ex1.cpp

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//                    MFEM Example 1 - High-Performance Version
//
// Compile with: make ex1
//
// Sample runs:  ex1 -m ../../data/fichera.mesh -perf -mf  -pc lor
//               ex1 -m ../../data/fichera.mesh -perf -asm -pc ho
//               ex1 -m ../../data/fichera.mesh -perf -asm -pc ho -sc
//               ex1 -m ../../data/fichera.mesh -std  -asm -pc ho
//               ex1 -m ../../data/fichera.mesh -std  -asm -pc ho -sc
//               ex1 -m ../../data/amr-hex.mesh -perf -asm -pc ho -sc
//               ex1 -m ../../data/amr-hex.mesh -std  -asm -pc ho -sc
//               ex1 -m ../../data/ball-nurbs.mesh -perf -asm -pc ho  -sc
//               ex1 -m ../../data/ball-nurbs.mesh -std  -asm -pc ho  -sc
//               ex1 -m ../../data/pipe-nurbs.mesh -perf -mf  -pc lor
//               ex1 -m ../../data/pipe-nurbs.mesh -std  -asm -pc ho  -sc
//               ex1 -m ../../data/star.mesh -perf -mf  -pc lor
//               ex1 -m ../../data/star.mesh -perf -asm -pc ho
//               ex1 -m ../../data/star.mesh -perf -asm -pc ho -sc
//               ex1 -m ../../data/star.mesh -std  -asm -pc ho
//               ex1 -m ../../data/star.mesh -std  -asm -pc ho -sc
//               ex1 -m ../../data/amr-quad.mesh -perf -asm -pc ho -sc
//               ex1 -m ../../data/amr-quad.mesh -std  -asm -pc ho -sc
//               ex1 -m ../../data/disc-nurbs.mesh -perf -asm -pc ho  -sc
//               ex1 -m ../../data/disc-nurbs.mesh -std  -asm -pc ho  -sc
//
// Description:  This example code demonstrates the use of MFEM to define a
//               simple finite element discretization of the Laplace problem
//               -Delta u = 1 with homogeneous Dirichlet boundary conditions.
//               Specifically, we discretize using a FE space of the specified
//               order, or if order < 1 using an isoparametric/isogeometric
//               space (i.e. quadratic for quadratic curvilinear mesh, NURBS for
//               NURBS mesh, etc.)
//
//               The example highlights the use of mesh refinement, finite
//               element grid functions, as well as linear and bilinear forms
//               corresponding to the left-hand side and right-hand side of the
//               discrete linear system. We also cover the explicit elimination
//               of essential boundary conditions, static condensation, and the
//               optional connection to the GLVis tool for visualization.
 
#include "mfem-performance.hpp"
#include <fstream>
#include <iostream>
 
using namespace std;
using namespace mfem;
 
enum class PCType { NONE, LOR, HO };
 
// Define template parameters for optimized build.
template <int dim> struct geom_t { };
template <>
struct geom_t<2> { static const Geometry::Type value = Geometry::SQUARE; };
template <>
struct geom_t<3> { static const Geometry::Type value = Geometry::CUBE; };
 
const int mesh_p   = 3; // mesh curvature (default: 3)
const int sol_p    = 3; // solution order (default: 3)
 
template <int dim>
struct ex1_t
{
   static const Geometry::Type geom = geom_t<dim>::value;
   static const int            rdim     = Geometry::Constants<geom>::Dimension;
   static const int            ir_order = 2*sol_p+rdim-1;
 
   // Static mesh type
   using mesh_fe_t = H1_FiniteElement<geom,mesh_p>;
   using mesh_fes_t = H1_FiniteElementSpace<mesh_fe_t>;
   using mesh_t = TMesh<mesh_fes_t>;
 
   // Static solution finite element space type
   using sol_fe_t = H1_FiniteElement<geom,sol_p>;
   using sol_fes_t = H1_FiniteElementSpace<sol_fe_t>;
 
