Tucker Babcock
04029239d4
Merging sbp-dev into hashtable-sbp-dev to test hashtable implementation with more recent sbp-dev branch before merging back to sbp-dev
360 lines
11 KiB
C++
360 lines
11 KiB
C++
// MFEM Example 1
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//
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// Compile with: make exSBP
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//
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// Sample runs: exSBP -sbp -o 0 -p 0 -r 1
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// exSBP -sbp -o 4 -p 3
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//
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//
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// Description: This example code builds on Example 1 but adds SBP operators.
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// It demonstrates the use of MFEM to define a simple finite
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// element discretization of the Laplace problem -Delta u = 1
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// with homogeneous Dirichlet boundary conditions. Specifically,
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// we discretize using a FE or SBP space of the specified order,
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// or if order < 1 using an isoparametric/isogeometric space
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// (i.e. quadratic for quadratic curvilinear mesh, NURBS for
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// NURBS mesh, etc.)
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//
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// The example highlights the use of mesh refinement, finite
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// element grid functions, as well as linear and bilinear forms
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// corresponding to the left-hand side and right-hand side of the
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// discrete linear system. We also cover the explicit elimination
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// of essential boundary conditions, static condensation, and the
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// optional connection to the GLVis tool for visualization.
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#include "mfem.hpp"
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#include <fstream>
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#include <iostream>
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#include <chrono>
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using namespace std;
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using namespace mfem;
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int problem;
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// Prescribed time-independent boundary and right-hand side functions.
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double bdr_func(const Vector &pt);
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double rhs_func(const Vector &pt);
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int main(int argc, char *argv[])
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{
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// 1. Parse command-line options.
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const char *mesh_file = "../data/unitGridTestMesh.msh";
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int order = 1;
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bool static_cond = false;
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bool visualization = 1;
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bool sbp = 1;
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problem = 1;
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int ref_levels = 0;
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bool convOut = false;
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OptionsParser args(argc, argv);
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args.AddOption(&mesh_file, "-m", "--mesh",
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"Mesh file to use.");
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args.AddOption(&order, "-o", "--order",
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"Finite element order (polynomial degree) or -1 for"
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" isoparametric space.");
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args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
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"--no-static-condensation", "Enable static condensation.");
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args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
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"--no-visualization",
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"Enable or disable GLVis visualization.");
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args.AddOption(&sbp, "-sbp", "--summationbyparts", "-no-sbp",
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"--no-summationbyparts",
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"Enable or disable use of SBP operators.");
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args.AddOption(&problem, "-p", "--problem",
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"Problem setup to use: 0 = transcendental manufactured solution, "
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"1 = linear displacement, "
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"2 = quadratic displacement, "
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"3 = cubic displacement, "
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"4 = quartic displacement.");
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args.AddOption(&ref_levels, "-r", "--ref-levels",
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"Number of initial uniform refinement levels.");
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args.Parse();
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if (!args.Good())
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{
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args.PrintUsage(cout);
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return 1;
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}
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args.PrintOptions(cout);
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// 2. Read the mesh from the given mesh file. We can handle triangular,
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// quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
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// the same code.
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Mesh *mesh = new Mesh(mesh_file, 1, 1);
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int dim = mesh->Dimension();
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// 3. Refine the mesh to increase the resolution. In this example we do
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// 'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
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// largest number that gives a final mesh with no more than 50,000
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// elements.
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{
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for (int l = 0; l < ref_levels; l++)
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{
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mesh->UniformRefinement();
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}
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}
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// 4. Define a finite element space on the mesh. Here we use continuous
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// Lagrange finite elements of the specified order. If order < 1, we
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// instead use an isoparametric/isogeometric space.
