268 lines
9.0 KiB
C++
268 lines
9.0 KiB
C++
// MFEM Example 28
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//
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// Compile with: make ex28
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//
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// Sample runs: ex28
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// ex28 --visit-datafiles
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// ex28 --order 2
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//
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// Description: Demonstrates a sliding boundary condition in an elasticity
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// problem. A trapezoid, roughly as pictured below, is pushed
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// from the right into a rigid notch. Normal displacement is
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// restricted, but tangential movement is allowed, so the
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// trapezoid compresses into the notch.
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//
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// /-------+
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// normal constrained --->/ | <--- boundary force (2)
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// boundary (4) /---------+
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// ^
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// |
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// normal constrained boundary (1)
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//
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// This example demonstrates the use of the ConstrainedSolver
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// framework.
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//
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// We recommend viewing Example 2 before viewing this example.
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#include "mfem.hpp"
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#include <fstream>
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#include <iostream>
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#include <set>
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using namespace std;
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using namespace mfem;
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// Return a mesh with a single element with vertices (0, 0), (1, 0), (1, 1),
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// (offset, 1) to demonstrate boundary conditions on a surface that is not
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// axis-aligned.
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Mesh * build_trapezoid_mesh(real_t offset)
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{
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MFEM_VERIFY(offset < 0.9, "offset is too large!");
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const int dimension = 2;
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const int nvt = 4; // vertices
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const int nbe = 4; // num boundary elements
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Mesh * mesh = new Mesh(dimension, nvt, 1, nbe);
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// vertices
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real_t vc[dimension];
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vc[0] = 0.0; vc[1] = 0.0;
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mesh->AddVertex(vc);
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vc[0] = 1.0; vc[1] = 0.0;
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mesh->AddVertex(vc);
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vc[0] = offset; vc[1] = 1.0;
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mesh->AddVertex(vc);
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vc[0] = 1.0; vc[1] = 1.0;
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mesh->AddVertex(vc);
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// element
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Array<int> vert(4);
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vert[0] = 0; vert[1] = 1; vert[2] = 3; vert[3] = 2;
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mesh->AddQuad(vert, 1);
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// boundary
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Array<int> sv(2);
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sv[0] = 0; sv[1] = 1;
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mesh->AddBdrSegment(sv, 1);
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sv[0] = 1; sv[1] = 3;
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mesh->AddBdrSegment(sv, 2);
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sv[0] = 2; sv[1] = 3;
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mesh->AddBdrSegment(sv, 3);
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sv[0] = 0; sv[1] = 2;
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mesh->AddBdrSegment(sv, 4);
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mesh->FinalizeQuadMesh(1, 0, true);
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return mesh;
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}
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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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int order = 1;
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bool visualization = 1;
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real_t offset = 0.3;
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bool visit = false;
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OptionsParser args(argc, argv);
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args.AddOption(&order, "-o", "--order",
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"Finite element order (polynomial degree).");
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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(&offset, "--offset", "--offset",
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"How much to offset the trapezoid.");
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args.AddOption(&visit, "-visit", "--visit-datafiles", "-no-visit",
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"--no-visit-datafiles",
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"Save data files for VisIt (visit.llnl.gov) visualization.");
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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. Build a trapezoidal mesh with a single quadrilateral element, where
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// 'offset' determines how far off it is from a rectangle.
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Mesh *mesh = build_trapezoid_mesh(offset);
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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 1,000
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// elements.
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{
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int ref_levels =
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(int)floor(log(1000./mesh->GetNE())/log(2.)/dim);
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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 vector finite
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// elements, i.e. dim copies of a scalar finite element space. The vector
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// dimension is specified by the last argument of the FiniteElementSpace
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// constructor.
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FiniteElementCollection *fec = new H1_FECollection(order, dim);
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FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec, dim);
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cout << "Number of finite element unknowns: " << fespace->GetTrueVSize()
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<< endl;
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cout << "Assembling matrix and r.h.s... " << flush;
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// 5. Determine the list of true (i.e. parallel conforming) essential
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// boundary dofs. In this example, there are no essential boundary
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// conditions in the usual sense, but we leave the machinery here for
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// users to modify if they wish.