   // Static quadrature, coefficient and integrator types
   using int_rule_t = TIntegrationRule<geom,ir_order>;
   using coeff_t = TConstantCoefficient<>;
   using integ_t = TIntegrator<coeff_t,TDiffusionKernel>;
 
   using HPCBilinearForm = TBilinearForm<mesh_t,sol_fes_t,int_rule_t,integ_t>;
 
   static int run(Mesh *mesh, int ref_levels, int order, int basis,
                  bool static_cond, PCType pc_choice, bool perf,
                  bool matrix_free, bool visualization);
};
 
int main(int argc, char *argv[])
{
   // 1. Parse command-line options.
   const char *mesh_file = "../../data/fichera.mesh";
   int ref_levels = -1;
   int order = sol_p;
   const char *basis_type = "G"; // Gauss-Lobatto
   bool static_cond = false;
   const char *pc = "none";
   bool perf = true;
   bool matrix_free = true;
   bool visualization = 1;
 
   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
                  "Mesh file to use.");
   args.AddOption(&ref_levels, "-r", "--refine",
                  "Number of times to refine the mesh uniformly;"
                  " -1 = auto: <= 50,000 elements.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree) or -1 for"
                  " isoparametric space.");
   args.AddOption(&basis_type, "-b", "--basis-type",
                  "Basis: G - Gauss-Lobatto, P - Positive, U - Uniform");
   args.AddOption(&perf, "-perf", "--hpc-version", "-std", "--standard-version",
                  "Enable high-performance, tensor-based, assembly/evaluation.");
   args.AddOption(&matrix_free, "-mf", "--matrix-free", "-asm", "--assembly",
                  "Use matrix-free evaluation or efficient matrix assembly in "
                  "the high-performance version.");
   args.AddOption(&pc, "-pc", "--preconditioner",
                  "Preconditioner: lor - low-order-refined (matrix-free) GS, "
                  "ho - high-order (assembled) GS, none.");
   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                  "--no-static-condensation", "Enable static condensation.");
   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 (static_cond && perf && matrix_free)
   {
      cout << "\nStatic condensation can not be used with matrix-free"
           " evaluation!\n" << endl;
      return 2;
   }
   MFEM_VERIFY(perf || !matrix_free,
               "--standard-version is not compatible with --matrix-free");
   args.PrintOptions(cout);
 
   PCType pc_choice;
   if (!strcmp(pc, "ho")) { pc_choice = PCType::HO; }
   else if (!strcmp(pc, "lor")) { pc_choice = PCType::LOR; }
   else if (!strcmp(pc, "none")) { pc_choice = PCType::NONE; }
   else
   {
      mfem_error("Invalid Preconditioner specified");
      return 3;
   }
 
   cout << "\nMFEM SIMD width: " << MFEM_SIMD_BYTES/sizeof(double)
        << " doubles\n" << endl;
 
   // See class BasisType in fem/fe_coll.hpp for available basis types
   int basis = BasisType::GetType(basis_type[0]);
   cout << "Using " << BasisType::Name(basis) << " basis ..." << endl;
 
   // 2. Read the mesh from the given mesh file. We can handle triangular,
   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
   //    the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();
 
   if (dim == 2)
   {
      return ex1_t<2>::run(mesh, ref_levels, order, basis, static_cond,
                           pc_choice, perf, matrix_free, visualization);
   }
   else if (dim == 3)
   {
      return ex1_t<3>::run(mesh, ref_levels, order, basis, static_cond,
                           pc_choice, perf, matrix_free, visualization);
   }
   else
   {
      MFEM_ABORT("Dimension must be 2 or 3.")
   }
 
   return 0;
}
 
template <int dim>
int ex1_t<dim>::run(Mesh *mesh, int ref_levels, int order, int basis,
                    bool static_cond, PCType pc_choice, bool perf,
                    bool matrix_free, bool visualization)
{
   // 3. Check if the optimized version matches the given mesh
   if (perf)
   {
      cout << "High-performance version using integration rule with "
           << int_rule_t::qpts << " points ..." << endl;
      if (!mesh_t::MatchesGeometry(*mesh))
      {
         cout << "The given mesh does not match the optimized 'geom' parameter.\n"
              << "Recompile with suitable 'geom' value." << endl;
         delete mesh;
         return 4;
      }
      else if (!mesh_t::MatchesNodes(*mesh))
      {
         cout << "Switching the mesh curvature to match the "
              << "optimized value (order " << mesh_p << ") ..." << endl;
         mesh->SetCurvature(mesh_p, false, -1, Ordering::byNODES);
      }
   }
 
