans, DenseMatrix &elmat)
+{
+   int dim = el1.GetDim();
+   MFEM_ASSERT(dim == 2, "Dimension must be 2.");
+
+   int ndof[2] = {el1.GetDof(), 0};
+   int num_elems = 1;
+   if (Trans.Elem2No >= 0)
+   {
+      ndof[1] = el2.GetDof();
+      num_elems++;
+   }
+
+   for (int i = 0; i < num_elems; i++)
+   {
+      normal[i].SetSize(dim);
+      dshape[i].SetSize(ndof[i], dim);
+      hessian[i].SetSize(ndof[i], dim * (dim + 1) / 2);
+      nv[i].SetSize(dim * (dim + 1) / 2);
+      dnshape[i].SetSize(ndof[i]);
+      nd2nshape[i].SetSize(ndof[i]);
+   }
+
+   for (int i = 0; i < num_elems; i++)
+   {
+      for (int j = 0; j < num_elems; j++)
+      {
+         blockJ[i][j].SetSize(ndof[i], ndof[j]);
+         blockC[i][j].SetSize(ndof[i], ndof[j]);
+      }
+   }
+
+   elmatJ_p.SetSize(ndof[0] + ndof[1]);
+   elmatC_p.SetSize(ndof[0] + ndof[1]);
+   elmat.SetSize(ndof[0] + ndof[1]);
+   elmat = 0.0;
+
+   const IntegrationRule *ir = IntRule;
+   if (ir == NULL)
+   {
+      int order = 2 * max(el1.GetOrder(), ndof[1] ? el2.GetOrder() : 0);
+      ir = &IntRules.Get(Trans.GetGeometryType(), order);
+   }
+
+   // Compute edge length
+   double h_e  = 0.0;
+   for (int p = 0; p < ir->GetNPoints(); p++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(p);
+      Trans.SetAllIntPoints(&ip);
+      h_e += ip.weight * Trans.Weight();
+   }
+
+   const FiniteElement *els[2] = {&el1, &el2};
+   ElementTransformation *el_trans[2] = {Trans.Elem1, Trans.Elem2};
+
+   for (int p = 0; p < ir->GetNPoints(); p++)
+   {
+      elmatJ_p = 0.0;
+      elmatC_p = 0.0;
+
+      const IntegrationPoint &ip = ir->IntPoint(p);
+
+      // Set the integration point in the face and the neighboring elements
+      Trans.SetAllIntPoints(&ip);
+
+      // Compute normal gradients + Hessians
+      for (int i = 0; i < num_elems; i++)
+      {
+         if (i == 0)
+         {
+            CalcOrtho(Trans.Jacobian(), normal[i]);
+            normal[i] /= normal[i].Norml2();
+         }
+         else
+         {
+            normal[i] = normal[0];
+            normal[i] *= -1;
+         }
+         els[i]->CalcPhysDShape(*el_trans[i], dshape[i]);
+         els[i]->CalcPhysHessian(*el_trans[i], hessian[i]);
+         dshape[i].Mult(normal[i], dnshape[i]);
+         nv[i][0] = normal[i][0]*normal[i][0];
+         nv[i][1] = 2*normal[i][0]*normal[i][1];
+         nv[i][2] = normal[i][1]*normal[i][1];
+         hessian[i].Mult(nv[i], nd2nshape[i]);
+      }
+
+      // Compute blocks
+      for (int i = 0; i < num_elems; i++)
+      {
+         for (int j = 0; j < num_elems; j++)
+         {
+            blockJ[i][j] = 0.0;
+            blockC[i][j] = 0.0;
+            AddMult_a_VWt(-1.0, dnshape[i], nd2nshape[j], blockJ[i][j]);
+            elmatJ_p.SetSubMatrix(i*ndof[0], j*ndof[0], blockJ[i][j]);
+
+            AddMult_a_VWt(eta/h_e, dnshape[i], dnshape[j], blockC[i][j]);
+            elmatC_p.SetSubMatrix(i*ndof[0], j*ndof[0], blockC[i][j]);
+         }
+      }
+
+      // Symmetrize the jump term
+      elmatJ_p.Symmetrize();
+      if (!ndof[1])
+      {
+         elmatJ_p *= 2;
+      }
+
+      // Add penalty term
+      elmatJ_p += elmatC_p;
+      elmatJ_p *= ip.weight * Trans.Weight();
+      elmat += elmatJ_p;
+   }
+}

fem/datacollection.cpp

@@ -809,7 +809,7 @@ ParaViewDataCollectionBase::ParaViewDataCollectionBase(
 
 void ParaViewDataCollectionBase::SetLevelsOfDetail(int levels_of_detail_)
 {
-   levels_of_detail = levels_of_detail_;
+   levels_of_detail = std::max(levels_of_detail_, 1);
 }
 
 void ParaViewDataCollectionBase::SetHighOrderOutput(bool high_order_output_)

fem/datacollection.hpp

@@ -25,35 +25,21 @@
 namespace mfem
 {
 
-/// Lightweight adaptor over an std::map from type K to type to V
-template<typename K, typename V,
-         typename = typename std::enable_if<std::is_default_constructible<V>::value>::type>
-class GenericFieldMap
+/// Lightweight adaptor over an std::map from strings to pointer to T
+template<typename T>
+class NamedFieldsMap
 {
-private:
-   static constexpr bool ValueIsPointer = std::is_pointer<V>::value;
-
 public:
-   typedef std::map<K, V> MapType;
+   typedef std::map<std::string, T*> MapType;
    typedef typename MapType::iterator iterator;
    typedef typename MapType::const_iterator const_iterator;
 
-   /// Register field @a field with name @a key
-   /// Only enabled if the template parameter V is not a pointer
-   template<typename = std::enable_if<!ValueIsPointer, bool>>
-   void Register(const K& key, V field)
+   /// Register field @a field with name @a fname
+   /** Replace existing field associated with @a fname (and optionally
+       delete associated pointer if @a own_data is true) */
+   void Register(const std::string& fname, T* field, bool own_data)
    {
-      field_map[key] = field;
-   }
-
-   /// Register field @a field with name @a key
-   /** Replace existing field associated with @a key (and optionally
-       delete associated pointer if @a own_data is true).
-       Only enabled if the template parameter V is a pointer*/
-   template<typename = std::enable_if<ValueIsPointer, bool>>
-   void Register(const K& key, V field, bool own_data)
-   {
-      V& ref = field_map[key];
+      T*& ref = field_map[fname];
       if (own_data)
       {
          delete ref; // if newly allocated -> ref is null -> OK
@@ -61,40 +47,23 @@ public:
       ref = field;
    }
 
-   /// Unregister association between field @a field and name @a key
-   /// Only enabled if the template parameter V is not a pointer
-   template<typename = std::enable_if<!ValueIsPointer, bool>>
-   void Deregister(const K& key)
+   /// Unregister association between field @a field and name @a fname
+   /** Optionally delete associated pointer if @a own_data is true */
+   void Deregister(const std::string& fname, bool own_data)
    {
-      iterator it = field_map.find(key);
-      if ( it != field_map.end() )
-      {
-         field_map.erase(it);
-      }
-   }
-
-   /// Unregister association between field @a field and name @a key
-   /** Optionally delete associated pointer if @a own_data is true.
-       Only enabled if the template parameter V is a pointer */
-   template<typename = std::enable_if<ValueIsPointer, bool>>
-   void Deregister(const K& key, bool own_data)
-   {
-      iterator it = field_map.find(key);
+      iterator it = field_map.find(fname);
       if ( it != field_map.end() )
       {
          if (own_data)
          {
             delete it->second;
-            it->second = nullptr;
          }
          field_map.erase(it);
       }
    }
 
    /// Clear all associations between names and fields
-   /** Delete associated pointers when @a own_data is true.
-       Only enabled if the template parameter V is a pointer */
-   template<typename = std::enable_if<ValueIsPointer, bool>>
+   /** Delete associated pointers when @a own_data is true */
    void DeleteData(bool own_data)
    {
       for (iterator it = field_map.begin(); it != field_map.end(); ++it)
@@ -107,37 +76,22 @@ public:
       }
    }
 
-   /// Predicate to check if a field is associated with name @a key
-   bool Has(const K& key) const
+   /// Predicate to check if a field is associated with name @a fname
+   bool Has(const std::string& fname) const
    {
-      return field_map.find(key) != field_map.end();
+      return field_map.find(fname) != field_map.end();
    }
 
-   /// Get a pointer to the field associated with name @a key
-   /** @return Field associated with @a key or NULL,
-       if value is pointer and key not found */
-   V Get(const K& key) const
+   /// Get a pointer to the field associated with name @a fname
+   /** @return Pointer to field associated with @a fname or NULL */
+   T* Get(const std::string& fname) const
    {
-      const_iterator it = field_map.find(key);
-      if (it != field_map.end())
-      {
-         return it->second;
-      }
-      else
-      {
-         if constexpr (ValueIsPointer)
-         {
-            return nullptr;
-         }
-         else
-         {
-            return V(); // Return default-constructed value for non-pointer types
-         }
-      }
+      const_iterator it = field_map.find(fname);
+      return it != field_map.end() ? it->second : NULL;
    }
 
    /// Returns a const reference to the underlying map
-   const MapType &GetMap() const { return field_map; }
+   const MapType& GetMap() const { return field_map; }
 
    /// Returns the number of registered fields
    int NumFields() const { return field_map.size(); }
@@ -152,24 +106,21 @@ public:
    /// Returns an end const iterator to the registered fields
    const_iterator end() const { return field_map.end(); }
 
-   /// Returns an iterator to the field @a key
-   iterator find(const K& key)
-   { return field_map.find(key); }
+   /// Returns an iterator to the field @a fname
+   iterator find(const std::string& fname)
+   { return field_map.find(fname); }
 
-   /// Returns a const iterator to the field @a key
-   const_iterator find(const K& key) const
-   { return field_map.find(key); }
+   /// Returns a const iterator to the field @a fname
+   const_iterator find(const std::string& fname) const
+   { return field_map.find(fname); }
 
-   /// Clears the map of registered fields
+   /// Clears the map of registered fields without reclaiming memory
    void clear() { field_map.clear(); }
 
 protected:
    MapType field_map;
 };
 
-/// Lightweight adaptor over an std::map from strings to pointer to T
-template<typename T>
-using NamedFieldsMap = GenericFieldMap<std::string, T*>;
 
 /** A class for collecting finite element data that is part of the same
     simulation. Currently, this class groups together grid functions (fields),

fem/dfem/util.hpp

@@ -671,20 +671,6 @@ public:
                     MPI_COMM_WORLD);
    }
 
-   Operator& GetGradient(const Vector &x0) const override
-   {
-      x = x0;
-      f.UseDevice(x.UseDevice());
-      xpev.UseDevice(x.UseDevice());
-
-      op.Mult(x, f);
-      const real_t xnorm_local = x.Norml2();
-      MPI_Allreduce(&xnorm_local, &xnorm, 1, MPITypeMap<real_t>::mpi_type, MPI_SUM,
-                    MPI_COMM_WORLD);
-
-      return const_cast<FDJacobian&>(*this);
-   }
-
    void Mult(const Vector &v, Vector &y) const override
    {
       // See [1] for choice of eps.
@@ -739,11 +725,11 @@ public:
 
 private:
    const Operator &op;
-   mutable Vector x, f;
+   Vector x, f;
    mutable Vector xpev;
    real_t lambda = 1.0e-6;
    real_t fixed_eps;
-   mutable real_t xnorm;
+   real_t xnorm;
 };
 
 /// @brief Find the index of a field descriptor in a vector of field descriptors.

fem/nonlinearform.hpp

@@ -224,9 +224,6 @@ public:
    /** @see GetGradient(const Vector &) */
    Operator &GetGradient(const Vector &x, bool finalize) const;
 
-   /// Suppress a warning about hiding overloaded virtual function.
-   using Operator::GetGradient;
-
    /// Update the NonlinearForm to propagate updates of the associated FE space.
    /** After calling this method, the essential boundary conditions need to be
        set again. */

general/forall.hpp

@@ -480,8 +480,8 @@ template <typename DBODY>
 void RajaHipWrap1D(const int N, DBODY &&d_body)
 {
    //true denotes asynchronous kernel
-   RAJA::forall<RAJA::hip_exec<MFEM_HIP_BLOCKS,true> >(RAJA::RangeSegment(0,N),
-                                                       d_body);
+   RAJA::forall<RAJA::hip_exec<MFEM_HIP_BLOCKS, true> >(
+      Device::GetRajaResource(), RAJA::RangeSegment(0, N), d_body);
 }
 
 template <typename DBODY>

linalg/CMakeLists.txt

@@ -27,7 +27,6 @@ list(APPEND SRCS
   handle.cpp
   matrix.cpp
   mma.cpp
-  multivector.cpp
   ode.cpp
   operator.cpp
   ordering.cpp
@@ -64,7 +63,6 @@ list(APPEND HDRS
   linalg.hpp
   matrix.hpp
   mma.hpp
-  multivector.hpp
   ode.hpp
   operator.hpp
   ordering.hpp

linalg/linalg.hpp

@@ -15,7 +15,6 @@
 // Linear algebra header file
 
 #include "vector.hpp"
-#include "multivector.hpp"
 #include "operator.hpp"
 #include "matrix.hpp"
 #include "sparsemat.hpp"

linalg/multivector.cpp

@@ -1,60 +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.
-
-#include "multivector.hpp"
-
-namespace mfem
-{
-
-MultiVector::MultiVector(const Array<int> &vector_sizes)
-{
-   SetSizes(vector_sizes);
-}
-
-MultiVector::MultiVector(const Array<int> &vector_sizes, MemoryType mt)
-{
-   SetSizes(vector_sizes, mt);
-}
-
-MultiVector::MultiVector(Vector &base, const Array<int> &vector_sizes)
-{
-   MakeRef(base, vector_sizes);
-}
-
-void MultiVector::SetSizes(const Array<int> &vector_sizes)
-{
-   blocks.resize(vector_sizes.Size());
-   for (int i = 0; i < vector_sizes.Size(); i++)
-   {
-      operator[](i).SetSize(vector_sizes[i]);
-   }
-}
-
-void MultiVector::SetSizes(const Array<int> &vector_sizes, MemoryType mt)
-{
-   blocks.resize(vector_sizes.Size());
-   for (int i = 0; i < vector_sizes.Size(); i++)
-   {
-      operator[](i).SetSize(vector_sizes[i], mt);
-   }
-}
-
-void MultiVector::MakeRef(Vector &base, const Array<int> &vector_sizes)
-{
-   blocks.resize(vector_sizes.Size());
-   for (int offset = 0, i = 0; i < vector_sizes.Size(); i++)
-   {
-      blocks[i].emplace<0>(base, offset, vector_sizes[i]);
-      offset += vector_sizes[i];
-   }
-}
-
-} // namespace mfem

