parheat.cpp

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// Copyright (c) 2010-2021, 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.
//
//     ----------------------------------------------------------------
//     ParHeat Miniapp: Gradients of PDE constrained objective function
//     ----------------------------------------------------------------
//                           (Parallel Version)
//
// The following example computes the gradients of a specified objective
// function with respect to parametric fields. The objective function is having
// the following form f(u(\rho)) where u(\rho) is a solution of a specific state
// problem (in the example that is the diffusion equation), and \rho is a
// parametric field discretized by finite elements. The parametric field (also
// called density in topology optimization) controls the coefficients of the
// state equation. For the considered case, the density controls the diffusion
// coefficient within the computational domain.
//
// For more information, the users are referred to:
//
//    Hinze, M.; Pinnau, R.; Ulbrich, M. & Ulbrich, S.
//    Optimization with PDE Constraints
//    Springer Netherlands, 2009
//
//    Bendsøe, M. P. & Sigmund, O.
//    Topology Optimization - Theory, Methods and Applications
//    Springer Verlag, Berlin Heidelberg, 2003
//
// Compile with: make parheat
//
// Sample runs:
//
//    mpirun -np 4 parheat --visualization
//    mpirun -np 4 parheat --visualization -m ../../data/beam-quad.mesh

#include "mfem.hpp"
#include <fstream>
#include <iostream>

#include "pparamnonlinearform.hpp"
#include "mtop_integrators.hpp"

int main(int argc, char *argv[])
{
   // Initialize MPI.
   int nprocs, myrank;
   MPI_Init(&argc, &argv);
   MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);

   // Parse command-line options.
   const char *mesh_file = "../../data/star.mesh";
   int order = 1;
   bool static_cond = false;
   int ser_ref_levels = 1;
   int par_ref_levels = 1;
   double newton_rel_tol = 1e-7;
   double newton_abs_tol = 1e-12;
   int newton_iter = 10;
   int print_level = 1;
   bool visualization = false;

   mfem::OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
                  "Mesh file to use.");
   args.AddOption(&ser_ref_levels,
                  "-rs",
                  "--refine-serial",
                  "Number of times to refine the mesh uniformly in serial.");
   args.AddOption(&par_ref_levels,
                  "-rp",
                  "--refine-parallel",
                  "Number of times to refine the mesh uniformly in parallel.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree) or -1 for"
                  " isoparametric space.");
   args.AddOption(&visualization,
                  "-vis",
                  "--visualization",
                  "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                  "--no-static-condensation", "Enable static condensation.");
   args.AddOption(&newton_rel_tol,
                  "-rel",
                  "--relative-tolerance",
                  "Relative tolerance for the Newton solve.");
   args.AddOption(&newton_abs_tol,
                  "-abs",
                  "--absolute-tolerance",
                  "Absolute tolerance for the Newton solve.");
   args.AddOption(&newton_iter,
                  "-it",
                  "--newton-iterations",
                  "Maximum iterations for the Newton solve.");
   args.Parse();
   if (!args.Good())
   {
      if (myrank == 0)
      {
         args.PrintUsage(std::cout);
      }
      MPI_Finalize();
      return 1;
   }

   if (myrank == 0)
   {
      args.PrintOptions(std::cout);
   }

   // Read the (serial) mesh from the given mesh file on all processors.  We
   // can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
   // and volume meshes with the same code.
   mfem::Mesh mesh(mesh_file, 1, 1);
   int dim = mesh.Dimension();

   // Refine the serial mesh on all processors to increase the resolution. In
   // this example we do 'ref_levels' of uniform refinement. We choose
   // 'ref_levels' to be the largest number that gives a final mesh with no
   // more than 10,000 elements.
   {
      int ref_levels =
         (int)floor(log(10000./mesh.GetNE())/log(2.)/dim);
      for (int l = 0; l < ref_levels; l++)
      {
         mesh.UniformRefinement();
      }
   }

   // Define a parallel mesh by a partitioning of the serial mesh. Refine
   // this mesh further in parallel to increase the resolution. Once the
   // parallel mesh is defined, the serial mesh can be deleted.
   mfem::ParMesh pmesh(MPI_COMM_WORLD, mesh);
   mesh.Clear();
   {
      for (int l = 0; l < par_ref_levels; l++)
      {
         pmesh.UniformRefinement();
      }
   }