   // 4. Refine the mesh 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 50,000
   //    elements, or as specified on the command line with the option
   //    '--refine'.
   {
      ref_levels = (ref_levels != -1) ? ref_levels :
                   (int)floor(log(50000./mesh->GetNE())/log(2.)/dim);
      for (int l = 0; l < ref_levels; l++)
      {
         mesh->UniformRefinement();
      }
   }
   if (mesh->MeshGenerator() & 1) // simplex mesh
   {
      MFEM_VERIFY(pc_choice != PCType::LOR, "triangle and tet meshes do not "
                  " support the LOR preconditioner yet");
   }
 
   // 5. Define a finite element space on the mesh. Here we use continuous
   //    Lagrange finite elements of the specified order. If order < 1, we
   //    instead use an isoparametric/isogeometric space.
   FiniteElementCollection *fec;
   if (order > 0)
   {
      fec = new H1_FECollection(order, dim, basis);
   }
   else if (mesh->GetNodes())
   {
      fec = mesh->GetNodes()->OwnFEC();
      cout << "Using isoparametric FEs: " << fec->Name() << endl;
   }
   else
   {
      fec = new H1_FECollection(order = 1, dim, basis);
   }
   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
   cout << "Number of finite element unknowns: "
        << fespace->GetTrueVSize() << endl;
 
   // Create the LOR mesh and finite element space. In the settings of this
   // example, we can transfer between HO and LOR with the identity operator.
   Mesh mesh_lor;
   FiniteElementCollection *fec_lor = NULL;
   FiniteElementSpace *fespace_lor = NULL;
   if (pc_choice == PCType::LOR)
   {
      int basis_lor = basis;
      if (basis == BasisType::Positive) { basis_lor=BasisType::ClosedUniform; }
      mesh_lor = Mesh::MakeRefined(*mesh, order, basis_lor);
      fec_lor = new H1_FECollection(1, dim);
      fespace_lor = new FiniteElementSpace(&mesh_lor, fec_lor);
   }
 
   // 6. Check if the optimized version matches the given space
   if (perf && !sol_fes_t::Matches(*fespace))
   {
      cout << "The given order does not match the optimized parameter.\n"
           << "Recompile with suitable 'sol_p' value." << endl;
      delete fespace;
      delete fec;
      delete mesh;
      return 5;
   }
 
   // 7. Determine the list of true (i.e. conforming) essential boundary dofs.
   //    In this example, the boundary conditions are defined by marking all
   //    the boundary attributes from the mesh as essential (Dirichlet) and
   //    converting them to a list of true dofs.
   Array<int> ess_tdof_list;
   if (mesh->bdr_attributes.Size())
   {
      Array<int> ess_bdr(mesh->bdr_attributes.Max());
      ess_bdr = 1;
      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
   }
 
   // 8. Set up the linear form b(.) which corresponds to the right-hand side of
   //    the FEM linear system, which in this case is (1,phi_i) where phi_i are
   //    the basis functions in the finite element fespace.
   LinearForm *b = new LinearForm(fespace);
   ConstantCoefficient one(1.0);
   b->AddDomainIntegrator(new DomainLFIntegrator(one));
   b->Assemble();
 
   // 9. Define the solution vector x as a finite element grid function
   //    corresponding to fespace. Initialize x with initial guess of zero,
   //    which satisfies the boundary conditions.
   GridFunction x(fespace);
   x = 0.0;
 
   // 10. Set up the bilinear form a(.,.) on the finite element space that will
   //     hold the matrix corresponding to the Laplacian operator -Delta.
   //     Optionally setup a form to be assembled for preconditioning (a_pc).
   BilinearForm *a = new BilinearForm(fespace);
   BilinearForm *a_pc = NULL;
   if (pc_choice == PCType::LOR) { a_pc = new BilinearForm(fespace_lor); }
   if (pc_choice == PCType::HO)  { a_pc = new BilinearForm(fespace); }
 