linalg/multivector.hpp

@@ -1,198 +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_MULTIVECTOR_HPP
-#define MFEM_MULTIVECTOR_HPP
-
-#include "../general/array.hpp"
-#include "vector.hpp"
-#include <vector>
-#include <array>
-#include <variant>
-
-namespace mfem
-{
-
-/// Class representing an array of Vectors with generally different sizes.
-/** This class is similar to BlockVector with the following two main
-    differences:
-    - the data for the individual Vector blocks does not need to be part of one
-      big contiguous memory allocation;
-    - this class does not inherit from class Vector (as a consequence of the
-      first bullet).
-
-    Internally, each Vector block is represented as either:
-    - (default) a Vector object constructed and owned by this class; this
-      object, in turn, as any Vector object, can own its Memory allocation or
-      refer to a sub-Memory of another Memory object; or
-    - a pointer to an externally allocated Vector or classes derived from
-      Vector. */
-class MultiVector
-{
-private:
-   std::vector<std::variant<Vector,Vector*>> blocks;
-
-public:
-   /// Create an empty MultiVector with zero blocks.
-   MultiVector() = default;
-
-   /** @brief Create a MultiVector with @a num_blocks blocks. The individual
-       Vector blocks are default initialized, i.e. they all have size zero. */
-   MultiVector(int num_blocks)
-      : blocks(num_blocks) { }
-
-   /** @brief Construct a MultiVector with number of blocks and individual block
-       Vector sizes given by @a vector_sizes.
-
-       @note The memory of the individual Vector blocks is NOT initialized. */
-   MultiVector(const Array<int> &vector_sizes);
-
-   /** @brief Construct a MultiVector with number of blocks and individual block
-       Vector sizes given by @a vector_sizes. All Vector blocks use the
-       MemoryType @a mt.
-
-       @note The memory of the individual Vector blocks is NOT initialized. */
-   MultiVector(const Array<int> &vector_sizes, MemoryType mt);
-
-   /** @brief Construct a MultiVector referencing data within a given monolithic
-       Vector @a base.
-
-       With this constructor, the Memory flags of @a base and of the individual
-       Vector blocks may need to be explicitly synchronized when data is moved
-       between host and device. */
-   MultiVector(Vector &base, const Array<int> &vector_sizes);
-
-   /** @brief Construct a MultiVector referencing multiple Vectors given as
-       arguments.
-
-       The VectorTypes reference arguments are expected to be static_cast-able
-       to (Vector &) which is the case if the types are derived from Vector,
-       e.g. HypreParVector, GridFunction, etc.
-
-       With this constructor, operations on individual Vector blocks are
-       performed directly on the objects @a vs. In particular, there is no need
-       to synchronize the Memory flags of @a vs and the ones of the individual
-       Vector blocks when data is moved between host and device. */
-   template <typename... VectorTypes,
-             std::enable_if_t<
-                std::conjunction_v<
-                   std::is_convertible<VectorTypes&,Vector&>...>, bool> = true>
-   MultiVector(VectorTypes &...vs) { MakeRef(vs...); }
-
-   /// Return the number of Vectors in the MultiVector.
-   int NumBlocks() const { return blocks.size(); }
-
-   /** @brief Set the number of Vectors in the MultiVector. Existing Vector
-       blocks will remain unmodified. New Vector blocks will be default
-       initialized, i.e. they all have size zero. */
-   void SetNumBlocks(int num_blocks) { blocks.resize(num_blocks); }
-
-   /// Read-write access to the i-th Vector.
-   inline Vector &operator[](int i);
-
-   /// Read-only access to the i-th Vector.
-   inline const Vector &operator[](int i) const;
-
-   /** @brief Update the MultiVector according to the given @a vector_sizes.
-
-       This method can be used to add or remove blocks. The individual Vector
-       sizes are updated using the method Vector::SetSize(int). */
-   void SetSizes(const Array<int> &vector_sizes);
-
-   /** @brief Update the MultiVector according to the given @a vector_sizes and
-       MemoryType @a mt.
-
-       This method can be used to add or remove blocks. The individual Vector
-       sizes and MemoryType are updated using the method
-       Vector::SetSize(int, MemoryType). */
-   void SetSizes(const Array<int> &vector_sizes, MemoryType mt);
-
-   /** @brief Update the MultiVector to reference data within a given monolithic
-       Vector @a base.
-
-       After calling this method, the Memory flags of @a base and of the
-       individual Vector blocks may need to be explicitly synchronized when data
-       is moved between host and device.*/
-   void MakeRef(Vector &base, const Array<int> &vector_sizes);
-
-   /** @brief Update the @a i-th MultiVector block to reference data within the
-       given monolithic Vector @a base at the given @a offset and with the given
-       @a size.
-
-       After calling this method, the Memory flags of @a base and of the @a i-th
-       Vector block may need to be explicitly synchronized when data is moved
-       between host and device.*/
-   inline void MakeRef(int i, Vector &base, int offset, int size)
-   {
-      blocks[i].emplace<0>(base, offset, size);
-   }
-
-   /** @brief Update the MultiVector to reference multiple Vectors given as
-       arguments.
-
-       The VectorTypes reference arguments are expected to be static_cast-able
-       to (Vector &) which is the case if the types are derived from Vector,
-       e.g. HypreParVector, GridFunction, etc.
-
-       After calling this method, operations on individual Vector blocks are
-       performed directly on the objects @a vs. In particular, there is no need
-       to synchronize the Memory flags of @a vs and the ones of the individual
-       Vector blocks when data is moved between host and device. */
-   template <typename... VectorTypes,
-             std::enable_if_t<
-                std::conjunction_v<
-                   std::is_convertible<VectorTypes&,Vector&>...>, bool> = true>
-   inline void MakeRef(VectorTypes &...vs);
-
-   /** @brief Update the @a i-th MultiVector block to reference the given
-       Vector @a v.
-
-       After calling this method, operations on the @a i-th Vector block are
-       performed directly on the Vector @a v. In particular, there is no need
-       to synchronize the Memory flags of @a v and the ones of the @a i-th
-       Vector blocks when data is moved between host and device. */
-   inline void MakeRef(int i, Vector &v) { blocks[i] = &v; }
-};
-
-// Inline and template methods
-
-inline Vector &MultiVector::operator[](int i)
-{
-   auto &bi = blocks[i];
-   return (bi.index() == 0) ? std::get<0>(bi) : *std::get<1>(bi);
-}
-
-inline const Vector &MultiVector::operator[](int i) const
-{
-   auto &bi = blocks[i];
-   return (bi.index() == 0) ? std::get<0>(bi) : *std::get<1>(bi);
-}
-
-template <typename... VectorTypes,
-          std::enable_if_t<
-             std::conjunction_v<
-                std::is_convertible<VectorTypes&,Vector&>...>, bool>>
-inline void MultiVector::MakeRef(VectorTypes &...vs)
-{
-   blocks.resize(sizeof...(vs));
-   if constexpr (sizeof...(vs) > 0)
-   {
-      const std::array vs_p{&static_cast<Vector&>(vs)...};
-      for (std::size_t i = 0; i < sizeof...(vs); i++)
-      {
-         blocks[i] = vs_p[i];
-      }
-   }
-}
-
-} // namespace mfem
-
-#endif // MFEM_MULTIVECTOR_HPP

linalg/operator.cpp

@@ -111,16 +111,6 @@ void Operator::ArrayAddMultTranspose(const Array<const Vector *> &X,
    }
 }
 
-void Operator::Mult(const MultiVector &, MultiVector &)
-{
-   MFEM_ABORT("this method is not overriden for this class!");
-}
-
-Operator &Operator::GetGradient(const MultiVector &) const
-{
-   MFEM_ABORT("this method is not overriden for this class!");
-}
-
 void Operator::FormLinearSystem(const Array<int> &ess_tdof_list,
                                 Vector &x, Vector &b,
                                 Operator* &Aout, Vector &X, Vector &B,

linalg/operator.hpp

@@ -13,7 +13,6 @@
 #define MFEM_OPERATOR
 
 #include "vector.hpp"
-#include "multivector.hpp"
 
 namespace mfem
 {
@@ -130,16 +129,6 @@ public:
    virtual void ArrayAddMultTranspose(const Array<const Vector *> &X,
                                       Array<Vector *> &Y, const real_t a = 1.0) const;
 
-   /** @brief Operator application, y = A(x), where the input @a x and the
-       output @a y are MultiVector objects, i.e. they generally use
-       non-contiguous memory representation.
-
-       The typical use case for this method are block operators like
-       DifferentiableOperator.
-
-       The base class implementation for the method is to generate an error. */
-   virtual void Mult(const MultiVector &x, MultiVector &y);
-
    /** @brief Evaluate the gradient operator at the point @a x. The default
        behavior in class Operator is to generate an error. */
    virtual Operator &GetGradient(const Vector &x) const
@@ -148,16 +137,6 @@ public:
       return const_cast<Operator &>(*this);
    }
 
-   /** @brief Evaluate the gradient operator at the point @a x. The input @a x
-       is provided as a MultiVector, i.e. it generally uses non-contiguous
-       memory representation.
-
-       The typical use case for this method are block operators like
-       DifferentiableOperator.
-
-       The base class implementation for the method is to generate an error. */
-   virtual Operator &GetGradient(const MultiVector &x) const;
-
    /** @brief Computes the diagonal entries into @a diag. Typically, this
        operation only makes sense for linear Operator%s. In some cases, only an
        approximation of the diagonal is computed. */

miniapps/CMakeLists.txt

@@ -22,7 +22,6 @@ add_subdirectory(common)
 add_subdirectory(contact)
 add_subdirectory(dfem)
 add_subdirectory(diag-smoothers)
-add_subdirectory(multiapp)
 add_subdirectory(dpg)
 add_subdirectory(electromagnetics)
 add_subdirectory(fluids/navier)

miniapps/hdiv-linear-solver/change_basis.hpp

@@ -80,8 +80,6 @@ public:
    // limitations
    void MultRT_2D(const Vector &x, Vector &y, Mode mode) const;
    void MultRT_3D(const Vector &x, Vector &y, Mode mode) const;
-   // suppress warning about hiding overloaded virtual function:
-   using Operator::Mult;
 };
 
 } // namespace mfem

miniapps/multiapp/CMakeLists.txt

@@ -1,52 +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.
-
-set(MESH_FILES
-  backward-facing-step.msh
-  channel-cylinder.msh
-)
-
-# Add a target to copy the mesh files from the source directory; used by sample
-# runs.
-set(SRC_MESH_FILES)
-foreach(MESH_FILE ${MESH_FILES})
-  list(APPEND SRC_MESH_FILES ${CMAKE_CURRENT_SOURCE_DIR}/${MESH_FILE})
-endforeach()
-add_custom_command(OUTPUT data_is_copied
-  COMMAND ${CMAKE_COMMAND} -E copy_if_different ${SRC_MESH_FILES} .
-  COMMAND ${CMAKE_COMMAND} -E touch data_is_copied
-  COMMENT "Copying multiapp miniapps data files ...")
-add_custom_target(copy_miniapps_multiapp_data DEPENDS data_is_copied)
-
-
-list(APPEND MULTIAPP_COMMON_SOURCES
-	multiapp.cpp)
-
-list(APPEND MULTIAPP_COMMON_HEADERS
-	multiapp.hpp)
-
-set(MULTIAPP_COMMON_FILES
-	EXTRA_SOURCES ${MULTIAPP_COMMON_SOURCES}
-	EXTRA_HEADERS ${MULTIAPP_COMMON_HEADERS})
-
-
-# Parallel apps.
-if (MFEM_USE_MPI)
-  add_mfem_miniapp(coupled-diffusion
-    MAIN coupled-diffusion.cpp
-    ${MFEM_MINIAPPS_COMMON_HEADERS} ${MULTIAPP_COMMON_FILES}
-    LIBRARIES mfem-common)
-  add_dependencies(coupled-diffusion copy_miniapps_multiapp_data)
-
-# Add parallel tests.
-  # if (MFEM_ENABLE_TESTING)
-  # endif()
-endif()