   // Define the Diffusion coefficient.
   mfem::ConstantCoefficient* diffco=new mfem::ConstantCoefficient(1.0);
   // Define the Heat source.
   mfem::ConstantCoefficient* loadco=new mfem::ConstantCoefficient(1.0);
   // Define the q-function.
   mfem::QLinearDiffusion* qfun=new mfem::QLinearDiffusion(*diffco,*loadco,1.0,
                                                           1e-7,4.0,0.5);

   // Define FE collection and space for the state solution.
   mfem::H1_FECollection sfec(order, dim);
   mfem::ParFiniteElementSpace* sfes=new mfem::ParFiniteElementSpace(&pmesh,&sfec,
                                                                     1);
   // Define FE collection and space for the density field.
   mfem::L2_FECollection pfec(order, dim);
   mfem::ParFiniteElementSpace* pfes=new mfem::ParFiniteElementSpace(&pmesh,&pfec,
                                                                     1);

   // Define the arrays for the nonlinear form.
   mfem::Array<mfem::ParFiniteElementSpace*> asfes;
   mfem::Array<mfem::ParFiniteElementSpace*> apfes;

   asfes.Append(sfes);
   apfes.Append(pfes);

   // Define parametric block nonlinear form using single scalar H1 field
   // and L2 scalar density field.
   mfem::ParParametricBNLForm* nf=new mfem::ParParametricBNLForm(asfes,apfes);
   // Add a parametric integrator.
   nf->AddDomainIntegrator(new mfem::ParametricLinearDiffusion(*qfun));

   // Define true block vectors for state, adjoint, resudual.
   mfem::BlockVector solbv; solbv.Update(nf->GetBlockTrueOffsets());    solbv=0.0;
   mfem::BlockVector adjbv; adjbv.Update(nf->GetBlockTrueOffsets());    adjbv=0.0;
   mfem::BlockVector resbv; resbv.Update(nf->GetBlockTrueOffsets());    resbv=0.0;
   // Define true block vectors for parametric field and gradients.
   mfem::BlockVector prmbv; prmbv.Update(nf->ParamGetBlockTrueOffsets());
   prmbv=0.0;
   mfem::BlockVector grdbv; grdbv.Update(nf->ParamGetBlockTrueOffsets());
   grdbv=0.0;

   // Set the BCs for the physics.
   mfem::Array<mfem::Array<int> *> ess_bdr;
   mfem::Array<mfem::Vector*>      ess_rhs;
   ess_bdr.Append(new mfem::Array<int>(pmesh.bdr_attributes.Max()));
   ess_rhs.Append(nullptr);
   (*ess_bdr[0]) = 1;
   nf->SetEssentialBC(ess_bdr,ess_rhs);
   delete ess_bdr[0];

   // Set the density field to 0.5.
   prmbv=0.5;
   // Set the density as parametric field in the parametric BNLForm.
   nf->SetParamFields(prmbv); //set the density

   // Compute the stiffness/tangent matrix for density prmbv=0.5.
   mfem::BlockOperator *A = &nf->GetGradient(solbv);
   mfem::HypreBoomerAMG* prec=new mfem::HypreBoomerAMG();
   prec->SetPrintLevel(print_level);
   // Use only block (0,0) as in this case we have a single field.
   prec->SetOperator(A->GetBlock(0,0));

   // Construct block preconditioner for the BNLForm.
   mfem::BlockDiagonalPreconditioner *blpr = new mfem::BlockDiagonalPreconditioner(
      nf->GetBlockTrueOffsets());
   blpr->SetDiagonalBlock(0,prec);

   // Define the solvers.
   mfem::GMRESSolver *gmres;
   gmres = new mfem::GMRESSolver(MPI_COMM_WORLD);
   gmres->SetAbsTol(newton_abs_tol/10);
   gmres->SetRelTol(newton_rel_tol/10);
   gmres->SetMaxIter(100);
   gmres->SetPrintLevel(print_level);
   gmres->SetPreconditioner(*blpr);
   gmres->SetOperator(*A);


   // Solve the problem.
   solbv=0.0;
   nf->Mult(solbv,resbv); resbv.Neg(); //compute RHS
   gmres->Mult(resbv, solbv);

   // Compute the energy of the state system.
   double energy = nf->GetEnergy(solbv);
   if (myrank==0)
   {
      std::cout << "energy =" << energy << std::endl;
   }