   // 11. Assemble the bilinear form and the corresponding linear system,
   //     applying any necessary transformations such as: eliminating boundary
   //     conditions, applying conforming constraints for non-conforming AMR,
   //     static condensation, etc.
   if (static_cond)
   {
      a->EnableStaticCondensation();
      MFEM_VERIFY(pc_choice != PCType::LOR,
                  "cannot use LOR preconditioner with static condensation");
   }
 
   cout << "Assembling the bilinear form ..." << flush;
   tic_toc.Clear();
   tic_toc.Start();
   // Pre-allocate sparsity assuming dense element matrices
   a->UsePrecomputedSparsity();
 
   HPCBilinearForm *a_hpc = NULL;
   Operator *a_oper = NULL;
 
   if (!perf)
   {
      // Standard assembly using a diffusion domain integrator
      a->AddDomainIntegrator(new DiffusionIntegrator(one));
      a->Assemble();
   }
   else
   {
      // High-performance assembly/evaluation using the templated operator type
      a_hpc = new HPCBilinearForm(integ_t(coeff_t(1.0)), *fespace);
      if (matrix_free)
      {
         a_hpc->Assemble(); // partial assembly
      }
      else
      {
         a_hpc->AssembleBilinearForm(*a); // full matrix assembly
      }
   }
   tic_toc.Stop();
   cout << " done, " << tic_toc.RealTime() << "s." << endl;
 
   // 12. Solve the system A X = B with CG. In the standard case, use a simple
   //     symmetric Gauss-Seidel preconditioner.
 
   // Setup the operator matrix (if applicable)
   SparseMatrix A;
   Vector B, X;
   if (perf && matrix_free)
   {
      a_hpc->FormLinearSystem(ess_tdof_list, x, *b, a_oper, X, B);
      cout << "Size of linear system: " << a_hpc->Height() << endl;
   }
   else
   {
      a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
      cout << "Size of linear system: " << A.Height() << endl;
      a_oper = &A;
   }
 
   // Setup the matrix used for preconditioning
   cout << "Assembling the preconditioning matrix ..." << flush;
   tic_toc.Clear();
   tic_toc.Start();
 
   SparseMatrix A_pc;
   if (pc_choice == PCType::LOR)
   {
      // TODO: assemble the LOR matrix using the performance code
      a_pc->AddDomainIntegrator(new DiffusionIntegrator(one));
      a_pc->UsePrecomputedSparsity();
      a_pc->Assemble();
      a_pc->FormSystemMatrix(ess_tdof_list, A_pc);
   }
   else if (pc_choice == PCType::HO)
   {
      if (!matrix_free)
      {
         A_pc.MakeRef(A); // matrix already assembled, reuse it
      }
      else
      {
         a_pc->UsePrecomputedSparsity();
         a_hpc->AssembleBilinearForm(*a_pc);
         a_pc->FormSystemMatrix(ess_tdof_list, A_pc);
      }
   }
 
   tic_toc.Stop();
   cout << " done, " << tic_toc.RealTime() << "s." << endl;
 
   // Solve with CG or PCG, depending if the matrix A_pc is available
   if (pc_choice != PCType::NONE)
   {
      GSSmoother M(A_pc);
      PCG(*a_oper, M, B, X, 1, 500, 1e-12, 0.0);
   }
   else
   {
      CG(*a_oper, B, X, 1, 500, 1e-12, 0.0);
   }
 
   // 13. Recover the solution as a finite element grid function.
   if (perf && matrix_free)
   {
      a_hpc->RecoverFEMSolution(X, *b, x);
   }
   else
   {
      a->RecoverFEMSolution(X, *b, x);
   }
 
   // 14. Save the refined mesh and the solution. This output can be viewed later
   //     using GLVis: "glvis -m refined.mesh -g sol.gf".
   ofstream mesh_ofs("refined.mesh");
   mesh_ofs.precision(8);
   mesh->Print(mesh_ofs);
   ofstream sol_ofs("sol.gf");
   sol_ofs.precision(8);
   x.Save(sol_ofs);
 
   // 15. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
      int  visport   = 19916;
      socketstream sol_sock(vishost, visport);
      sol_sock.precision(8);
      sol_sock << "solution\n" << *mesh << x << flush;
   }
 
   // 16. Free the used memory.
   delete a;
   delete a_hpc;
   if (a_oper != &A) { delete a_oper; }
   delete a_pc;
   delete b;
   delete fespace;
   delete fespace_lor;
   delete fec_lor;
   if (order > 0) { delete fec; }
   delete mesh;
 
   return 0;
}