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FiniteElementCollection *fec;
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if (sbp)
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{
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fec = new C_SBPCollection(order, dim);
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}
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else if (order > 0)
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{
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fec = new H1_FECollection(order, dim);
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}
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else if (mesh->GetNodes())
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{
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fec = mesh->GetNodes()->OwnFEC();
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cout << "Using isoparametric FEs: " << fec->Name() << endl;
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}
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else
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{
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fec = new H1_FECollection(order = 1, dim);
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}
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FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
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cout << "Number of finite element unknowns: "
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<< fespace->GetTrueVSize() << endl;
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// 7. Define the solution vector x as a finite element grid function
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// corresponding to fespace. Initialize x with initial guess of zero,
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// which satisfies the boundary conditions.
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GridFunction x(fespace);
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x = 0.0;
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// Create function coefficient bdr which holds the exact solution and is
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// used to strongly impose boundary conditions.
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FunctionCoefficient bdr(bdr_func);
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// 5. Determine the list of true (i.e. conforming) essential boundary dofs.
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// In this example, the boundary conditions are defined by marking all
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// the boundary attributes from the mesh as essential (Dirichlet) and
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// converting them to a list of true dofs.
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Array<int> ess_tdof_list;
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if (mesh->bdr_attributes.Size())
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{
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Array<int> ess_bdr(mesh->bdr_attributes.Max());
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ess_bdr = 1;
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// Project boundary conditions onto grid function to strongly impose
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// boundary conditions. BC's are defined in the function `bdr_func`.
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x.ProjectBdrCoefficient(bdr, ess_bdr);
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fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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}
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// 6. Set up the linear form b(.) which corresponds to the right-hand side of
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// the FEM linear system, which in this case is (1,phi_i) where phi_i are
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// the basis functions in the finite element fespace.
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LinearForm *b = new LinearForm(fespace);
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FunctionCoefficient rhs(rhs_func);
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b->AddDomainIntegrator(new DomainLFIntegrator(rhs));
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if (problem < 0 || problem > 4)
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{
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mfem::out << "Invalid problem type: " << problem << "\n";
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delete mesh;
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return 3;
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}
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// // Start timing
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// std::chrono::time_point<std::chrono::high_resolution_clock> start = std::chrono::high_resolution_clock::now();
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b->Assemble();
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// // End timing and compute interval
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// std::chrono::time_point<std::chrono::high_resolution_clock> finish = std::chrono::high_resolution_clock::now();
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// std::chrono::duration<double> elapsed = finish - start;
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// std::cout << "\nb->Assemble() elapsed time: " << elapsed.count() << " s\n";
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// 8. Set up the bilinear form a(.,.) on the finite element space
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// corresponding to the Laplacian operator -Delta, by adding the Diffusion
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// domain integrator.
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BilinearForm *a = new BilinearForm(fespace);
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ConstantCoefficient one(1.0);
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a->AddDomainIntegrator(new DiffusionIntegrator(one));
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// 9. Assemble the bilinear form and the corresponding linear system,
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// applying any necessary transformations such as: eliminating boundary
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// conditions, applying conforming constraints for non-conforming AMR,
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// static condensation, etc.
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if (static_cond) { a->EnableStaticCondensation(); }
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// // Start timing
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// start = std::chrono::high_resolution_clock::now();
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a->Assemble();
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// // End timing and compute interval
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// finish = std::chrono::high_resolution_clock::now();
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// elapsed = finish - start;
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// std::cout << "\na->Assemble() elapsed time: " << elapsed.count() << " s\n";
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SparseMatrix A;
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Vector B, X;
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a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
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mfem::out << "Size of linear system: " << A.Height() << endl;
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#ifndef MFEM_USE_SUITESPARSE
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// 10. Define a simple symmetric Gauss-Seidel preconditioner and use it to
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// solve the system A X = B with PCG.
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GSSmoother M(A);
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PCG(A, M, B, X, 1, 1000, 1e-12, 0.0);
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#else
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// 10. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
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UMFPackSolver umf_solver;
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umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
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umf_solver.SetOperator(A);
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umf_solver.Mult(B, X);
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#endif
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// 11. Recover the solution as a finite element grid function.
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a->RecoverFEMSolution(X, *b, x);
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// 12. Compute and print the L^2 norm of the error.
