mfem/tests/unit/linalg/test_amgfsolver.cpp

// 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 "unit_tests.hpp"
#include "mfem.hpp"
#include "../../config/config.hpp"

namespace mfem
{
#ifdef MFEM_USE_MPI

class DenseMatrixSolver : public Solver
{
private:
   DenseMatrix A;
   LUFactors LU;
   int * ipiv = nullptr;
public:
   DenseMatrixSolver() : Solver() {}

   void SetOperator(const Operator &op) override
   {
      auto Oph = const_cast<HypreParMatrix *>(dynamic_cast<const HypreParMatrix *>
                                              (&op));
      MFEM_VERIFY(Oph, "Not a compatible matrix type");
      SparseMatrix Sp;
      Oph->MergeDiagAndOffd(Sp);
      Sp.ToDenseMatrix(A);
      delete [] ipiv;
      ipiv = new int[A.Height()];
      LU.data = A.Data();
      LU.ipiv = ipiv;
      LU.Factor(A.Height());
   }

   void Mult(const Vector &x, Vector &y) const override
   {
      y = x;
      LU.Solve(A.Height(), 1, y.GetData());
   }

   ~DenseMatrixSolver() { delete [] ipiv; }
};

HypreParMatrix * GetProlongationMatrix(const ParFiniteElementSpace* pfes,
                                       int element_attribute)
{
   Array<int> dofs;
   Array<int> tdofs;
   for (int i = 0; i < pfes->GetNE(); i++)
   {
      if (pfes->GetAttribute(i) == element_attribute)
      {
         pfes->GetElementVDofs(i, dofs);
         tdofs.Append(dofs);
      }
   }
   tdofs.Sort();
   tdofs.Unique();

   HYPRE_BigInt h = tdofs.Size();
   SparseMatrix St(h,pfes->GlobalTrueVSize());

   for (int i = 0; i<h; i++)
   {
      int col = tdofs[i];
      St.Set(i,col,1.0);
   }
   St.Finalize();
   HYPRE_BigInt rows[2];
   HYPRE_BigInt cols[2];
   int nrows = St.Height();

   rows[0] = 0; rows[1] = nrows;
   for (int i = 0; i < 2; i++)
   {
      cols[i] = pfes->GetTrueDofOffsets()[i];
   }
   HYPRE_BigInt glob_nrows = nrows;
   HYPRE_BigInt glob_ncols = pfes->GlobalTrueVSize();

   HYPRE_BigInt * J;
#if !(defined(HYPRE_BIGINT) || defined(HYPRE_MIXEDINT))
   J = St.GetJ();
#else
   J = new HYPRE_BigInt[St.NumNonZeroElems()];
   std::copy(St.GetJ(), St.GetJ() + St.NumNonZeroElems(), J);
#endif
   HypreParMatrix * Pt = new HypreParMatrix(pfes->GetComm(), nrows, glob_nrows,
                                            glob_ncols, St.GetI(), J,
                                            St.GetData(), rows,cols);

   HypreParMatrix * P = Pt->Transpose();
   delete Pt;
#if (defined(HYPRE_BIGINT) || defined(HYPRE_MIXEDINT))
   delete [] J;
#endif
   return P;
}


TEST_CASE("FilteredSolver and AMGFSolver", "[Parallel]")
{
   // Note: This test is restricted to a single processor for convenience,
   // allowing the use of a serial dense direct solver on the filtered subspace
   // and avoiding any dependency on external parallel sparse direct solvers.
   // In general, both AMGFSolver and FilteredSolver are designed to work in parallel.
   if (Mpi::Root())
   {
      MPI_Comm comm = MPI_COMM_SELF;

      auto ref_levels = 2;

      auto [order, eps, iteration_bound] =
         GENERATE(table<int, real_t, int>(
      {
         {2, 1e-3, 12},
         {2, 1e-4, 12},
         {3, 1e-3, 18},
         {3, 1e-4, 18}
      }));

      CAPTURE(order, eps);