miniapps/multiapp/coupled-diffusion.cpp

@@ -1,895 +0,0 @@
-#include "mfem.hpp"
-#include "multiapp.hpp"
-#include <fstream>
-using namespace mfem;
-using namespace std;
-
-struct CaseContext
-{
-   int ser_ref = 1;         // Serial mesh refinement
-   int order = 3;           // Finite element order
-   bool visualization = true;// Visualization on/off
-   int grad_mode = 1;       // Gradient mode for the coupled operator - 0: finite difference,
-                            //                                          1: back/forward propagation
-   bool coupled = true;     // Coupled (true) vs. uncoupled (false) solves
-   int nl_iter = 50;        // Maximum number of nonlinear iterations
-   int lin_iter = 2000;     // Maximum number of linear iterations
-
-#if defined(MFEM_USE_DOUBLE)
-   real_t tol_nsolve = 1e-4;
-   real_t tol_lsolve = 1e-6;
-#elif defined(MFEM_USE_SINGLE)
-   real_t tol_nsolve = 1e-3;
-   real_t tol_lsolve = 1e-3;
-#else
-#error "Only single and double precision are supported!"
-   real_t tol_nsolve = 0;
-   real_t tol_lsolve = 0;
-#endif
-} ctx;
-
-void SetSolverParameters(IterativeSolver *solver, real_t rtol, real_t atol , int max_it,
-                         int print_level, bool iterative_mode);
-
-
-/// A functional diffusion coefficient (i.e., k(T))
-class FunctionalCoefficient : public Coefficient
-{
-public:
-   enum Mode { FUNC = 0, GRAD = 1};
-
-protected:
-   ParGridFunction *T_gf = nullptr;
-   real_t kref = 1.0;
-   real_t a0 = 0.0, a1 = 0.0, a2 = 0.0;
-   int findex = 0;
-   Mode mode = Mode::FUNC; // otherwise, grad
-
-public:
-   FunctionalCoefficient(ParGridFunction *T_gf, real_t kref): 
-                         T_gf(T_gf), kref(kref) { }
-
-   FunctionalCoefficient(ParGridFunction *T_gf, real_t kref, real_t a0):
-                         T_gf(T_gf), kref(kref), a0(a0) { findex = 1; }
-
-   FunctionalCoefficient(ParGridFunction *T_gf, real_t kref,
-                         real_t a0, real_t a1, real_t a2): T_gf(T_gf),
-                         kref(kref), a0(a0), a1(a1), a2(a2) { findex = 2; }
-
-    real_t Exponential(real_t x, bool eval_f) const
-    { 
-      real_t f = kref*exp(a0*x);
-      return (eval_f ? f : a0*f);
-    }
-    real_t Polynomial(real_t x, bool eval_f) const
-    { 
-      return (eval_f ? kref*(a0 + a1*x + a2*x*x) : kref*(a1 + 2*a2*x));
-    }
-
-    void SetMode(Mode mode) { this->mode = mode; }
-    Mode GetMode() const { return mode; }
-    
-    void UpdateGridFunction(ParGridFunction *gf) { T_gf = gf; }
-
-    real_t Eval(real_t x, bool eval_f) const
-    {
-        switch (findex)
-        {
-        case 1:
-         return Exponential(x, eval_f);
-        case 2:
-         return Polynomial(x, eval_f);
-        default:
-         return kref;
-        }
-    }
-
-    real_t Eval(ElementTransformation &Tr,
-              const IntegrationPoint &ip) override
-    {
-        real_t T = T_gf ? T_gf->GetValue(Tr, ip) : 0.0;
-        bool eval_f = (mode == Mode::FUNC);
-        return Eval(T, eval_f);
-    }
-};
-
-
-/// A coefficient defined by the product of grid functions, e.g. k(T) = prod_i x_i
-class GridFunctionProductCoefficient : public Coefficient
-{
-protected:
-   std::vector<ParGridFunction*> &x;
-
-public:
-   GridFunctionProductCoefficient(std::vector<ParGridFunction*> &x) : x(x) { }
-
-   real_t Eval(ElementTransformation &Tr, const IntegrationPoint &ip) override
-   {
-      real_t prod = 1.0;
-      for(size_t i = 0; i < x.size(); i++)
-      {
-         real_t val = x[i]->GetValue(Tr, ip);
-         prod *= val;
-      }
-      return prod;
-   }
-};
-
-class CoefficientIntegrator : public NonlinearFormIntegrator
-{
-protected:
-   FunctionalCoefficient *func = nullptr;
-   Vector shape;
-
-public:
-   CoefficientIntegrator(FunctionalCoefficient *func) : func(func) { }
-
-
-   void SetCoefficient(FunctionalCoefficient *f) { func = f; }
-
-   void AssembleElementVector(const FiniteElement &el,
-                              ElementTransformation &Tr,
-                              const Vector &elfun, Vector &elvect)
-   {
-      int dof = el.GetDof();
-      shape.SetSize(dof);
-      elvect.SetSize(dof);
-      elvect = 0.0;
-
-      const IntegrationRule *ir = &el.GetNodes();
-
-      for (int i = 0; i < ir->GetNPoints(); i++)
-      {
-         const IntegrationPoint &ip = ir->IntPoint(i);
-         el.CalcShape(ip, shape);
-         Tr.SetIntPoint(&ip);
-         real_t x = elfun * shape; // Evaluate the function at the integration point
-         real_t fval = func->Eval(x, true);
-         for (int j = 0; j < dof; j++)
-         {
-            elvect(j) += fval * shape(j);
-         }
-      }
-   }
-
-   void AssembleElementGrad(const FiniteElement &el, ElementTransformation &Tr,
-                            const Vector &elfun, DenseMatrix &elmat)
-   {
-      int dof = el.GetDof();
-      shape.SetSize(dof);
-      elmat.SetSize(dof);
-      elmat = 0.0;
-
-      const IntegrationRule *ir = &el.GetNodes();
-
-      for (int i = 0; i < ir->GetNPoints(); i++)
-      {
-         const IntegrationPoint &ip = ir->IntPoint(i);
-         el.CalcShape(ip, shape);
-         Tr.SetIntPoint(&ip);
-         real_t x = elfun * shape; // Evaluate the function at the integration point
-         real_t dfdx = func->Eval(x, false); // Evaluate the derivative of the function at the integration point
-         for (int j = 0; j < dof; j++)
-         {
-            elmat(j,j) += dfdx * shape(j); // Diagonal contribution to the Jacobian
-         }
-      }
-   }
-};
-
-
-class NonlinearDiffusionIntegrator : public NonlinearFormIntegrator
-{
-protected:
-   Coefficient *k;
-   Coefficient *dk;
-
-   Vector u, vec, shape;
-   DenseMatrix dshape, dshapedxt, adjJ;
-public:
-   NonlinearDiffusionIntegrator(Coefficient *kappa, Coefficient *dkappa) :
-                                k(kappa), dk(dkappa) { }
-
-   virtual void AssembleElementVector(const FiniteElement &el,
-                                      ElementTransformation &Tr,
-                                      const Vector &elfun, Vector &elvec)
-   {
-      int dim = el.GetDim();
-      int dof = el.GetDof();
-      real_t w;
-
-      elvec.SetSize(dof);
-      elvec = 0.0;
-
-      const IntegrationRule *ir = IntRule ? IntRule : &IntRules.Get(el.GetGeomType(), 2*el.GetOrder());
-      u.SetSize(dim);
-      vec.SetSize(dim);
-      dshape.SetSize(dof, dim);
-      adjJ.SetSize(dim, dim);
-
-      for (int i = 0; i < ir->GetNPoints(); i++)
-      {
-         const IntegrationPoint &ip = ir->IntPoint(i);
-         el.CalcDShape(ip, dshape);
-
-         Tr.SetIntPoint(&ip);
-         CalcAdjugate(Tr.Jacobian(), adjJ);
-         w = ip.weight / Tr.Weight();
-
-         dshape.MultTranspose(elfun, u);
-         adjJ.MultTranspose(u, vec);
-         if(k)
-         {
-            w *= k->Eval(Tr, ip);
-         }
-
-         vec *= w;
-         adjJ.Mult(vec, u);
-         dshape.AddMult(u, elvec);
-      }
-   }
-
-   void AssembleElementGrad(const FiniteElement &el, ElementTransformation &Tr,
-                            const Vector &elfun, DenseMatrix &elmat)
-   {
-      int dim = el.GetDim();
-      int dof = el.GetDof();
-      real_t w, k0 = 0.0, dk0 = 0.0;
-
-      elmat.SetSize(dof);
-      elmat = 0.0;
-
-      const IntegrationRule *ir = IntRule ? IntRule : &IntRules.Get(el.GetGeomType(), 2*el.GetOrder());
-      u.SetSize(dim);
-      shape.SetSize(dof);
-      vec.SetSize(dof);
-      dshape.SetSize(dof, dim);
-      dshapedxt.SetSize(dof, dim);
-
-      // f = grad(psi) * k(u) * grad(T)
-      // df/dT = grad(psi) ( k(u0) * grad(T) + k'(u0) * grad(u0) * T )
-      for (int i = 0; i < ir->GetNPoints(); i++)
-      {
-         const IntegrationPoint &ip = ir->IntPoint(i);
-         el.CalcShape(ip, shape);
-         el.CalcDShape(ip, dshape);
-
-         Tr.SetIntPoint(&ip);
-         w = ip.weight / Tr.Weight();
-
-         Mult(dshape, Tr.AdjugateJacobian(), dshapedxt);
-
-         k0  = k ? k->Eval(Tr, ip) : 0.0;
-         dk0 = dk ? dk->Eval(Tr, ip) : 0.0;
-
-         if(k0 != 0.0) // grad(psi) * k(u0) * grad(T)
-         {
-            real_t kdT = w*k0;
-            AddMult_a_AAt(kdT, dshapedxt, elmat);
-         }
-
-         if(dk0 != 0.0) // grad(psi) * (k'(T0) * grad(T0)) * T
-         {
-            dk0 = w*dk->Eval(Tr, ip);
-            dshapedxt.MultTranspose(elfun, u); // grad(T0) in physical space
-            u *= dk0; // k'(T0) * grad(T0)
-            dshapedxt.Mult(u, vec); // grad(psi) * k'(T0) * grad(T0)
-            AddMultVWt(vec, shape, elmat); // grad(psi) * k'(T0) * grad(T0) * T
-         }
-      }
-   }
-};
-
-/// An application that takes an input field T, and computes an output field k(T)
-// represented by the FunctionalCoefficient class.
-class DiffusionCoefficient : public GraphNode
-{
-public:
-   using Mode = FunctionalCoefficient::Mode;
-
-protected:
-   ParFiniteElementSpace &fes;
-   mutable ParGridFunction T, k;
-   mutable FunctionalCoefficient *kc;
-   // mutable Vector tdof, kdof, dk_dof, dT_dof;
-   mutable Mode mode = Mode::FUNC;
-
-   mutable ParNonlinearForm Nform;
-   mutable Operator *J = nullptr; // Jacobian for the nonlinear form
-
-   CoefficientIntegrator *coeff_integrator = nullptr;
-
-public:
-   DiffusionCoefficient(ParFiniteElementSpace &fes) :
-                        GraphNode(fes.GetTrueVSize()), fes(fes), T(&fes), k(&fes),
-                        kc(new FunctionalCoefficient(&T, 1.0, 5.0e-2)),
-                        Nform(&fes),
-                        coeff_integrator(new CoefficientIntegrator(kc))
-   {
-      k = 0.0;
-      T = 0.0;
-      k.ProjectCoefficient(*kc);
-
-      // Testing with the nonlinear form framework to compute k(T) and dk/dT
-      Nform.AddDomainIntegrator(coeff_integrator); // Transfer ownership
-      Nform.SetGradientType(Operator::Type::Hypre_ParCSR);
-      Nform.Setup();
-
-      SetInputOffsets(Array<int>({0, fes.GetTrueVSize()}));
-      SetOutputOffsets(Array<int>({0, fes.GetTrueVSize()}));
-   }
-
-   void SetMode(Mode mode) { this->mode = mode; }
-
-   FunctionalCoefficient* GetCoefficient() { return kc; }
-
-   void SetCoefficient(FunctionalCoefficient *fc)
-   {
-      if(kc) delete kc;
-      kc = fc;
-      kc->SetMode(mode);
-      kc->UpdateGridFunction(&T);
-      coeff_integrator->SetCoefficient(kc);
-   }
-
-   void Mult(const Vector &x, Vector &y) const override
-   {
-      BlockVector xb(x.GetData(), InputOffsets());
-      BlockVector yb(y.GetData(), OutputOffsets());
-
-      MultiVector xmv(1), ymv(1);
-      xmv.MakeRef(0, xb.GetBlock(0));
-      ymv.MakeRef(0, yb.GetBlock(0));
-
-      const_cast<DiffusionCoefficient*>(this)->Mult(xmv, ymv);
-   }
-
-   void Mult(const MultiVector &x, MultiVector &y) override
-   {
-      const Vector &tdof = x[0];
-      Vector &kdof = y[0];
-
-      Nform.Mult(tdof, kdof);
-      if(exec_mode == GraphNode::GRADIENT_MODE)
-      {
-         J = &Nform.GetGradient(tdof); // Store jacobian for JVP
-      }
-      else
-      {
-         J = nullptr; // Clear the Jacobian if not in gradient mode
-      }
-   }
-
-   // TODO: Possibly delete and only support MultiVector version of GradientMult
-   void GradientMult(const Vector &x, const Vector &dx, Vector &dy) const override
-   {
-      BlockVector xb(x.GetData(), InputOffsets());
-      BlockVector dxb(dx.GetData(), InputOffsets());
-      BlockVector dyb(dy.GetData(), OutputOffsets());
-
-      MultiVector xmv(1), dxmv(1), dymv(1);
-      xmv.MakeRef(0, xb.GetBlock(0));
-      dxmv.MakeRef(0, dxb.GetBlock(0));
-      dymv.MakeRef(0, dyb.GetBlock(0));
-      const_cast<DiffusionCoefficient*>(this)->GradientMult(xmv, dxmv, dymv);
-   }
-
-   void GradientMult(const MultiVector &x, const MultiVector &dx, MultiVector &dy) const override
-   {
-      const Vector &tdof = x[0];
-      const Vector &xadj = dx[0];
-      Vector &yadj = dy[0];
-
-      if(J)
-      {
-         J->Mult(xadj, yadj);
-      }
-      else
-      {
-         J = &Nform.GetGradient(tdof); // Store jacobian for JVP
-         J->Mult(xadj, yadj);
-      }
-   }
-
-   ~DiffusionCoefficient() override
-   {
-      if(kc) delete kc;
-   }
-};
-
-/// An application that takes n input fields x_i, and computes an output 
-/// field prod(x) := y = prod_i x_i.
-/// Also provides the derivative dy/dx_i = prod_{j!=i} x_j * dx_i/dx for i = 0,...,n-1.
-class ProductGridFunctions : public GraphNode
-{
-protected:
-
-   ParFiniteElementSpace &fes;
-   mutable std::vector<ParGridFunction*> x_gf;
-   mutable Vector dfdx;
-   mutable ParGridFunction y_gf;
-   mutable GridFunctionProductCoefficient prod_coeff;
-
-public:
-   ProductGridFunctions(ParFiniteElementSpace &fes, int n) :
-                     //   GraphNode(fes.GetTrueVSize()),
-                       GraphNode(fes.GetTrueVSize(), fes.GetTrueVSize() * n),
-                       fes(fes), x_gf(n),
-                       y_gf(&fes), prod_coeff(x_gf)
-   {
-      Array<int> offsets(n+1);
-      offsets[0] = 0;
-      for (int i = 0; i < n; i++)
-      {
-         x_gf[i]  = new ParGridFunction(&fes);
-         *x_gf[i] = 0.0;
-         offsets[i+1] = offsets[i] + fes.GetTrueVSize();
-      }
-      y_gf = 0.0;
-      y_gf.ProjectCoefficient(prod_coeff);
-
-      SetInputOffsets(offsets);
-      SetOutputOffsets(Array<int>({0, fes.GetTrueVSize()}));
-   }
-
-   void Mult(const Vector &x, Vector &y) const override
-   {
-      BlockVector xb(x.GetData(), InputOffsets());
-      BlockVector yb(y.GetData(), OutputOffsets());
-
-      MultiVector xmv(x_gf.size()), ymv(1);
-      for (size_t i = 0; i < x_gf.size(); i++)
-      {
-         xmv.MakeRef(i, xb.GetBlock(i));
-      }
-      ymv.MakeRef(0, yb.GetBlock(0));
-      const_cast<ProductGridFunctions*>(this)->Mult(xmv, ymv);
-   }
-
-   void Mult(const MultiVector &x, MultiVector &y) override
-   {
-      for (size_t i = 0; i < x_gf.size(); i++)
-      {
-         const Vector &x_dof = x[i];
-         x_gf[i]->SetFromTrueDofs(x_dof);
-      }
-
-      Field *out_field = OutputField(0);
-      Vector &y_dof = y[0];
-      y_gf.ProjectCoefficient(prod_coeff);
