text: //                                MFEM Example 1
  //                              AmgX Modification
  //
  // Compile with: make ex1
  //
  // AmgX sample runs:
  //               ex1
  //               ex1 -d cuda
  //               ex1 --amgx-file multi_gs.json --amgx-solver
  //               ex1 --amgx-file precon.json --amgx-preconditioner
  //               ex1 --amgx-file multi_gs.json --amgx-solver -d cuda
  //               ex1 --amgx-file precon.json --amgx-preconditioner -d cuda
  //
  // 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.hpp"
  #include <fstream>
  #include <iostream>
  
  #ifndef MFEM_USE_AMGX
  #error This example requires that MFEM is built with MFEM_USE_AMGX=YES
  #endif
  
  using namespace std;
  using namespace mfem;
  
  int main(int argc, char *argv[])
  {
     // 1. Parse command-line options.
     const char *mesh_file = "../../data/star.mesh";
     int order = 1;
     bool static_cond = false;
     bool pa = false;
     const char *device_config = "cpu";
     bool visualization = true;
     bool amgx_lib = true;
     bool amgx_solver = true;
     const char* amgx_json_file = ""; // JSON file for AmgX
  
     OptionsParser args(argc, argv);
     args.AddOption(&mesh_file, "-m", "--mesh",
                    "Mesh file to use.");
     args.AddOption(&order, "-o", "--order",
                    "Finite element order (polynomial degree) or -1 for"
                    " isoparametric space.");
     args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                    "--no-static-condensation", "Enable static condensation.");
     args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                    "--no-partial-assembly", "Enable Partial Assembly.");
     args.AddOption(&amgx_lib, "-amgx", "--amgx-lib", "-no-amgx",
                    "--no-amgx-lib", "Use AmgX in example.");
     args.AddOption(&amgx_json_file, "--amgx-file", "--amgx-file",
                    "AMGX solver config file (overrides --amgx-solver, --amgx-verbose)");
     args.AddOption(&amgx_solver, "--amgx-solver", "--amgx-solver",
                    "--amgx-preconditioner", "--amgx-preconditioner",
                    "Configure AMGX as solver or preconditioner.");
     args.AddOption(&device_config, "-d", "--device",
                    "Device configuration string, see Device::Configure().");
     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);
  
     // 2. Enable hardware devices such as GPUs, and programming models such as
     //    CUDA, OCCA, RAJA and OpenMP based on command line options.
     Device device(device_config);
     device.Print();
  
     // 3. 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(mesh_file, 1, 1);
     int dim = mesh.Dimension();
  
     // 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.
     {
        int ref_levels =
           (int)floor(log(50000./mesh.GetNE())/log(2.)/dim);
        for (int l = 0; l < ref_levels; l++)
        {
           mesh.UniformRefinement();
        }
     }
  
     // 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;
     bool delete_fec;
     if (order > 0)
     {
        fec = new H1_FECollection(order, dim);
        delete_fec = true;
     }
     else if (mesh.GetNodes())
     {
        fec = mesh.GetNodes()->OwnFEC();
        delete_fec = false;
        cout << "Using isoparametric FEs: " << fec->Name() << endl;
     }
     else
     {
        fec = new H1_FECollection(order = 1, dim);
        delete_fec = true;
     }
     FiniteElementSpace fespace(&mesh, fec);
     cout << "Number of finite element unknowns: "
          << fespace.GetTrueVSize() << endl;
  
     // 6. 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);
     }
  
     // 7. 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(&fespace);
     ConstantCoefficient one(1.0);
     b.AddDomainIntegrator(new DomainLFIntegrator(one));
     b.Assemble();
  
     // 8. 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;
  
     // 9. Set up the bilinear form a(.,.) on the finite element space
     //    corresponding to the Laplacian operator -Delta, by adding the Diffusion
     //    domain integrator.
     BilinearForm a(&fespace);
     if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
     a.AddDomainIntegrator(new DiffusionIntegrator(one));
  
     // 10. 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(); }
     a.Assemble();
  
     OperatorPtr A;
     Vector B, X;
     a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
  
     cout << "Size of linear system: " << A->Height() << endl;
  
     // 11. Solve the linear system A X = B.
     if (pa)
     {
        // Jacobi preconditioning in partial assembly mode
        if (UsesTensorBasis(fespace))
        {
           OperatorJacobiSmoother M(a, ess_tdof_list);
           PCG(*A, M, B, X, 1, 400, 1e-12, 0.0);
        }
        else
        {
           CG(*A, B, X, 1, 400, 1e-12, 0.0);
        }
     }
     else if (amgx_lib && strcmp(amgx_json_file,"") == 0)
     {
        bool amgx_verbose = false;
        AmgXSolver amgx(AmgXSolver::PRECONDITIONER, amgx_verbose);
        amgx.SetOperator(*A.As<SparseMatrix>());
        PCG(*A, amgx, B, X, 1, 200, 1e-12, 0.0);
     }
     else if (amgx_lib && strcmp(amgx_json_file,"") != 0)
     {
        AmgXSolver amgx;
        amgx.ReadParameters(amgx_json_file, AmgXSolver::EXTERNAL);
        amgx.InitSerial();
        amgx.SetOperator(*A.As<SparseMatrix>());
  
        if (amgx_solver)
        {
           amgx.SetConvergenceCheck(true);
           amgx.Mult(B,X);
        }
        else
        {
           // Omit convergence check at the AmgX level when using as a
           // preconditioner.
           amgx.SetConvergenceCheck(false);
           PCG(*A.As<SparseMatrix>(), amgx, B, X, 3, 40, 1e-12, 0.0);
        }
     }
     else
     {
  #ifndef MFEM_USE_SUITESPARSE
        // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
        GSSmoother M((SparseMatrix&)(*A));
        PCG(*A, M, B, X, 1, 200, 1e-12, 0.0);
  #else
        // If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
        UMFPackSolver umf_solver;
        umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
        umf_solver.SetOperator(*A);
        umf_solver.Mult(B, X);
  #endif
     }
  
     // 12. Recover the solution as a finite element grid function.
     a.RecoverFEMSolution(X, b, x);
  
     // 13. 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);
  
     // 14. 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;
     }
  
     // 15. Free the used memory.
     if (delete_fec)
     {
        delete fec;
     }
  
     return 0;
  }
  