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mfem::out << "\n|| u_h - u ||_{L^2} = " << x.ComputeL2Error(bdr) << '\n' << endl;
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// mfem::out << "h: " << 0.1 / pow(2, ref_levels) << "\n";
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// 12. Save the refined mesh and the solution. This output can be viewed later
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// using GLVis: "glvis -m refined.mesh -g sol.gf".
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ofstream mesh_ofs("refined.mesh");
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mesh_ofs.precision(8);
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mesh->Print(mesh_ofs);
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// mesh->PrintVTK(mesh_ofs);
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ofstream sol_ofs("sol.gf");
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sol_ofs.precision(8);
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x.Save(sol_ofs);
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// Save solution mesh in vtk file
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char solFileName[32];
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if (sbp)
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{
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snprintf(solFileName, 32, "exSBP_SBP_O%d_P%d.vtk", order, problem);
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}
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else
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{
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snprintf(solFileName, 32, "exSBP_FE_O%d_P%d.vtk", order, problem);
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}
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if (convOut)
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{
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// Save convergence study information in output file
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char outfileName[32];
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if (problem == 0)
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{
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snprintf(outfileName, 32, "convOutputP%d_manufactured.txt", order);
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}
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else if (problem == 1)
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{
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snprintf(outfileName, 32, "convOutputP%d_lin.txt", order);
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}
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else if (problem == 2)
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{
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snprintf(outfileName, 32, "convOutputP%d_quad.txt", order);
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}
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else if (problem == 3)
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{
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snprintf(outfileName, 32, "convOutputP%d_cubic.txt", order);
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}
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else if (problem == 4)
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{
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snprintf(outfileName, 32, "convOutputP%d_quartic.txt", order);
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}
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ofstream outputFile;
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outputFile.open(outfileName, ios::out | ios::app);
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if (outputFile.is_open())
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{
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outputFile << x.ComputeL2Error(bdr) << ", " << 0.1 / pow(2, ref_levels) << "\n";
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}
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outputFile.close();
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}
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ofstream omesh(solFileName);
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omesh.precision(14);
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mesh->PrintVTK(omesh, 1);
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x.SaveVTK(omesh, "sol", 1);
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// 13. Send the solution by socket to a GLVis server.
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if (visualization)
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{
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char vishost[] = "localhost";
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int visport = 19916;
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socketstream sol_sock(vishost, visport);
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sol_sock.precision(8);
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sol_sock << "solution\n" << *mesh << x << flush;
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}
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// 14. Free the used memory.
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delete a;
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delete b;
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delete fespace;
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if (order > 0) { delete fec; }
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delete mesh;
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return 0;
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}
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// Exact solution, used for the Dirichlet BC.
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double bdr_func(const Vector &pt)
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{
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double x = pt(0), y = pt(1), z = 0.0;
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if (problem == 0) // manufactured solution
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{
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z = sin(M_PI*x)*sin(M_PI*y);
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}
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else if (problem == 1) // linear displacement
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{
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z = 0.5*x + 0.5*y;
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}
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else if (problem == 2) // quadratic displacement
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{
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z = 0.5*x*x + 0.5*y*y;
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}
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else if (problem == 3) // manufactured solution
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{
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z = 0.5*x*x*x + 0.5*y*y*y;
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}
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else if (problem == 4) // manufactured solution
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{
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z = 0.5*x*x*x*x + 0.5*y*y*y*y;
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}
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return z;
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}
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// right hand side function for manufactured solution
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double rhs_func(const Vector &pt)
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{
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double x = pt(0), y = pt(1), z = 0.0;
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if (problem == 0)
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{
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z = 2*M_PI*M_PI*sin(M_PI*x)*sin(M_PI*y);
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}
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else if (problem == 1)
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{
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z = 0;
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}
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else if (problem == 2)
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{
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z = -2;
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}
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else if (problem == 3)
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{
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z = -3*(x+y);
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}
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else if (problem == 4)
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{
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z = -6*(x*x + y*y);
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}
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return z;
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}
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