-      y_gf.GetTrueDofs(y_dof);
-   }
-
-   // TODO: Possibly delete and only support MultiVector version of GradientMult
-   void GradientMult(const Vector &x, const Vector &dx, Vector &dy) const override
-   {
-      BlockVector xb(x.GetData(), InputOffsets());
-      BlockVector dxb(dx.GetData(), InputOffsets());
-      BlockVector dyb(dy.GetData(), OutputOffsets());
-
-      MultiVector xmv(x_gf.size()), dxmv(x_gf.size()), dymv(1);
-      for (size_t i = 0; i < x_gf.size(); i++)
-      {
-         xmv.MakeRef(i, xb.GetBlock(i));
-         dxmv.MakeRef(i, dxb.GetBlock(i));
-      }
-      dymv.MakeRef(0, dyb.GetBlock(0));
-      const_cast<ProductGridFunctions*>(this)->GradientMult(xmv, dxmv, dymv);
-   }
-
-   void GradientMult(const MultiVector &x, const MultiVector &dx, MultiVector &dy) const override
-   {
-      // Jacobian vector product for y = prod_i x_i is:
-      // dy/dx = sum_i (prod_{j!=i} x_j * dx_i/dx)
-      for (size_t i = 0; i < x_gf.size(); i++)
-      {
-         const Vector &x_dof = x[i];
-         x_gf[i]->SetFromTrueDofs(x_dof); // Set all x_i
-      }
-
-      Vector &jvp = dy[0];
-      jvp = 0.0;
-      for (size_t i = 0; i < x_gf.size(); i++)
-      {
-         const Vector &x_dof = x[i];
-         const Vector &dx_dof = dx[i]; // Get dx_i/dx
-
-         x_gf[i]->SetFromTrueDofs(dx_dof); // Set x_i = dx_i/dx for i-th term in the product
-         y_gf.ProjectCoefficient(prod_coeff); // Recompute product with x_i replaced by dx_i/dx
-         y_gf.GetTrueDofs(dfdx); // Get prod_{j!=i} x_j * dx_i/dx for i-th term
-         jvp += dfdx; // Accumulate contribution from i-th term
-         x_gf[i]->SetFromTrueDofs(x_dof); // reset to original value for next iteration
-      }
-   }
-
-   ~ProductGridFunctions() override
-   {
-      for (size_t i = 0; i < x_gf.size(); i++)
-      {
-         if(x_gf[i]) delete x_gf[i];
-      }
-   }
-};
-
-
-/// An application that represents the nonlinear diffusion operator: f(T) = -Div(k(u) grad(T)) 
-/// with input field T and k, and output field f(T).
-class DiffusionOperator : public GraphNode
-{
-public:
-
-   // Mesh and finite element space
-   ParMesh &mesh;
-   ParFiniteElementSpace &fes;
-
-   /// Essential dof array.
-   Array<int> ess_tdofs;
-
-   /// Grid functions for the temperature and heat flux
-   mutable ParGridFunction T, k, dk;
-   mutable GridFunctionCoefficient k_gfc, dk_gfc;
-   mutable ParNonlinearForm Nform;
-   mutable ParLinearForm bform;
-   mutable Vector b;
-
-   ConstantCoefficient zero_coeff, one_coeff;
-
-   mutable FunctionalCoefficient *kc = nullptr;
-   mutable HypreParMatrix *dfdk_mat = nullptr, *dfdT_mat = nullptr;
-
-public:
-
-   DiffusionOperator(ParFiniteElementSpace &fes_) :
-                     // GraphNode(fes_.GetTrueVSize()),
-                     GraphNode(fes_.GetTrueVSize(),2*fes_.GetTrueVSize()),
-                     mesh(*fes_.GetParMesh()), fes(fes_),
-                     T(&fes), k(&fes), dk(&fes),
-                     k_gfc(&k), dk_gfc(&dk),
-                     Nform(&fes), bform(&fes),
-                     zero_coeff(0.0), one_coeff(1.0)
-   {
-      fes.GetBoundaryTrueDofs(ess_tdofs);
-      T = 0.0;
-      k = 0.0;
-      dk = 0.0;
-
-      bform.AddDomainIntegrator(new DomainLFIntegrator(one_coeff));
-      Nform.AddDomainIntegrator(new NonlinearDiffusionIntegrator(&k_gfc, &dk_gfc));
-      Nform.SetGradientType(Operator::Type::Hypre_ParCSR);
-
-      b.SetSize(fes.GetTrueVSize()); b = 0.0;
-      Assemble();
-
-      SetInputOffsets(Array<int>({0, fes.GetTrueVSize(), 2*fes.GetTrueVSize()}));
-      SetOutputOffsets(Array<int>({0, fes.GetTrueVSize()}));
-   }
-
-   void SetCoefficient(FunctionalCoefficient *fc) { kc = fc; }
-
-   void Assemble()
-   {
-      AssembleLinearForms();
-      AssembleBilinearForms();
-      AssembleNonlinearForms();
-   }
-
-   void AssembleBilinearForms()
-   {}
-
-   void AssembleNonlinearForms()
-   {
-      Nform.SetEssentialTrueDofs(ess_tdofs);
-      Nform.Setup();
-   }
-
-   void AssembleLinearForms()
-   {
-      bform.Assemble();
-      bform.ParallelAssemble(b);
-   }
-
-   void Mult(const Vector &x, Vector &y) const override
-   {
-      BlockVector xb(x.GetData(), InputOffsets());
-      BlockVector yb(y.GetData(), OutputOffsets());
-
-      MultiVector xmv(2), ymv(1);
-      xmv.MakeRef(0, xb.GetBlock(0));
-      xmv.MakeRef(1, xb.GetBlock(1));
-      ymv.MakeRef(0, yb.GetBlock(0));
-
-      const_cast<DiffusionOperator*>(this)->Mult(xmv, ymv);
-   }
-
-   void Mult(const MultiVector &x, MultiVector &y) override
-   {
-      const Vector &tdofs = x[0];
-      const Vector &kdofs = x[1];
-      Vector &fdofs = y[0];
-
-      k.SetFromTrueDofs(kdofs); // update for use in k_gfc
-
-      if(exec_mode == GraphNode::GRADIENT_MODE)
-      {
-         if(dfdT_mat) delete dfdT_mat;
-         if(dfdk_mat) delete dfdk_mat;
-
-         dk = 0.0;
-         k.SetFromTrueDofs(kdofs);
-         Operator* grad = &Nform.GetGradient(tdofs);
-         dfdT_mat = new HypreParMatrix(dynamic_cast<const HypreParMatrix&>(*grad)); // deep copy
-
-         dk = 1.0;
-         k  = 0.0;
-         grad = &Nform.GetGradient(tdofs);
-         dfdk_mat = new HypreParMatrix(dynamic_cast<const HypreParMatrix&>(*grad)); // deep copy
-      }
-      else
-      {
-         if(dfdT_mat) { delete dfdT_mat; dfdT_mat = nullptr; }
-         if(dfdk_mat) { delete dfdk_mat; dfdk_mat = nullptr; }
-      }
-
-      Nform.Mult(tdofs, fdofs);
-      fdofs.SetSubVector(ess_tdofs, 0.0);
-   }
-
-   // Exact block jacobian [df/dT, df/dk]
-   Operator& GetGradient(const Vector &x) const override
-   {
-      MFEM_ABORT("GetGradient not implemented for DiffusionOperator");
-   }
-
-   // TODO: Possibly delete and only support MultiVector version of GradientMult
-   void GradientMult(const Vector &x, const Vector &dx, Vector &dy) const override
-   {
-      BlockVector xb(x.GetData(), InputOffsets());
-      BlockVector dxb(dx.GetData(), InputOffsets());
-      BlockVector dyb(dy.GetData(), OutputOffsets());
-
-      Vector &Tadj = dxb.GetBlock(0);
-      Vector &kadj = dxb.GetBlock(1);
-      Vector &yadj = dyb.GetBlock(0);
-
-      Vector &tdofs = xb.GetBlock(0);
-      Vector &kdofs = xb.GetBlock(1);
-
-      dfdT_mat->Mult(Tadj, yadj);
-      dfdk_mat->AddMult(kadj, yadj);
-   }
-
-   void GradientMult(const MultiVector &x, const MultiVector &dx, MultiVector &dy) const override
-   {
-      const Vector &Tadj = dx[0];
-      const Vector &kadj = dx[1];
-      Vector &yadj = dy[0];
-
-      const Vector &tdofs = x[0];
-      const Vector &kdofs = x[1];
-
-      dfdT_mat->Mult(Tadj, yadj);
-      dfdk_mat->AddMult(kadj, yadj);
-   }
-
-   /// @brief Destroy the DiffusionOperator object
-   ~DiffusionOperator() override
-   {
-      if(dfdT_mat) delete dfdT_mat;
-      if(dfdk_mat) delete dfdk_mat;
-   }
-};
-
-
-int main(int argc, char *argv[])
-{
-   Mpi::Init();
-   Hypre::Init();
-
-   using GradMode = DAGraph::GradMode;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&ctx.order, "-o", "--order",
-                  "Finite element order (polynomial degree).");
-   args.AddOption(&ctx.visualization, "-vis", "--visualization", "-no-vis",
-                  "--no-visualization",
-                  "Enable or disable GLVis visualization.");
-   args.AddOption(&ctx.ser_ref, "-rs", "--serial-refine",
-                  "Number of times to refine the mesh in serial.");
-
-   args.AddOption(&ctx.grad_mode, "-gm", "--grad-mode",
-                  "Gradient mode for the coupled operator (0: exact, 1: finite difference, 2: algorithmic differentiation)");
-   args.AddOption(&ctx.coupled, "-cp", "--coupled", "-ucp", "--uncoupled",
-                  "Coupled (true) vs. uncoupled (false) solves.");
-   args.ParseCheck();
-
-
-   int order = ctx.order;
-   std::string mesh_file = "../../data/star.mesh";
-   Mesh *serial_mesh = new Mesh(mesh_file);
-   int dim = serial_mesh->Dimension();
-
-   for (int i = 0; i < ctx.ser_ref; ++i) { serial_mesh->UniformRefinement(); }
-   serial_mesh->SetCurvature(order, false, dim, Ordering::byNODES);
-
-   ParMesh pmesh(MPI_COMM_WORLD, *serial_mesh);
-   delete serial_mesh;
-   pmesh.UniformRefinement();
-
-   // Finite element spaces
-   H1_FECollection fec(order, dim);
-   ParFiniteElementSpace fes(&pmesh, &fec);
-
-   // Build all operator nodes
-   DiffusionCoefficient diff_coeff_1(fes);
-   diff_coeff_1.SetName("k(T1)");
-   diff_coeff_1.SetCoefficient(new FunctionalCoefficient(nullptr, 1.0, 3.5e-2));
-   // diff_coeff_1.SetCoefficient(new FunctionalCoefficient(nullptr, 1.0, 1.0, 0.1, 0.0));
-
-   DiffusionCoefficient diff_coeff_2(fes);
-   diff_coeff_2.SetName("k(T2)");
-   diff_coeff_2.SetCoefficient(new FunctionalCoefficient(nullptr, 1.0, 1.0, 2.0, 0.0));
-   // diff_coeff_2.SetCoefficient(new FunctionalCoefficient(nullptr, 1.5, 2.5e-2));
-
-   ProductGridFunctions prod_coeff(fes, 2);
-   prod_coeff.SetName("k(T1,T2)");
-
-   DiffusionOperator diff_op1(fes);
-   diff_op1.SetName("Div(k(T1,T2) grad(T1))");
-   diff_op1.SetCoefficient(diff_coeff_1.GetCoefficient());
-
-   DiffusionOperator diff_op2(fes);
-   diff_op2.SetName("Div(k(T1,T2) grad(T2))");
-   diff_op2.SetCoefficient(diff_coeff_2.GetCoefficient());
-
-
-   // Build the DAG in any order, and then sort it to ensure the correct execution order
-   DAGraph dag(5);
-   dag.AddOperator(&diff_coeff_1);
-   dag.AddOperator(&diff_op1, fes.GetTrueVSize());
-   dag.AddOperator(&diff_op2, fes.GetTrueVSize());
-   dag.AddOperator(&diff_coeff_2);
-   dag.AddOperator(&prod_coeff);
-
-   Vector k1vec(fes.GetTrueVSize()); k1vec = 0.0;
-   Vector k2vec(fes.GetTrueVSize()); k2vec = 0.0;
-   Vector kpvec(fes.GetTrueVSize()); kpvec = 0.0;
-
-   Vector k1adj(fes.GetTrueVSize()); k1adj = 0.0;
-   Vector k2adj(fes.GetTrueVSize()); k2adj = 0.0;
-   // Vector kpadj(fes.GetTrueVSize()); kpadj = 0.0;
-
-   // Input fields get data from 'x' in DAGraph::Mult(x, y)
-   Field T1_field(nullptr, nullptr);
-   Field T2_field(nullptr, nullptr);
-
-   // Write space for data and adjoint only needed
-   // for the intermediate fields k1, k2, and k_prod
-   Field k1_field(&k1vec, &k1adj);
-   Field k2_field(&k2vec, &k2adj);
-   Field kp_field(&kpvec, &kpvec); // can use same space for data & adjoint
-
-   // Output fields get data from 'y' in DAGraph::Mult(x, y)
-   Field f1_field(nullptr, nullptr);
-   Field f2_field(nullptr, nullptr);
-
-
-   // Add input and output to the DAG
-   int sz = fes.GetTrueVSize();
-   dag.AddInput(&T1_field, sz);
-   dag.AddInput(&T2_field, sz);
-   dag.AddOutput(&f1_field, sz);
-   dag.AddOutput(&f2_field, sz);
-
-   // Form connections between the nodes in the DAG
-   diff_coeff_1.AddInput(&T1_field);
-   diff_coeff_1.AddOutput(&k1_field);
-
-   diff_coeff_2.AddInput(&T2_field);
-   diff_coeff_2.AddOutput(&k2_field);
-
-   prod_coeff.AddInputs(&k1_field, &k2_field);
-   prod_coeff.AddOutput(&kp_field);
-
-   diff_op1.AddInput(&T1_field);
-   diff_op1.AddOutput(&f1_field);
-
-   diff_op2.AddInput(&T2_field);
-   diff_op2.AddOutput(&f2_field);
-
-   if(ctx.coupled)
-   {
-      diff_op1.AddInput(&kp_field); // kp_field
-      diff_op2.AddInput(prod_coeff.OutputField(0)); // Can also use kp_field directly
-   }
-   else
-   {
-      diff_op1.AddInput(&k1_field); // Can also use diff_coeff_1.OutputField(0)
-      diff_op2.AddInput(&k2_field); // Can also use diff_coeff_2.OutputField(0)
-   }
-
-   // Assemble DAG: topological sort, validate nodes, etc.
-   dag.Assemble();
-
-   std::string output_prefix = ctx.coupled ? "Coupled_Diffusion" : "Uncoupled_Diffusion";
-
-   if(Mpi::Root())
-   {
-      std::ofstream fout(output_prefix+"-dag.txt");
-      fout << "{\n";
-      dag.Save(fout);
-      fout << "}\n";
-      fout << std::flush;
-      fout.close();
-   }
-
-   // Set initial guess and boundary conditions for T1 and T2
-   Array<int> ess_tdofs;
-   fes.GetBoundaryTrueDofs(ess_tdofs);
-
-   int T1_idx = 0;
-   int T2_idx = 1;
-
-   BlockVector xb(dag.InputOffsets());
-   BlockVector yb(dag.OutputOffsets());
-
-   xb.GetBlock(T1_idx).Randomize();
-   xb.GetBlock(T2_idx).Randomize();
-   xb.GetBlock(T1_idx).SetSubVector(ess_tdofs, 0.0);
-   xb.GetBlock(T2_idx).SetSubVector(ess_tdofs, 0.0);
-
-   // Build the nonlinear solver and linear solver for the DAG
-   NewtonSolver newton_solver(pmesh.GetComm());
-   GMRESSolver linear_solver(pmesh.GetComm());
-   linear_solver.SetKDim(500);
-   SetSolverParameters(&newton_solver, ctx.tol_nsolve, 0.0, ctx.nl_iter, 1, true);
-   SetSolverParameters(&linear_solver, ctx.tol_lsolve, 0.0, ctx.lin_iter, 1, false);
-
-   newton_solver.SetPreconditioner(linear_solver);
-   linear_solver.SetPrintLevel(1);
-
-   // Set the gradient mode for the DAG and solve the coupled system
-   GradMode gm = static_cast<GradMode>(ctx.grad_mode);
-   dag.SetGradientMode(gm);
-   newton_solver.SetOperator(dag);
-   newton_solver.Mult(xb, yb);
-
-   ParaViewDataCollection *pv = nullptr;
-   if (ctx.visualization)
-   {
-      std::string pv_prefix;
-      switch (ctx.grad_mode)
-      {
-         case 0: pv_prefix = "FD"; break;
-         case 1: pv_prefix = "MF"; break;
-         default: pv_prefix = "Unknown"; break;
-      }
-
-      pv = new ParaViewDataCollection(output_prefix+"-"+pv_prefix, &pmesh);
-      pv->SetLevelsOfDetail(order);
-      pv->SetDataFormat(VTKFormat::BINARY);
-      pv->SetHighOrderOutput(true);
-
-      ParGridFunction T1_gf(&fes);
-      ParGridFunction T2_gf(&fes);
-      T1_gf.SetFromTrueDofs(yb.GetBlock(T1_idx));
-      T2_gf.SetFromTrueDofs(yb.GetBlock(T2_idx));
-
-      pv->RegisterField("T1", &T1_gf);
-      pv->RegisterField("T2", &T2_gf);
-      pv->Save();
-      delete pv;
-   }
-
-   std::cout << "Finished solving the coupled diffusion problem." << std::endl;
-   return 0;
-}
-
-void SetSolverParameters(IterativeSolver *solver, real_t rtol, real_t atol,
-                         int max_it, int print_level, bool iterative_mode)
-{
-    solver->SetRelTol(rtol);
-    solver->SetAbsTol(atol);
-    solver->SetMaxIter(max_it);
-    solver->SetPrintLevel(print_level);
-    solver->iterative_mode = iterative_mode;
-}