   // Define the block nonlinear form utilized for representing the objective -
   // use the state array from the BNLForm.
   mfem::ParBlockNonlinearForm* ob=new mfem::ParBlockNonlinearForm(asfes);
   // Add the integrator for the objective.
   ob->AddDomainIntegrator(new mfem::DiffusionObjIntegrator());

   // Compute the objective.
   double obj=ob->GetEnergy(solbv);
   if (myrank==0)
   {
      std::cout << "Objective =" << obj << std::endl;
   }

   // Solve the adjoint.
   {
      mfem::BlockVector adjrhs; adjrhs.Update(nf->GetBlockTrueOffsets());  adjrhs=0.0;
      // Compute the RHS for the adjoint, i.e., the gradients with respect to
      // the parametric fields.
      ob->Mult(solbv, adjrhs);
      // Get the tangent matrix from the state problem. We do not need to
      // transpose the operator for diffusion.  Compute the adjoint solution.
      gmres->Mult(adjrhs, adjbv);
   }

   // Compute gradients.
   // First set the adjoint field.
   nf->SetAdjointFields(adjbv);
   // Set the state field.
   nf->SetStateFields(solbv);
   // Call the parametric Mult.
   nf->ParamMult(prmbv, grdbv);

   // Dump out the data.
   if (visualization)
   {
      mfem::ParaViewDataCollection *dacol=new mfem::ParaViewDataCollection("ParHeat",
                                                                           &pmesh);
      mfem::ParGridFunction gfgrd(pfes); gfgrd.SetFromTrueDofs(grdbv.GetBlock(0));
      mfem::ParGridFunction gfdns(pfes); gfdns.SetFromTrueDofs(prmbv.GetBlock(0));
      // Define state grid function.
      mfem::ParGridFunction gfsol(sfes); gfsol.SetFromTrueDofs(solbv.GetBlock(0));
      mfem::ParGridFunction gfadj(sfes); gfadj.SetFromTrueDofs(adjbv.GetBlock(0));

      dacol->SetLevelsOfDetail(order);
      dacol->RegisterField("sol", &gfsol);
      dacol->RegisterField("adj", &gfadj);
      dacol->RegisterField("dns", &gfdns);
      dacol->RegisterField("grd", &gfgrd);

      dacol->SetTime(1.0);
      dacol->SetCycle(1);
      dacol->Save();

      delete dacol;
   }

   // FD check
   {
      mfem::BlockVector prtbv;
      mfem::BlockVector tmpbv;
      prtbv.Update(nf->ParamGetBlockTrueOffsets());
      tmpbv.Update(nf->ParamGetBlockTrueOffsets());
      prtbv.GetBlock(0).Randomize();
      prtbv*=1.0;
      double lsc=1.0;

      double gQoI=ob->GetEnergy(solbv);
      double lQoI;

      double nd=mfem::InnerProduct(MPI_COMM_WORLD,prtbv,prtbv);
      double td=mfem::InnerProduct(MPI_COMM_WORLD,prtbv,grdbv);
      td=td/nd;

      for (int l = 0; l < 10; l++)
      {
         lsc/=10.0;
         prtbv/=10.0;
         add(prmbv,prtbv,tmpbv);
         nf->SetParamFields(tmpbv);
         // Solve the physics.
         solbv=0.0;
         nf->Mult(solbv,resbv); resbv.Neg(); //compute RHS
         A = &nf->GetGradient(solbv);
         prec->SetPrintLevel(0);
         prec->SetOperator(A->GetBlock(0,0));
         gmres->SetOperator(*A);
         gmres->SetPrintLevel(0);
         gmres->Mult(resbv,solbv);
         // Compute the objective.
         lQoI=ob->GetEnergy(solbv);
         double ld=(lQoI-gQoI)/lsc;
         if (myrank==0)
         {
            std::cout << "dx=" << lsc <<" FD approximation=" << ld/nd
                      << " adjoint gradient=" << td
                      << " err=" << std::fabs(ld/nd-td) << std::endl;
         }
      }
   }

   delete ob;
   delete gmres;
   delete blpr;
   delete prec;

   delete nf;
   delete pfes;
   delete sfes;

   delete qfun;
   delete loadco;
   delete diffco;

   MPI_Finalize();
   return 0;
}