      Mesh mesh = Mesh::MakeCartesian2D(3, 3, Element::QUADRILATERAL, 1.0, 1.0);
      mesh.EnsureNodes();
      GridFunction *nodes = mesh.GetNodes();
      (*nodes)[2] = 0.5*(1-eps);   (*nodes)[10] = 0.5*(1-eps);
      (*nodes)[18] = 0.5*(1-eps);  (*nodes)[26] = 0.5*(1-eps);
      (*nodes)[4] = 0.5*(1+eps);   (*nodes)[12] = 0.5*(1+eps);
      (*nodes)[20] = 0.5*(1+eps);  (*nodes)[28] = 0.5*(1+eps);
      mesh.SetAttribute(3, 2);
      mesh.SetAttribute(6, 2);
      mesh.SetAttribute(7, 2);
      mesh.SetAttributes();

      int dim = mesh.Dimension();

      ParMesh pmesh(comm, mesh);
      mesh.Clear();
      for (int l = 0; l < ref_levels; l++)
      {
         pmesh.UniformRefinement();
      }

      H1_FECollection fec(order, dim);
      ParFiniteElementSpace fespace(&pmesh, &fec);

      Array<int> ess_bdr, ess_tdof_list;
      ess_bdr.SetSize(pmesh.bdr_attributes.Max());
      ess_bdr = 1;
      fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
      ParGridFunction x(&fespace);   x = 0.0;

      ParLinearForm b(&fespace);
      ConstantCoefficient one(1.0);
      b.AddDomainIntegrator(new DomainLFIntegrator(one));
      b.Assemble();

      ParBilinearForm a(&fespace);
      ConstantCoefficient eps_cf(eps);;
      Vector vec(pmesh.attributes.Max());
      vec(0) = 1.0;
      vec(1) = 1/eps;
      PWConstCoefficient eps_cg(vec);
      a.AddDomainIntegrator(new DiffusionIntegrator(eps_cg));
      a.Assemble();

      OperatorPtr A;
      Vector B, X;
      a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);

      HypreParMatrix *P = GetProlongationMatrix(&fespace, 2);

      // 1st preconditioner: AMG
      HypreBoomerAMG amg;
      // 2nd preconditioner: AMGF
      AMGFSolver amgf;
      amg.SetPrintLevel(0);
      DenseMatrixSolver subspacesolver;
      amgf.GetAMG().SetPrintLevel(0);
      amgf.SetFilteredSubspaceSolver(subspacesolver);
      amgf.SetFilteredSubspaceTransferOperator(*P);
      // 3rd preconditioner: FilteredSolver
      FilteredSolver fs;
      fs.SetSolver(amg);
      fs.SetFilteredSubspaceTransferOperator(*P);
      fs.SetFilteredSubspaceSolver(subspacesolver);

      X = 0.0;
      Vector Xamgf(X);
      Vector Xfs(X);

      CGSolver cg(comm);
      cg.SetAbsTol(1e-16);
      cg.SetMaxIter(5000);
      cg.SetPrintLevel(3);
      cg.SetPreconditioner(amg);
      cg.SetOperator(*A);
      cg.Mult(B, X);

      cg.SetPreconditioner(amgf);
      cg.SetOperator(*A);
      cg.Mult(B, Xamgf);
      int amgf_iter = cg.GetNumIterations();

      cg.SetPreconditioner(fs);
      cg.SetOperator(*A);
      cg.Mult(B, Xfs);
      int fs_iter = cg.GetNumIterations();

      Xamgf -= X;
      REQUIRE(Xamgf.Norml2() == MFEM_Approx(0.0,1e-7));
      Xfs -= X;
      REQUIRE(Xfs.Norml2() == MFEM_Approx(0.0,1e-7));

      REQUIRE(amgf_iter == fs_iter);
      REQUIRE(amgf_iter <= iteration_bound);
      REQUIRE(fs_iter <= iteration_bound);

      delete P;
   }
}
#endif

} // namespace mfem