miniapps/multiapp/multiapp.cpp

@@ -1,873 +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.
-
-#include "multiapp.hpp"
-
-namespace mfem
-{
-
-DAGraph::~DAGraph()
-{
-    for(int i=0; i < nnodes; i++)
-    {
-        if(node_owned[i] && nodes[i]) delete nodes[i];
-    }
-    if(grad) delete grad;
-}
-
-void DAGraph::Assemble()
-{
-    // Sort graph nodes topologically to ensure correct execution order
-    // Ordering is not unique, hence, id->index maps are needed
-    TopologicalSort();
-
-    // Collect all fields from the nodes into the field map
-    CollectFieldMaps();
-
-    // Compute depth of the graph nodes
-    ComputeDepth();
-
-    // Validate each node
-    for (auto &node : nodes)
-    {
-        ValidateNode(*node);
-    }
-
-    // Update width and height of the DAG from offsets
-    // Check that the input and output offsets are consistent
-    ValidateOffsets();
-    width  = input_offsets.Last();
-    height = output_offsets.Last();
-
-    // Delete any existing gradient operator as node ordering may have changed
-    if (grad) delete grad;
-
-    assembled = true;
-}
-
-void DAGraph::ValidateOffsets()
-{
-    // Check that the input and output offsets are consistent
-    // with the number of inputs and outputs
-    if(InputFields().Size() > 1)
-    {
-        MFEM_ASSERT(input_offsets.Size() == InputFields().Size() + 1,
-                    "Input offsets size inconsistent with number of input fields");
-    }
-    else
-    {
-        input_offsets = Array<int>({0, nodes[0]->Width()});
-    }
-
-    if(OutputFields().Size() > 1)
-    {
-        MFEM_ASSERT(output_offsets.Size() == OutputFields().Size() + 1,
-                    "Output offsets size inconsistent with number of output fields");
-    }
-    else
-    {
-        output_offsets = Array<int>({0, nodes.Last()->Height()});
-    }
-}
-
-void DAGraph::ValidateNode(GraphNode &node)
-{
-    // Validate that the node's input and output fields are consistent with the graph's field map
-    auto inputs = node.InputFields();
-    auto outputs = node.OutputFields();
-
-    // Check offsets match width and height of the node
-    MFEM_ASSERT(node.InputOffsets().Last() == node.Width(),
-                "Node ID: " << node.ID() << " input offsets do not match node width.");
-    MFEM_ASSERT(node.OutputOffsets().Last() == node.Height(),
-                "Node ID: " << node.ID() << " output offsets do not match node height.");
-
-    // Check number of input and output fields match the offsets
-    MFEM_ASSERT(node.InputOffsets().Size() == inputs.Size() + 1,
-                "Node input offsets size inconsistent with number of input fields");
-    MFEM_ASSERT(node.OutputOffsets().Size() == outputs.Size() + 1,
-                "Node output offsets size inconsistent with number of output fields");
-
-    // Check that all input and output fields are registered in the graph's field map
-    for(auto input_field : inputs)
-    {
-        MFEM_ASSERT(fid_to_index.Has(input_field->ID()),
-                    "Input field ID " << input_field->ID() << " not found in graph's field map");
-    }
-    for(auto output_field : outputs)
-    {
-        MFEM_ASSERT(fid_to_index.Has(output_field->ID()),
-                    "Output field ID " << output_field->ID() << " not found in graph's field map");
-    }
-}
-
-void DAGraph::TopologicalSort()
-{
-    Array<int> sorted_indices;
-    sorted_indices.Reserve(nnodes);
-
-    Array<bool> visited(nnodes);
-    visited = false; // Initialize all nodes as unvisited
-
-    // Perform a depth-first search to sort the nodes topologically
-    std::function<void(int)> DepthFirstSearch = [&](int node_index)
-    {
-        if(visited[node_index]) return;
-        visited[node_index] = true;
-        auto node = nodes[node_index];
-        // Visit all nodes that this node depends on
-        for(auto input_field : node->InputFields())
-        {
-            for(int j=0; j < nnodes; j++)
-            {
-                auto other_node = nodes[j];
-                if(other_node == node) continue;
-                for(auto output_field : other_node->OutputFields())
-                {
-                    if(input_field->ID() == output_field->ID()) // Compare by unique ID
-                    {
-                        DepthFirstSearch(j);
-                    }
-                }
-            }
-        }
-        sorted_indices.push_back(node_index);
-    };
-
-    for(int i=0; i < nnodes; i++)
-    {
-        DepthFirstSearch(i);
-    }
-
-    nodes.Permute(sorted_indices);
-    node_owned.Permute(sorted_indices);
-
-    // Update the node indices after sorting
-    for(int i=0; i < nnodes; i++)
-    {
-        nodes[i]->SetNodeIndex(i);
-    }
-
-    sorted = true;
-}
-
-void DAGraph::ComputeDepth()
-{
-    // Compute depth of ordered nodes
-    node_depth.SetSize(nnodes);
-    node_depth = 0;
-    for(int i=0; i < nnodes; i++)
-    {
-        int max_depth = 0;
-        auto node = nodes[i];
-        for(auto input_field : node->InputFields())
-        {
-            for(int j=0; j < i; j++)
-            {
-                auto other_node = nodes[j];
-                if(other_node == node) continue;
-                for(auto output_field : other_node->OutputFields())
-                {
-                    if(input_field->ID() == output_field->ID()) // Compare by unique ID
-                    {
-                        max_depth = std::max(max_depth, node_depth[j] + 1);
-                    }
-                }
-            }
-        }
-        node_depth[i] = max_depth;
-    }
-}
-
-void DAGraph::CollectFieldMaps()
-{
-    MFEM_ASSERT(sorted, "DAGraph must be topologically sorted before collecting fields");
-
-    fid_to_index.clear();
-    fid_to_field.clear();
-
-    int nfields = 0;
-    for (auto f : InputFields())
-    {
-        fid_to_index.Register(f->ID(), nfields++);
-        fid_to_field.Register(f->ID(), f);
-    }
-
-    for (auto &node : nodes)
-    {
-        for (auto f : node->OutputFields())
-        {
-            if (!fid_to_index.Has(f->ID()))
-            {
-                fid_to_index.Register(f->ID(), nfields++);
-            }
-            if (!fid_to_field.Has(f->ID()))
-            {
-                fid_to_field.Register(f->ID(), f);
-            }
-        }
-    }
-    // TODO: Possibly add all intermediate fields from nodes to the graph's FieldCollection
-}
-
-void DAGraph::Mult(const Vector &x, Vector &y) const
-{
-    MFEM_ASSERT(width == x.Size(), "Input vector size (" << x.Size()
-                << ") must match matrix width (" << width << ")");
-
-    MFEM_ASSERT(height == y.Size(), "Output vector size (" << y.Size()
-                << ") must match matrix height (" << height << ")");
-
-    auto inputs  = InputFields();
-    auto outputs = OutputFields();
-
-    BlockVector xb(x.GetData(), input_offsets);
-    BlockVector yb(y.GetData(), output_offsets);
-    MultiVector xmv(inputs.Size()), ymv(outputs.Size());
-
-    // Set the data pointers of the input and output fields
-    // of the graph to point to the corresponding blocks of
-    // the input and output vectors
-    for(int i=0; i < inputs.Size(); i++)
-    {
-        xmv.MakeRef(i, xb.GetBlock(i));
-    }
-
-    for(int i=0; i < outputs.Size(); i++)
-    {
-        ymv.MakeRef(i, yb.GetBlock(i));
-    }
-
-    const_cast<DAGraph*>(this)->Mult(xmv, ymv);
-}
-
-void DAGraph::Mult(const MultiVector &x, MultiVector &y)
-{
-    auto inputs  = InputFields();
-    auto outputs = OutputFields();
-
-    MFEM_ASSERT(inputs.Size() == x.NumBlocks(), "Number of input blocks (" << x.NumBlocks()
-                << ") must match number of input fields (" << inputs.Size() << ")");
-
-    MFEM_ASSERT(outputs.Size() == y.NumBlocks(), "Number of output blocks (" << y.NumBlocks()
-                << ") must match number of output fields (" << outputs.Size() << ")");
-
-    for(int i=0; i < inputs.Size(); i++)
-    {
-        inputs[i]->SetData(const_cast<Vector*>(&x[i]));
-    }
-    for (int i=0; i < outputs.Size(); i++)
-    {
-        outputs[i]->SetData(&y[i]);
-    }
-
-    auto index_map = GetFieldIdToIndexMap();
-    auto fld_map = GetFieldIdToFieldMap();
-    int nfields = index_map.NumFields();
-    MultiVector ymv(nfields); // TODO: Should this be a member function?
-
-    // Assemble the multivector from the individual fields based on their IDs
-    // This multivector contains all input, output, and intermediate fields in the graph
-    for (auto const& [id, idx] : index_map)
-    {
-        if (fld_map.Has(id))
-        {
-            auto field = fld_map.Get(id);
-            ymv.MakeRef(idx, *field->Data());
-        }
-        else
-        {
-            MFEM_ABORT("Field ID " << id << " not found in field map");
-        }
-    }
-    
-    Execute(x, ymv);
-
-    for(auto &f : inputs)
-    {
-        f->SetData(nullptr);
-    }
-    for(auto &f : outputs)
-    {
-        f->SetData(nullptr);
-    }
-}
-
-void DAGraph::Execute(const MultiVector &x, MultiVector &y) const
-{
-    MFEM_ASSERT(assembled, "DAGraph must be assembled before calling Execute()");
-
-    MFEM_ASSERT(x.NumBlocks() == InputFields().Size(),
-                "Number of input blocks (" << x.NumBlocks()
-                << ") must match number of input fields (" << InputFields().Size() << ")");
-    
-    auto index_map = GetFieldIdToIndexMap();
-    
-    MFEM_ASSERT(y.NumBlocks() == index_map.NumFields(),
-                "Number of output blocks (" << y.NumBlocks()
-                << ") must match number of fields (" << index_map.NumFields() << ")");
-
-    auto inputs  = InputFields();
-    for(int i=0; i < inputs.Size(); i++)
-    {
-        int idx = index_map.Get(inputs[i]->ID());
-        if(&y[idx] != &x[i]) // copy data, if address is different
-        {
-            y[idx] = x[i];
-        }
-    }
-
-    if(input_type == InputType::VECTOR)
-    {
-        x_node.SetSize(MaxWidth());
-        y_node.SetSize(MaxHeight());
-
-        for (auto node : nodes)
-        {
-            x_node.SetSize(node->Width());
-            y_node.SetSize(node->Height());
-
-            // Assemble input fields into a single vector for the node
-            auto node_inputs = node->InputFields();
-            auto ioffsets = node->InputOffsets();
-            for (int i=0; i < node_inputs.Size(); i++)
-            {
-                auto in_field = node_inputs[i];
-                int idx = index_map.Get(in_field->ID());
-                x_node.SetVector(y[idx],ioffsets[i]);
-            }
-
-            node->Mult(x_node, y_node);
-
-            // Disassemble output vector back
-            auto node_outputs = node->OutputFields();
-            BlockVector ynb(y_node.GetData(), node->OutputOffsets());
-            for (int i=0; i < node_outputs.Size(); i++)
-            {
-                auto out_field = node_outputs[i];
-                int idx = index_map.Get(out_field->ID());
-                y[idx] = ynb.GetBlock(i);
-            }
-        }
-    }
-    else if(input_type == InputType::MULTIVECTOR)
-    {
-        for (auto node : nodes)
-        {
-            auto node_inputs = node->InputFields();
-            auto node_outputs = node->OutputFields();
-            xmv_node.SetNumBlocks(node_inputs.Size());
-            ymv_node.SetNumBlocks(node_outputs.Size());
-
-            for (int i=0; i < node_inputs.Size(); i++)
-            {
-                int idx = index_map.Get(node_inputs[i]->ID());
-                xmv_node.MakeRef(i, y[idx]);
-            }
-            for (int i=0; i < node_outputs.Size(); i++)
-            {
-                int idx = index_map.Get(node_outputs[i]->ID());
-                ymv_node.MakeRef(i, y[idx]);
-            }
-            node->Mult(xmv_node, ymv_node);
-        }
-    }
-    else if(input_type == InputType::NONE)
-    {
-        Vector x_unused, y_unused;
-        for (auto node : nodes)
-        {
-            node->Mult(x_unused, y_unused);
-        }
-    }
-    else
-    {
-        MFEM_ABORT("DAGraph::Execute() not implemented for input type: "
-                    << static_cast<int>(input_type));
-    }
-}
-
-Operator& DAGraph::GetGradient(const Vector &x) const
-{
-    // TODO: Should/could be removed
-    if(grad_mode == GradMode::FINITE_DIFF)
-    {
-        if(!grad)
-        {
-            grad = new future::FDJacobian(*this, x, 1e-6);
-        }
-        else
-        {
-            grad->GetGradient(x); // Update the FDJacobian with new point x
-        }
-        return *grad;
-    }
-
-    MFEM_ASSERT(static_cast<int>(grad_mode) < static_cast<int>(GradMode::NONE),
-                "DAGraph::GetGradient() called with invalid grad_mode: "
-                << static_cast<int>(grad_mode));
-
-    if(!grad)
-    {
-        grad = new GraphGradient(const_cast<DAGraph&>(*this));
-    }
-
-    if(grad_mode == GradMode::ASSEMBLED)
-    {
-        return grad->GetGradient(x); // Assemble the Jacobian matrix
-    }
-    else // GradMode::MATRIX_FREE
-    {
-        dynamic_cast<GraphGradient*>(grad)->Update(x); // Update the GraphGradient with new point x
-    }
-
-    return *grad;
-}
-
-GraphGradient::GraphGradient(DAGraph &dag) : Operator(dag.Height(), dag.Width()),
-                                             graph(&dag)
-{
-    MFEM_ASSERT(graph->IsAssembled(), "GraphGradient requires an assembled DAGraph.");
-    MFEM_ASSERT(graph->IsSorted(), "GraphGradient requires a topologically sorted DAGraph.");
-
-    auto index_map = graph->GetFieldIdToIndexMap();
-    auto field_map = graph->GetFieldIdToFieldMap();
-
-    MFEM_ASSERT(index_map.NumFields() == field_map.NumFields(),
-                "Mismatch in number of fields between index_map and field_map");
-
-    x_work.DeleteAll(); // Clear any existing pointers
-    x_work.SetSize(index_map.NumFields());
-    x_work = nullptr; // Initialize all pointers to nullptr
-    xlin.SetNumBlocks(index_map.NumFields());
-
-    for (auto const& [id, idx] : index_map)
-    {
-        MFEM_ASSERT(idx >= 0 && idx < x_work.Size(), "Index out of bounds for field ID: " << id);
-        MFEM_ASSERT(field_map.Has(id), "Field ID not found in field_map: " << id);
-
-        if(x_work[idx] == nullptr)
-        {
-            x_work[idx] = new Vector(); // Allocate a new Vector for this field
