1 // libCEED + MFEM Example: BP1 2 // 3 // This example illustrates a simple usage of libCEED with the MFEM (mfem.org) 4 // finite element library. 5 // 6 // The example reads a mesh from a file and solves a simple linear system with a 7 // mass matrix (L2-projection of a given analytic function provided by 8 // 'solution'). The mass matrix required for performing the projection is 9 // expressed as a new class, CeedMassOperator, derived from mfem::Operator. 10 // Internally, CeedMassOperator uses a CeedOperator object constructed based on 11 // an mfem::FiniteElementSpace. All libCEED objects use a Ceed device object 12 // constructed based on a command line argument (-ceed). 13 // 14 // The mass matrix is inverted using a simple conjugate gradient algorithm 15 // corresponding to CEED BP1, see http://ceed.exascaleproject.org/bps. Arbitrary 16 // mesh and solution orders in 1D, 2D and 3D are supported from the same code. 17 // 18 // Build with: 19 // 20 // make bp1 [MFEM_DIR=</path/to/mfem>] [CEED_DIR=</path/to/libceed>] 21 // 22 // Sample runs: 23 // 24 // bp1 25 // bp1 -ceed /cpu/self 26 // bp1 -ceed /gpu/occa 27 // bp1 -ceed /cpu/occa 28 // bp1 -ceed /omp/occa 29 // bp1 -ceed /ocl/occa 30 // bp1 -m ../../../mfem/data/fichera.mesh 31 // bp1 -m ../../../mfem/data/star.vtk -o 3 32 // bp1 -m ../../../mfem/data/inline-segment.mesh -o 8 33 34 #include <ceed.h> 35 #include <mfem.hpp> 36 #include "bp1.hpp" 37 38 /// Continuous function to project on the discrete FE space 39 double solution(const mfem::Vector &pt) { 40 return pt.Norml2(); // distance to the origin 41 } 42 43 //TESTARGS -ceed {ceed_resource} -t -no-vis 44 int main(int argc, char *argv[]) { 45 // 1. Parse command-line options. 46 const char *ceed_spec = "/cpu/self"; 47 #ifndef MFEM_DIR 48 const char *mesh_file = "../../../mfem/data/star.mesh"; 49 #else 50 const char *mesh_file = MFEM_DIR "/data/star.mesh"; 51 #endif 52 int order = 1; 53 bool visualization = true; 54 bool test = false; 55 56 mfem::OptionsParser args(argc, argv); 57 args.AddOption(&ceed_spec, "-c", "-ceed", "Ceed specification."); 58 args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use."); 59 args.AddOption(&order, "-o", "--order", 60 "Finite element order (polynomial degree)."); 61 args.AddOption(&visualization, "-vis", "--visualization", "-no-vis", 62 "--no-visualization", 63 "Enable or disable GLVis visualization."); 64 args.AddOption(&test, "-t", "--test", "-no-test", 65 "--no-test", 66 "Enable or disable test mode."); 67 args.Parse(); 68 if (!args.Good()) { 69 args.PrintUsage(std::cout); 70 return 1; 71 } 72 if (!test) { 73 args.PrintOptions(std::cout); 74 } 75 76 // 2. Initialize a Ceed device object using the given Ceed specification. 77 Ceed ceed; 78 CeedInit(ceed_spec, &ceed); 79 80 // 3. Read the mesh from the given mesh file. 81 mfem::Mesh *mesh = new mfem::Mesh(mesh_file, 1, 1); 82 int dim = mesh->Dimension(); 83 84 // 4. Refine the mesh to increase the resolution. In this example we do 85 // 'ref_levels' of uniform refinement. We choose 'ref_levels' to be the 86 // largest number that gives a final system with no more than 50,000 87 // unknowns, approximately. 88 { 89 double max_dofs = 50000; 90 int ref_levels = 91 (int)floor((log(max_dofs/mesh->GetNE())-dim*log(order))/log(2.)/dim); 92 for (int l = 0; l < ref_levels; l++) { 93 mesh->UniformRefinement(); 94 } 95 } 96 if (mesh->GetNodalFESpace() == NULL) { 97 mesh->SetCurvature(1, false, -1, mfem::Ordering::byNODES); 98 } 99 if (mesh->NURBSext) { 100 mesh->SetCurvature(order, false, -1, mfem::Ordering::byNODES); 101 } 102 103 // 5. Define a finite element space on the mesh. Here we use continuous 104 // Lagrange finite elements of the specified order. 105 MFEM_VERIFY(order > 0, "invalid order"); 106 mfem::FiniteElementCollection *fec = new mfem::H1_FECollection(order, dim); 107 mfem::FiniteElementSpace *fespace = new mfem::FiniteElementSpace(mesh, fec); 108 if (!test) { 109 std::cout << "Number of finite element unknowns: " 110 << fespace->GetTrueVSize() << std::endl; 111 } 112 113 // 6. Construct a rhs vector using the linear form f(v) = (solution, v), where 114 // v is a test function. 115 mfem::LinearForm b(fespace); 116 mfem::FunctionCoefficient sol_coeff(solution); 117 b.AddDomainIntegrator(new mfem::DomainLFIntegrator(sol_coeff)); 118 b.Assemble(); 119 120 // 7. Construct a CeedMassOperator utilizing the 'ceed' device and using the 121 // 'fespace' object to extract data needed by the Ceed objects. 122 CeedMassOperator mass(ceed, fespace); 123 124 // 8. Solve the discrete system using the conjugate gradients (CG) method. 125 mfem::CGSolver cg; 126 cg.SetRelTol(1e-6); 127 cg.SetMaxIter(100); 128 if (test) { 129 cg.SetPrintLevel(0); 130 } else { 131 cg.SetPrintLevel(3); 132 } 133 cg.SetOperator(mass); 134 135 mfem::GridFunction sol(fespace); 136 sol = 0.0; 137 cg.Mult(b, sol); 138 139 // 9. Compute and print the L2 projection error. 140 if (!test) { 141 std::cout << "L2 projection error: " << sol.ComputeL2Error(sol_coeff) 142 << std::endl; 143 } else { 144 if (fabs(sol.ComputeL2Error(sol_coeff))>1e-4) { 145 std::cout << "Error too large" << std::endl; 146 } 147 } 148 149 // 10. Open a socket connection to GLVis and send the mesh and solution for 150 // visualization. 151 if (visualization) { 152 char vishost[] = "localhost"; 153 int visport = 19916; 154 mfem::socketstream sol_sock(vishost, visport); 155 sol_sock.precision(8); 156 sol_sock << "solution\n" << *mesh << sol << std::flush; 157 } 158 159 // 11. Free memory and exit. 160 delete fespace; 161 delete fec; 162 delete mesh; 163 CeedDestroy(&ceed); 164 return 0; 165 } 166