-        }
-        xlin.MakeRef(idx, *x_work[idx]); // Make xlin refer to the allocated Vector
-    }
-
-}
-
-void GraphGradient::Update(const Vector &x)
-{
-    MFEM_ASSERT(graph != nullptr, "GraphGradient operator requires a non-null DAGraph pointer.");
-
-    auto set_exec_mode = [&](DAGraph::ExecutionMode mode)
-    {
-        for (auto &node : graph->Nodes())
-        {
-            node->SetExecutionMode(mode);
-        }
-    };
-
-    auto inputs = graph->InputFields();
-    BlockVector xb(x.GetData(), graph->InputOffsets());
-    MultiVector xmv(inputs.Size());
-    for(int i=0; i < inputs.Size(); i++)
-    {
-        xmv.MakeRef(i, xb.GetBlock(i));
-    }
-
-    set_exec_mode(DAGraph::ExecutionMode::GRADIENT_MODE);
-    graph->Execute(xmv, xlin); // Forward pass to populate fields for gradient computations
-    set_exec_mode(DAGraph::ExecutionMode::DEFAULT_MODE); // Reset execution mode for forward pass
-}
-
-void GraphGradient::Mult(const Vector &x, Vector &y) const
-{
-    MFEM_ASSERT(x.Size() == graph->Width(), "Input vector size (" << x.Size()
-                << ") must match graph width (" << graph->Width() << ")");
-
-    MFEM_ASSERT(y.Size() == graph->Height(), "Output vector size (" << y.Size()
-                << ") must match graph height (" << graph->Height() << ")");
-
-    auto in_offsets  = graph->InputOffsets();
-    auto out_offsets = graph->OutputOffsets();
-
-    auto inputs  = graph->InputFields();
-    auto outputs = graph->OutputFields();
-
-    BlockVector xb(x.GetData(), in_offsets);
-    BlockVector yb(y.GetData(), out_offsets);
-    MultiVector xmv(inputs.Size()), ymv(outputs.Size());
-
-    for(int i=0; i < inputs.Size(); i++)
-    {
-        xmv.MakeRef(i, xb.GetBlock(i));
-    }
-
-    for(int i=0; i < outputs.Size(); i++)
-    {
-        ymv.MakeRef(i, yb.GetBlock(i));
-    }
-
-    const_cast<GraphGradient*>(this)->Mult(xmv, ymv); // Forward mode: compute JVP, y = J(z) * x
-}
-
-void GraphGradient::Mult(const MultiVector &x, MultiVector &y)
-{
-    auto inputs  = graph->InputFields();
-    auto outputs = graph->OutputFields();
-
-    MFEM_ASSERT(inputs.Size() == x.NumBlocks(), "Number of input blocks (" << x.NumBlocks()
-                << ") must match number of input fields (" << inputs.Size() << ")");
-
-    MFEM_ASSERT(outputs.Size() == y.NumBlocks(), "Number of output blocks (" << y.NumBlocks()
-                << ") must match number of output fields (" << outputs.Size() << ")");
-
-    for(int i=0; i < inputs.Size(); i++)
-    {
-        inputs[i]->SetAdjoint(const_cast<Vector*>(&x[i]));
-    }
-    for (int i=0; i < outputs.Size(); i++)
-    {
-        outputs[i]->SetAdjoint(&y[i]);
-    }
-
-    auto index_map = graph->GetFieldIdToIndexMap();
-    auto fld_map = graph->GetFieldIdToFieldMap();
-    int nfields = index_map.NumFields();
-    MultiVector ymv(nfields); // TODO: Should this be a member function?
-
-    // Assemble the multivector from the individual fields based on their IDs
-    // This multivector contains all input, output, and intermediate fields in the graph
-    for (auto const& [id, idx] : index_map)
-    {
-        if (fld_map.Has(id))
-        {
-            auto field = fld_map.Get(id);
-            ymv.MakeRef(idx, *field->Adjoint());
-        }
-        else
-        {
-            MFEM_ABORT("Field ID " << id << " not found in field map");
-        }
-    }
-
-    Forward(x, ymv); // Forward mode: compute JVP, y = J(z) * x
-
-    for (auto &f : inputs)
-    {
-        f->SetAdjoint(nullptr);
-    }
-    for (auto &f : outputs)
-    {
-        f->SetAdjoint(nullptr);
-    }
-}
-
-void GraphGradient::MultTranspose(const Vector &x, Vector &y) const
-{
-    MFEM_ASSERT(x.Size() == graph->Height(), "Input vector size (" << x.Size()
-                << ") must match graph height (" << graph->Height() << ")");
-    MFEM_ASSERT(y.Size() == graph->Width(), "Output vector size (" << y.Size()
-                << ") must match graph width (" << graph->Width() << ")");
-
-    auto in_offsets  = graph->InputOffsets();
-    auto out_offsets = graph->OutputOffsets();
-
-    auto inputs  = graph->InputFields();
-    auto outputs = graph->OutputFields();
-
-    BlockVector xb(x.GetData(), out_offsets);
-    BlockVector yb(y.GetData(), in_offsets);
-    MultiVector xmv(outputs.Size()), ymv(inputs.Size());
-
-    for(int i=0; i < inputs.Size(); i++)
-    {
-        xmv.MakeRef(i, xb.GetBlock(i));
-    }
-
-    for(int i=0; i < outputs.Size(); i++)
-    {
-        ymv.MakeRef(i, yb.GetBlock(i));
-    }
-    const_cast<GraphGradient*>(this)->MultTranspose(xmv, ymv); // Reverse mode: compute VJP, y = J(z)^T * x
-}
-
-void GraphGradient::MultTranspose(const MultiVector &x, MultiVector &y)
-{
-    auto inputs  = graph->InputFields();
-    auto outputs = graph->OutputFields();
-
-    MFEM_ASSERT(outputs.Size() == x.NumBlocks(), "Number of input blocks (" << x.NumBlocks()
-                << ") must match number of output fields (" << outputs.Size() << ")");
-
-    MFEM_ASSERT(inputs.Size() == y.NumBlocks(), "Number of output blocks (" << y.NumBlocks()
-                << ") must match number of input fields (" << inputs.Size() << ")");
-
-    for(int i=0; i < outputs.Size(); i++)
-    {
-        outputs[i]->SetAdjoint(const_cast<Vector*>(&x[i]));
-    }
-    for (int i=0; i < inputs.Size(); i++)
-    {
-        inputs[i]->SetAdjoint(&y[i]);
-    }
-
-    auto index_map = graph->GetFieldIdToIndexMap();
-    auto fld_map = graph->GetFieldIdToFieldMap();
-    int nfields = index_map.NumFields();
-    MultiVector ymv(nfields); // TODO: Should this be a member function?
-
-    for(auto const& [id, idx] : index_map)
-    {
-        if (fld_map.Has(id))
-        {
-            auto field = fld_map.Get(id);
-            ymv.MakeRef(idx, *field->Adjoint());
-        }
-        else
-        {
-            MFEM_ABORT("Field ID " << id << " not found in field map");
-        }
-    }
-
-    Reverse(x, ymv); // Reverse mode: compute VJP, y = J(z)^T * x
-
-    for (auto &f : outputs)
-    {
-        f->SetAdjoint(nullptr);
-    }
-    for (auto &f : inputs)
-    {
-        f->SetAdjoint(nullptr);
-    }
-}
-
-void GraphGradient::Forward(const MultiVector &x, MultiVector &y) const
-{
-    MFEM_ASSERT(x.NumBlocks() == graph->InputFields().Size(),
-                "Number of input blocks (" << x.NumBlocks()
-                << ") must match number of input fields (" << graph->InputFields().Size() << ")");
-    
-    auto in_type = graph->GetInputType();
-    auto index_map  = graph->GetFieldIdToIndexMap();
-    auto field_map = graph->GetFieldIdToFieldMap();
-
-    MFEM_ASSERT(y.NumBlocks() == index_map.NumFields(),
-                "Number of output blocks (" << y.NumBlocks()
-                << ") must match number of fields (" << index_map.NumFields() << ")");
-
-    auto inputs  = graph->InputFields();
-    for(int i=0; i < inputs.Size(); i++)
-    {
-        int idx = index_map.Get(inputs[i]->ID());
-        if(&y[idx] != &x[i]) // copy data, if address is different
-        {
-            y[idx] = x[i];
-        }
-    }
-
-    if(in_type == InputType::VECTOR)
-    {
-        x0.SetSize(graph->MaxWidth());
-        dx.SetSize(graph->MaxWidth());
-        dy.SetSize(graph->MaxHeight());
-
-        auto nodes = graph->Nodes();
-        for (auto node : nodes)
-        {
-            x0.SetSize(node->Width());
-            dx.SetSize(node->Width());
-            dy.SetSize(node->Height());
-
-            // Assemble input fields into a single vector for the node
-            auto node_inputs = node->InputFields();
-            auto ioffsets = node->InputOffsets();
-            for(int i=0; i < node_inputs.Size(); i++)
-            {
-                auto in_field = node_inputs[i];
-                MFEM_ASSERT(index_map.Has(in_field->ID()), "Input field ID not found in index_map");
-                int idx = index_map.Get(in_field->ID());
-                x0.SetVector(xlin[idx], ioffsets[i]);
-                dx.SetVector(y[idx], ioffsets[i]);
-            }
-
-            node->GradientMult(x0, dx, dy); // Compute JVP for the node
-
-            // Disassemble output vector back
-            auto node_outputs = node->OutputFields();
-            BlockVector ynb(dy.GetData(), node->OutputOffsets());
-            for(int i=0; i < node_outputs.Size(); i++)
-            {
-                auto out_field = node_outputs[i];
-                MFEM_ASSERT(index_map.Has(out_field->ID()), "Output field ID not found in index_map");
-                int idx = index_map.Get(out_field->ID());
-                y[idx] = ynb.GetBlock(i);
-            }
-        }
-    }
-    else if(in_type == InputType::MULTIVECTOR)
-    {
-        auto nodes = graph->Nodes();
-        for (auto node : nodes)
-        {
-            auto node_inputs = node->InputFields();
-            auto node_outputs = node->OutputFields();
-            x0_mv.SetNumBlocks(node_inputs.Size());
-            dx_mv.SetNumBlocks(node_inputs.Size());
-            dy_mv.SetNumBlocks(node_outputs.Size());
-
-            for(int i=0; i < node_inputs.Size(); i++)
-            {
-                int idx = index_map.Get(node_inputs[i]->ID());
-                x0_mv.MakeRef(i, xlin[idx]);
-                dx_mv.MakeRef(i, y[idx]);
-            }
-            for(int i=0; i < node_outputs.Size(); i++)
-            {
-                int idx = index_map.Get(node_outputs[i]->ID());
-                dy_mv.MakeRef(i, y[idx]);
-            }
-            node->GradientMult(x0_mv, dx_mv, dy_mv); // Compute JVP for the node
-        }
-    }
-    else if(in_type == InputType::NONE)
-    {
-        Vector x_unused, dx_unused, dy_unused;
-        auto nodes = graph->Nodes();
-        for (auto node : nodes)
-        {
-            node->GradientMult(x_unused, dx_unused, dy_unused);
-        }
-    }
-    else
-    {
-        MFEM_ABORT("GraphGradient::Forward() not implemented for input type: "
-                    << static_cast<int>(in_type));
-    }
-}
-
-void GraphGradient::Reverse(const MultiVector &x, MultiVector &y) const
-{
-    MFEM_ASSERT(x.NumBlocks() == graph->OutputFields().Size(),
-                "Number of input blocks (" << x.NumBlocks()
-                << ") must match number of output fields (" << graph->OutputFields().Size() << ")");
-
-    auto in_type = graph->GetInputType();
-    auto index_map  = graph->GetFieldIdToIndexMap();
-    auto field_map = graph->GetFieldIdToFieldMap();
-    int nnodes  = graph->Size();
-
-    MFEM_ASSERT(y.NumBlocks() == index_map.NumFields(),
-                "Number of output blocks (" << y.NumBlocks()
-                << ") must match number of fields (" << index_map.NumFields() << ")");
-
-    auto outputs  = graph->OutputFields();
-    for(int i=0; i < outputs.Size(); i++)
-    {
-        int idx = index_map.Get(outputs[i]->ID());
-        if(&y[idx] != &x[i]) // copy data, if address is different
-        {
-            y[idx] = x[i];
-        }
-    }
-
-    if(in_type == InputType::VECTOR)
-    {
-        x0.SetSize(graph->MaxWidth());
-        dx.SetSize(graph->MaxHeight());
-        dy.SetSize(graph->MaxWidth());
-
-        for (int i=nnodes-1; i >= 0; i--)
-        {
-            auto node = graph->GetNode(i);
-            x0.SetSize(node->Width());
-            dx.SetSize(node->Height());
-            dy.SetSize(node->Width());
-
-            auto node_inputs = node->InputFields();
-            auto ioffsets = node->InputOffsets();
-            for(int i=0; i < node_inputs.Size(); i++)
-            {
-                auto in_field = node_inputs[i];
-                MFEM_ASSERT(index_map.Has(in_field->ID()), "Input field ID not found in index_map");
-                int idx = index_map.Get(in_field->ID());
-                x0.SetVector(xlin[idx], ioffsets[i]);
-            }
-
-            auto node_outputs = node->OutputFields();
-            auto ooffsets = node->OutputOffsets();
-            for(int i=0; i < node_outputs.Size(); i++)
-            {
-                auto out_field = node_outputs[i];
-                MFEM_ASSERT(index_map.Has(out_field->ID()), "Output field ID not found in index_map");
-                int idx = index_map.Get(out_field->ID());
-                dx.SetVector(y[idx], ooffsets[i]);
-            }
-
-            node->GradientMultTranspose(x0, dx, dy); // Compute JVP for the node
-
-            BlockVector dynb(dy.GetData(), node->InputOffsets());
-            for(int i=0; i < node_inputs.Size(); i++)
-            {
-                int idx = index_map.Get(node_inputs[i]->ID());
-                y[idx] = dynb.GetBlock(i);
-            }
-        }
-    }
-    else if(in_type == InputType::MULTIVECTOR)
-    {
-        for (int i=nnodes-1; i >= 0; i--)
-        {
-            auto node = graph->GetNode(i);
-            auto node_inputs = node->InputFields();
-            auto node_outputs = node->OutputFields();
-            x0_mv.SetNumBlocks(node_inputs.Size());
-            dx_mv.SetNumBlocks(node_outputs.Size());
-            dy_mv.SetNumBlocks(node_inputs.Size());
-
-            for(int i=0; i < node_inputs.Size(); i++)
-            {
-                int idx = index_map.Get(node_inputs[i]->ID());
-                x0_mv.MakeRef(i, xlin[idx]);
-                dy_mv.MakeRef(i, y[idx]);
-            }
-            for(int i=0; i < node_outputs.Size(); i++)
-            {
-                int idx = index_map.Get(node_outputs[i]->ID());
-                dx_mv.MakeRef(i, y[idx]);
-            }
-            node->GradientMultTranspose(x0_mv, dx_mv, dy_mv); // Compute JVP for the node
-        }
-    }
-    else if(in_type == InputType::NONE)
-    {
-        Vector x_unused, dx_unused, dy_unused;
-        for (int i=nnodes-1; i >= 0; i--)
-        {
-            auto node = graph->GetNode(i);
-            node->GradientMultTranspose(x_unused, dx_unused, dy_unused); // Compute VJP for the node
-        }
-    }
-    else
-    {
-        MFEM_ABORT("GraphGradient::Reverse() not implemented for input type: "
-                    << static_cast<int>(in_type));
-    }
-}
-
-Operator& GraphGradient::GetGradient(const Vector &x) const
-{
-    // Used to build Jacobian matrix
-    MFEM_ABORT("GraphGradient::GetGradient() not implemented");
-}
-
-
-} // namespace mfem

miniapps/multiapp/multiapp.hpp

@@ -1,838 +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_MULTIAPP_HPP
-#define MFEM_MULTIAPP_HPP
-
-#include "mfem.hpp"
-
-namespace mfem
-{
-
-/// Forward declarations needed below
-class Field;
-class FieldCollection;
-class GraphNode;
-class DAGraph;
-class GraphGradient;
-
-
-/// @brief Base class for storing data (Vector) and distinguishing
-/// fields variables
-class Field
-{
-public:
-    enum Type ///< Not used for now, but could be used to distinguish between input/output fields
-    {
-        INPUT , ///< Input field
-        OUTPUT, ///< Output field
-        DEFAULT ///< Any field
-    };
-
-    friend class GraphNode;
-
-private:
-    Type type = Type::DEFAULT;
-    inline static int next_id = 0;
-
-protected:
-    Vector *data = nullptr;
-    Vector *adjoint = nullptr; // For storing derivative info
-    int id = -1; // initialized to invalid id
-
-    std::string name; // Optional name for the field
-    Operator *oper  = nullptr; // Operator that outputs this field
-
-    int GetValidID(int id_, int lb=0, int ub = std::numeric_limits<int>::max())
-    {
-        return (id_ >= lb && id_ <= ub) ? id_ : next_id++;
-    }
-
-public:
-
-    ///@brief Constructor for a Field of type Type with optional ID
-    Field(Vector *field, Vector *adjoint, Type type, int id_ = -1) :
-          type(type), data(field), adjoint(adjoint), id(GetValidID(id_)),
-          name("Field_" + std::to_string(id)) { }
-
-    ///@brief Constructor for a Field of Default type with optional ID
-    Field(Vector *field, Vector *adjoint, int id_ = -1) : 
-          Field(field, adjoint, Type::DEFAULT, id_) { }
-
-    ///@brief Constructor for an input field
-    Field(Vector *field, int id_ = -1) :
-          Field(field, nullptr, Type::DEFAULT, id_) { }
-
-    ///@brief Constructor for a Field of type Type
-    Field(Vector *field, Type type, int id_ = -1) :
-          Field(field, nullptr, type, id_) { }
-
-    ///@brief Get the stored internally stored data pointer
-    Vector* Data() const { return data; }
-    Vector* Adjoint() const { return adjoint; }
-    Operator* GetOperator() const { return oper; }
-
-    ///@brief Set the internally stored data pointer
-    virtual void SetData(Vector *field) { data = field; }
-    virtual void SetAdjoint(Vector *adj) { adjoint = adj; }
-    virtual void SetOperator(Operator *op) { oper = op; }
-
-    virtual void GetData(Vector &field) const { field = *data; }
-    virtual void GetAdjoint(Vector &adj) const { adj = *adjoint; }
-
-    std::string Name() const { return name; }
-    void SetName(const std::string &n) { name = n; }
-    int ID() const { return id; }
-
-    void SetID(int i)
-    {
-        MFEM_ASSERT(i >= 0, "ID must be non-negative.");
-        id = i;
-    }
-
-    bool IsInput() const {return (type == Type::INPUT);}
-    bool IsOutput() const {return (type == Type::OUTPUT);}
-    bool IsDefault() const {return (type == Type::DEFAULT);}
-
-    virtual ~Field() = default;
-
-protected:
-
-    ///@brief Set the type of the field (prevents changing type of input/output fields)
-    void SetType(Type t)
-    {
-        type = t;
-    }
-};
-
-/// @brief A collection of Fields, each identified by a name
-class FieldCollection
-{
-public:
-    using FieldMap = GenericFieldMap<std::string, Field*>;
-    using IndexMap = GenericFieldMap<std::string, int>;
-
-private:
-    std::string name; /// Name of the collection
-    Operator *oper = nullptr; /// Operator associated with this collection (not owned)
-    FieldMap fields; /// Map from field name to Field pointer
-    IndexMap index_map; /// Map from field name to index in input/output vectors
-
-    Array<Field*> input_fields;  // Input fields for this node
-    Array<Field*> output_fields; // Output fields for this node
-
-public:
-
-    FieldCollection() = default;
-
-    /// @brief Constructor with collection name and optional associated operator
-    FieldCollection(std::string collection_name, Operator *op = nullptr):
-                    name(collection_name), oper(op) {}
-
-    /// @brief Constructor with associated operator and default collection name
-    FieldCollection(Operator *op) : name("FieldCollection"), oper(op) {}
-
-    /// @brief Get the number of fields in the collection
-    int Size() const { return fields.NumFields(); }
-
-    /// @brief Set the name of the collection
-    void SetName(const std::string &collection_name) { name = collection_name;}
-
-    /// @brief Get the name of the collection
-    std::string Name() const { return name; }
-
-    /// @brief Set the operator associated with this collection
-    void SetOperator(Operator *op){ oper = op; }
-
-    /// @brief Get the operator associated with this collection
-    const Operator* GetOperator() const { return oper; }
-
-    /// @brief Get the field associated with the given name, or nullptr if not found
-    Field* GetField(const std::string &field_name) const
-    {
-        return fields.Get(field_name);
-    }
-
-    /// @brief Add a field to the collection with a given name and ownership flag
-    void AddField(const std::string &field_name, Field *field, bool own = false)
-    {
-        if(fields.Has(field_name))
-        {
-            MFEM_WARNING("FieldCollection::AddField: Field with name "
-                         << field_name << " already exists. Replacing existing field.");
-        }
-        fields.Register(field_name, field, own);
-    }
-
-    void AddInput(const std::string &field_name,
-                  Field *field, bool own = false)
-    {
-        bool has_field = fields.Has(field_name);
-        bool has_index = index_map.Has(field_name);
-        if(has_field && has_index)
-        {
-            int i = index_map.Get(field_name);
-            input_fields[i] = field;
-        }
-        else
-        {
-            input_fields.push_back(field);
-            index_map.Register(field_name, input_fields.Size() - 1);
-        }
-        AddField(field_name, field, own);
-    }
-
-    void AddOutput(const std::string &field_name,
-                   Field *field, bool own = false)
-    {
-        bool has_field = fields.Has(field_name);
-        bool has_index = index_map.Has(field_name);
-        if(has_field && has_index)
-        {
-            int i = index_map.Get(field_name);
-            output_fields[i] = field;
-        }
-        else
-        {
-            output_fields.push_back(field);
-            index_map.Register(field_name, output_fields.Size() - 1);
-        }
-
-        AddField(field_name, field, own);
-        if(field->GetOperator() == nullptr)
-        {
-            field->SetOperator(oper);
-        }
-    }
-
-    Array<Field*>& InputFields() { return input_fields; }
-    Array<Field*>& OutputFields() { return output_fields; }
-
-    Field* InputField(int i) const { return input_fields[i]; }
-    Field *InputField(const std::string &field_name) const
-    {
-        bool has_index = index_map.Has(field_name);
-        if(!has_index)
-        {
-            MFEM_WARNING("FieldCollection::InputField: Field with name "
-                         << field_name << " does not exist in the collection.");
-            return nullptr;
-        }
-
-        int index = index_map.Get(field_name);
-        MFEM_VERIFY(index >= 0 && index < input_fields.Size(),
-                    "FieldCollection::InputField: Invalid index for field name: "
-                    << field_name << ".");
-        return input_fields[index];
-    }
-
-    Field* OutputField(int i) const { return output_fields[i]; }
-    Field *OutputField(const std::string &field_name) const
-    {
-        bool has_index = index_map.Has(field_name);
-        if(!has_index)
-        {
-            MFEM_WARNING("FieldCollection::OutputField: Field with name "
-                         << field_name << " does not exist in the collection.");
-            return nullptr;
-        }
-
-        int index = index_map.Get(field_name);
-        MFEM_VERIFY(index >= 0 && index < output_fields.Size(),
-                    "FieldCollection::OutputField: Invalid index for field name: "
-                    << field_name << ".");
-        return output_fields[index];
-    }
-
-    FieldMap &Fields() { return fields; }
-    FieldMap Fields() const { return fields; }
-
-    virtual void Save (std::ostream &out) const
-    {
-        out << "\"Fields\":\n";
-        out << "{\n";
-        for (auto f = fields.begin(); f != fields.end(); ++f)
-        {
-            std::string f_name = f->first;
-            Field *f_obj = f->second;
-            // out << "  " << f_name << ": ID " << f_obj->ID() << ",\n";
-            // out << f_obj->ID() << ": " << f_name << ",\n";
-            out << '\"' << f_obj->ID() << "\": \"" << f_name << "\"";
-            if(f != std::prev(fields.end())) out << ",";
-            out << "\n";
-        }
-        out << "},\n";
-
-        out << "\"Inputs\":\n";
-        out << "{\n";
-        for (int i = 0; i < input_fields.Size(); ++i)
-        {
-            Field *f_obj = input_fields[i];
-            out << '\"' << f_obj->ID() << "\": \"" << f_obj->Name() << "\"";
-            if(i != input_fields.Size() - 1) out << ",";
-            out << "\n";
-        }
-        out << "},\n";
-
-        out << "\"Outputs\":\n";
-        out << "{\n";
-        for (int i = 0; i < output_fields.Size(); ++i)
-        {
-            Field *f_obj = output_fields[i];
-            out << '\"' << f_obj->ID() << "\": \"" << f_obj->Name() << "\"";
-            if(i != output_fields.Size() - 1) out << ",";
-            out << "\n";
-        }
-        out << "}\n";
-    }
-
-    Field* HasField(const Field &field) const
-    {
-        for (auto f = fields.begin(); f != fields.end(); ++f)
-        {
-            if(f->second == &field)
-            {
-                return f->second;
-            }
-        }
-        return nullptr;
-    }
-
-    Field* HasField(const std::string &field_name) const
-    {
-        return fields.Get(field_name);
-    }
-
-    Field* HasField(const int id) const
-    {
-        for (auto f = fields.begin(); f != fields.end(); ++f)
-        {
-            if(f->second->ID() == id)
-            {
-                return f->second;
-            }
-        }
-        return nullptr;
-    }
-
-    ~FieldCollection(){}
-
-};
-
-
-class GraphNode : public Operator
-{
-public:
-    enum ExecutionMode
-    {
-        GRADIENT_MODE, ///< Node is being executed as part of a gradient evaluation
-        DEFAULT_MODE   ///< Node is being executed as default, operator evaluation
-    };
-
-private:
-    inline static int next_id = 0;
-
-protected:
-    int id = -1;
-    int node_index = -1;
-    mutable ExecutionMode exec_mode = DEFAULT_MODE;
-
-    std::string name;
-    mutable FieldCollection field_collection; ///< Collection of fields associated with this node
-
-    // Offsets to be used for operation on BlockVector
-    Array<int> input_offsets;  ///< Offsets for input fields
-    Array<int> output_offsets; ///< Offsets for output fields
-
-    int GetValidID(int id_, int lb=0, int ub = std::numeric_limits<int>::max())
-    {
-        return (id_ >= lb && id_ <= ub) ? id_ : next_id++;
-    }
-
-public:
-
-    GraphNode(int h, int w) : Operator(h,w), id(GetValidID(-1)),
-                              name("Node_" + std::to_string(id)),
-                              field_collection(this) { }
-
-    GraphNode(int s = 0) : GraphNode(s, s) { }
-
-    void SetNodeIndex(int index){ node_index = index; }
-    int GetNodeIndex() const { return node_index; }
-
-    void SetExecutionMode(ExecutionMode mode) { exec_mode = mode; }
-    ExecutionMode GetExecutionMode() const { return exec_mode; }
-
-    void SetName(const std::string &name_) { name = name_; }
-    std::string Name() const { return name; }
-
-    void SetID(int id_) { id = id_; }
-    int ID() const { return id; }
-
-    FieldCollection::FieldMap& Fields() { return field_collection.Fields(); }
-    Field* Fields(const std::string &f) { return field_collection.GetField(f); }
-
-    FieldCollection::FieldMap Fields() const { return field_collection.Fields(); }
-    Field* Fields(const std::string &f) const { return field_collection.GetField(f); }
-
-    Array<Field*>& InputFields() const { return field_collection.InputFields(); }
-    Array<Field*>& OutputFields() const { return field_collection.OutputFields(); }
-    Field* InputField(int i) const { return field_collection.InputField(i); }
-    Field* OutputField(int i) const { return field_collection.OutputField(i); }
-
-
-    virtual void AddInput(const std::string &field_name,
-                          Field *field, bool own = false)
-    { field_collection.AddInput(field_name, field, own); }
-
-    virtual void AddInput(Field *field, bool own = false)
-    { AddInput(field->Name(), field, own); }
-
-    template<bool OwnInputs = false,
-             typename... Args,
-             bool AreFields = std::conjunction<std::is_base_of<Field, std::remove_pointer_t<Args>> ...>::value,
-             typename std::enable_if<AreFields, bool>::type = true >
-    void AddInputs(Args... args)
-    {
-        ((AddInput(std::forward<Args>(args), OwnInputs)), ...);
-    }
-
-    virtual void AddOutput(const std::string &field_name,
-                           Field *field, bool own = false)
-    { field_collection.AddOutput(field_name, field, own); }
-
-    virtual void AddOutput(Field *field, bool own = false)
-    { AddOutput(field->Name(), field, own); }
-
-    template<bool OwnOutputs = false,
-             typename... Args,
-             bool AreFields = std::conjunction<std::is_base_of<Field, std::remove_pointer_t<Args>> ...>::value,
-             typename std::enable_if<AreFields, bool>::type = true >
-    void AddOutputs(Args... args)
-    {
-        ((AddOutput(std::forward<Args>(args), OwnOutputs)), ...);
-    }
-
-    virtual void Save (std::ostream &out) const
-    {
-        out << "\"Node-" << id << "\" : " << std::endl;
-        out << "{\n";
-        out << "\"Name\": \"" << name << "\",\n";
-        field_collection.Save(out);
-        out << "}";
-    }
-
-    virtual void Mult(const Vector &x, Vector &y) const override
-    {
-        MFEM_ABORT("GraphNode::Mult() not implemented");
-    }
-
-    virtual void Mult(const MultiVector &x, MultiVector &y) override
-    {
-        MFEM_ABORT("GraphNode::Mult(MultiVector) not implemented");
-    }
-
-    using Operator::GetGradient;
-
-    // TODO: Possibly remove this and only support MultiVector version of GradientMult
-    virtual void GradientMult(const Vector &x, const Vector &dx, Vector &dy) const
-    {
-        MFEM_ABORT("GraphNode::GradientMult() not implemented");
-        GetGradient(x).Mult(dx, dy);
-    }
-
-    virtual void GradientMult(const MultiVector &x, const MultiVector &dx, MultiVector &dy) const
-    {
-        MFEM_ABORT("GraphNode::GradientMult() not implemented");
-        GetGradient(x).Mult(dx, dy);
-    }
-
-    // TODO: Possibly remove this and only support MultiVector version of GradientMultTranspose
-    virtual void GradientMultTranspose(const Vector &x, const Vector &dx, Vector &dy) const
-    {
-        MFEM_ABORT("GraphNode::GradientMultTranspose() not implemented");
-        GetGradient(x).MultTranspose(dx, dy);
-    }
-
-    virtual void GradientMultTranspose(const MultiVector &x, const MultiVector &dx, MultiVector &dy) const
-    {
-        MFEM_ABORT("GraphNode::GradientMultTranspose() not implemented");
-        // GetGradient(x).MultTranspose(dx, dy); // Not yet implemented
-    }
-
-    /// @brief Return the input offsets for block starts.
-    Array<int>& InputOffsets() { return input_offsets; }
-
-    /// @brief Read only access to the input offsets for block starts.
-    const Array<int>& InputOffsets() const { return input_offsets; }
-
-    void SetInputOffsets(const Array<int> &offsets) { input_offsets = offsets; }
-
-    /// @brief Return the output offsets for block starts.
-    Array<int>& OutputOffsets() { return output_offsets; }
-
-    /// @brief Read only access to the output offsets for block starts.
-    const Array<int>& OutputOffsets() const { return output_offsets; }
-
-    void SetOutputOffsets(const Array<int> &offsets) { output_offsets = offsets; }
-
-    virtual ~GraphNode() = default;
-};
-
-
-/**
-   @brief An abstract, type-erased class to define the interface for 
-   operators, not inherited from @a GraphNode. It performs SFINAE 
-   checks for stored operator's member functions and override the Mult
-   to call the stored object's functions.
- */
-template <typename OpType>
-class AbstractOperator : public GraphNode
-{
-protected:
-    /// Define a template class 'check' to test for the existence of member functions
-    template <typename C>
-    class CheckMember{
-        private:
-
-        /// @brief A type trait to check if the erased class has the function Mult
-        /// with the needed signatures.
-        template<class T>
-        using Mult = decltype(std::declval<T&>().Mult(std::declval<const Vector&>(),
-                                                      std::declval<Vector&>()));
-
-        template<class T>
-        using MultPtr = decltype(std::declval<T&>().Mult(std::declval<const int>(),
-                                                         std::declval<const real_t*>(),
-                                                         std::declval<const int>(),
-                                                         std::declval<real_t*>()));
-        // ---------------------------------------------------------------------
-        
-        template <typename T, template<typename> typename Func, typename R>
-        static constexpr auto Check(T*) -> typename std::is_same< Func<T>, R>::type;
-
-        template <typename, template<typename> typename, typename >
-        static constexpr std::false_type Check(...);
-
-        // --- Check for the existence of the member functions
-        typedef decltype(Check<C,Mult,void>(0)) Has_Mult;
-        typedef decltype(Check<C,MultPtr,void>(0)) Has_MultPtr;
-    public:
-        static constexpr bool HasMult  = Has_Mult::value;
-        static constexpr bool HasMultPtr  = Has_MultPtr::value;
-    };
-
-    OpType *op;  ///< Pointer to the operator
-
-public:
-
-    constexpr bool HasExecute(){return CheckMember<OpType>::HasStep;}
-    constexpr bool HasMult(){return CheckMember<OpType>::HasMult;}
-
-
-    /// @brief Constructor for the type-erased AbstractOperator class
-    AbstractOperator(OpType *op_, int h, int w) : GraphNode(h,w), op(op_)
-    { }
-
-    /// @brief Constructor for the type-erased AbstractOperator class.
-    AbstractOperator(OpType *op_, int s = 0) : AbstractOperator(op_,s,s) {}
-
-    /**
-       @brief Perform Mult operation with the stored operator, if it exists.
-     */
-    void Mult(const Vector &x, Vector &y) const override
-    {
-        if constexpr (CheckMember<OpType>::HasMult)
-        {
-            op->Mult(x,y);
-        }
-        else if constexpr (CheckMember<OpType>::HasMultPtr)
-        {
-            op->Mult(x.Size(), x.GetData(), y.Size(), y.GetData());
-        }
-        else
-        {
-            MFEM_ABORT("The AbstractOperator does not have the function, "
-                       "Mult(const Vector&, Vector&) or "
-                       "Mult(int, double*, int, double*).");
-        }
-    }
-};
-
-
-/**
-   @brief A class to store and coupled multiple operators together.
- */
-class DAGraph : public GraphNode
-{
-public:
-
-    using IntToIntMap = GenericFieldMap<int, int>;
-    using IntToFieldMap = GenericFieldMap<int, Field*>;
-
-    enum class GradMode
-    {
-        FINITE_DIFF = 0,  ///< Finite difference Jacobian
-        MATRIX_FREE = 1,  ///< Matrix-free Jacobian
-        ASSEMBLED = 2,    ///< Assembled Jacobian
-        NONE = 3          ///< Not implemented
-    };
-
-    enum InputType
-    {
-        VECTOR,      ///< Asemble the input blockvector from individual fields
-        MULTIVECTOR, ///< Asemble the multivector from individual fields
-        NONE         ///< No input
-    };
-
-protected:
-    Array<GraphNode*> nodes; ///< Vector of individual operators
-    Array<bool> node_owned; ///< Whether the operators are owned
-    Array<int> node_depth; ///< Depth of each operator in the graph
-
-    int max_width  = 0;     ///< Largest operator width
-    int max_height = 0;     ///< Largest operator height
-    int nnodes     = 0;     ///< The number of nodes
-    bool sorted    = false; ///< True if the nodes are topologically sorted
-    bool assembled = false; ///< True if the graph is assembled
-
-    GradMode grad_mode = GradMode::MATRIX_FREE; ///< Gradient mode for the graph
-    mutable Operator *grad = nullptr; ///< Gradient operator
-
-    InputType input_type = InputType::MULTIVECTOR; ///< Input type for the graph
-    mutable Vector x_node, y_node; ///< Temporary vectors for evaluating nodes
-    mutable MultiVector xmv_node, ymv_node; ///< Temporary multivectors for evaluating nodes
-
-    IntToFieldMap fid_to_field; ///< Map from Field ID to Field pointer
-    IntToIntMap fid_to_index; ///< Map from ID to index in an array; needed since ordering is not unique
-
-    friend class GraphGradient;
-
-public:
-    /**
-       @brief Construct a new CoupledOperator object.
-       @param nop Total number of operators to couple
-     */
-    DAGraph(const int nop) : GraphNode()
-    {
-        nodes.Reserve(nop);
-        node_owned.Reserve(nop);
-    }
-
-    /**
-       @brief Construct a new CoupledOperator object for an 
-       abstract non/mfem operator.
-     */
-    template <class OpType>
-    DAGraph(const OpType &op) : DAGraph(1)
-    {
-        AddOperator(op);
-    }
-
-    /**
-       @brief Add an operator to the list of coupled operator and
-       return pointer to it. Not owned unless it's not derived from GraphNode.
-     */
-    template <class OpType>
-    GraphNode* AddOperator(OpType *op_, int h, int w)
-    {
-        // Add operator to list of operators
-        if constexpr(std::is_base_of<GraphNode, OpType>::value)
-        {
-            nodes.push_back(op_);
-            node_owned.Append(false);
-        } 
-        else
-        {
-            nodes.push_back(new AbstractOperator<OpType>(op_,h,w));
-            node_owned.Append(true);
-        }
-        nnodes++;
-
-        // Update size of the coupled operator and the block offsets
-        GraphNode* op = nodes.Last();
-        op->SetNodeIndex(nnodes-1); // Set the index of the operator
-
-        int ht = op->Height();
-        int wt = op->Width();
-
-        max_width = std::max(max_width, wt);
-        max_height = std::max(max_height, ht);
-        sorted = false;
-
-        return op;
-    }
-
-    /// @brief Add an operator to the list of coupled operator and return pointer to it.
-    template <class OpType>
-    GraphNode* AddOperator(OpType *op_, int s = 0) { return AddOperator(op_,s,s);}
-
-    /// @brief Get the number of coupled operators
-    int Size(){return nnodes;}
-
-    /// @brief Get the size of the largest operator
-    int MaxWidth() const {return max_width;}
-    int MaxHeight() const {return max_height;}
-
-    IntToIntMap &GetFieldIdToIndexMap() { return fid_to_index; }
-    IntToIntMap GetFieldIdToIndexMap() const { return fid_to_index; }
-
-    IntToFieldMap &GetFieldIdToFieldMap() { return fid_to_field; }
-    IntToFieldMap GetFieldIdToFieldMap() const { return fid_to_field; }
-
-    /// @brief Get the operator at index @a i
-    GraphNode* GetNode(const int i)
-    {
-        MFEM_ASSERT(i >= 0 && i < nnodes,
-               "index [" << i << "] is out of range [0," << nnodes << ")");
-        return nodes[i];
-    }
-
-    Array<GraphNode*>& Nodes() { return nodes; }
-
-    /// @brief Specify whether the operator at index @a i is owned.
-    void OwnNode(const int i, bool own = true)
-    {
-        MFEM_ASSERT(i >= 0 && i < nnodes,
-               "index [" << i << "] is out of range [0," << nnodes << ")");
-        node_owned[i] = own;
-    }
-
-    void Assemble();
-    bool IsAssembled() const { return assembled; }
-
-    void TopologicalSort();
-    bool IsSorted() const { return sorted; }
-
-    void ComputeDepth();
-
-    void ValidateOffsets();
-
-    void ValidateNode(GraphNode &node);
-
-    void CollectFieldMaps();
-
-    using GraphNode::AddInput;
-    void AddInput(Field *field, int sz, bool own = false)
-    {
-        if(input_offsets.Size() == 0)
-        {   // First entry
-            input_offsets.Append(0);
-        }
-        input_offsets.Append(input_offsets.Last() + sz);
-        AddInput(field, own);
-    }
-
-    using GraphNode::AddOutput;
-    void AddOutput(Field *field, int sz, bool own = false)
-    {
-        if(output_offsets.Size() == 0)
-        {   // First entry
-            output_offsets.Append(0);
-        }
-        output_offsets.Append(output_offsets.Last() + sz);
-        AddOutput(field, own);
-    }
-
-    /// @brief Set the gradient mode for the coupled operator
-    void SetGradientMode(GradMode mode)
-    {
-        if(mode != grad_mode)
-        {
-            if(grad) { delete grad; grad = nullptr; }
-            grad_mode = mode;
-        }
-    }
-
-    void SetInputType(InputType type) { input_type = type; }
-    InputType GetInputType() const { return input_type; }
-
-    /**
-       @brief Apply the operator to the vector @a x 
-       and return the result in @a y.
-     */
-    virtual void Mult(const Vector &x, Vector &y) const override;
-
-    virtual void Mult(const MultiVector &x, MultiVector &y) override;
-
-    virtual void Execute(const MultiVector &x, MultiVector &y) const;
-
-    virtual void Save (std::ostream &out) const
-    {
-        out << "\"DAGraph\":\n";
-        out << "{\n";
-        // out << "\"nodes\" : " << nnodes << ",\n";
-        out << "\"Nodes\":\n";
-        out << "{\n";
-        for (int i = 0; i < nodes.Size(); i++)
-        {
-            nodes[i]->Save(out);
-            if(i != nodes.Size()-1) out << ",";
-            out << "\n";
-        }
-        out << "},\n"; // End of Nodes
-        field_collection.Save(out);
-        out << "}\n";
-    }
-
-    Operator& GetGradient(const Vector &x) const override;
-
-    /// @brief Destroy the Coupled Application object
-    ~DAGraph();
-};
-
-
-
-class GraphGradient : public Operator
-{
-public:
-    using InputType = DAGraph::InputType;
-
-protected:
-    mutable DAGraph *graph = nullptr; ///< Pointer to the DAGraph for which this is the gradient operator
-    Array<Vector*> x_work; ///< Array to store linearization point (intermediate fields)
-    mutable MultiVector xlin;
-    mutable Vector x0, dx, dy;
-    mutable MultiVector x0_mv, dx_mv, dy_mv;
-
-public:
-    GraphGradient(DAGraph &dag);
-
-    void Update(const Vector &x);
-
-    void Mult(const Vector &x, Vector &y) const override;
-
-    void Mult(const MultiVector &x, MultiVector &y) override;
-
-    void MultTranspose(const Vector &x, Vector &y) const override;
-
-    void MultTranspose(const MultiVector &x, MultiVector &y);
-
-    Operator &GetGradient(const Vector &x) const override;
-
-    void Forward(const MultiVector &x, MultiVector &y) const;
-
-    void Reverse(const MultiVector &x, MultiVector &y) const;
-
-    ~GraphGradient()
-    {
-        for (auto &v : x_work)
-        {
-            if(v) { delete v; v = nullptr; }
-        }
-        x_work.DeleteAll();
-    }
-};
-
-} //mfem namespace
-
-#endif