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Array<int> ess_tdof_list, ess_bdr(mesh->bdr_attributes.Max());
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ess_bdr = 0;
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fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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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. In this case, b_i equals the boundary integral
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// of f*phi_i where f represents a "push" force on the right side of the
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// trapezoid.
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VectorArrayCoefficient f(dim);
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for (int i = 0; i < dim-1; i++)
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{
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f.Set(i, new ConstantCoefficient(0.0));
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}
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{
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Vector push_force(mesh->bdr_attributes.Max());
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push_force = 0.0;
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push_force(1) = -5.0e-2; // index 1 attribute 2
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f.Set(0, new PWConstCoefficient(push_force));
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}
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LinearForm *b = new LinearForm(fespace);
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b->AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f));
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b->Assemble();
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// 7. Define the solution vector x as a finite element grid function
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// corresponding to fespace.
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GridFunction x(fespace);
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x = 0.0;
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// 8. Set up the bilinear form a(.,.) on the finite element space
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// corresponding to the linear elasticity integrator with piece-wise
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// constants coefficient lambda and mu. We use constant coefficients,
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// but see ex2 for how to set up piecewise constant coefficients based
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// on attribute.
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Vector lambda(mesh->attributes.Max());
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lambda = 1.0;
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PWConstCoefficient lambda_func(lambda);
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Vector mu(mesh->attributes.Max());
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mu = 1.0;
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PWConstCoefficient mu_func(mu);
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BilinearForm *a = new BilinearForm(fespace);
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a->AddDomainIntegrator(new ElasticityIntegrator(lambda_func, mu_func));
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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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a->Assemble();
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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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cout << "done." << endl;
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cout << "Size of linear system: " << A.Height() << endl;
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// 10. Set up constraint matrix to constrain normal displacement (but
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// allow tangential displacement) on specified boundaries.
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Array<int> constraint_atts(2);
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constraint_atts[0] = 1; // attribute 1 bottom
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constraint_atts[1] = 4; // attribute 4 left side
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Array<int> lagrange_rowstarts;
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SparseMatrix* local_constraints =
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BuildNormalConstraints(*fespace, constraint_atts, lagrange_rowstarts);
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// 11. Define and apply an iterative solver for the constrained system
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// in saddle-point form with a Gauss-Seidel smoother for the
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// displacement block.
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GSSmoother M(A);
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SchurConstrainedSolver * solver =
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new SchurConstrainedSolver(A, *local_constraints, M);
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solver->SetRelTol(1e-5);
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solver->SetMaxIter(2000);
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solver->SetPrintLevel(1);
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solver->Mult(B, X);
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// 12. Recover the solution as a finite element grid function. Move the
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// mesh to reflect the displacement of the elastic body being
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// simulated, for purposes of output.
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a->RecoverFEMSolution(X, *b, x);
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mesh->SetNodalFESpace(fespace);
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GridFunction *nodes = mesh->GetNodes();
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*nodes += x;
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// 13. Save the refined mesh and the solution in VisIt format.
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if (visit)
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{
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VisItDataCollection visit_dc("ex28", mesh);
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visit_dc.SetLevelsOfDetail(4);
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visit_dc.RegisterField("displacement", &x);
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visit_dc.Save();
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}
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// 14. Save the displaced mesh and the inverted solution (which gives the
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// backward displacements to the original grid). This output can be
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// viewed later using GLVis: "glvis -m displaced.mesh -g sol.gf".
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{
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x *= -1; // sign convention for GLVis displacements
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ofstream mesh_ofs("displaced.mesh");
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mesh_ofs.precision(8);
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mesh->Print(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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}
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// 15. Send the above data by socket to a GLVis server. Use the "n" and "b"
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// keys in GLVis to visualize the displacements.
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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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// 16. Free the used memory.
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delete local_constraints;
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delete solver;
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delete a;
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delete b;
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if (fec)
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{
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delete fespace;
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delete fec;
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}
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delete mesh;
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return 0;
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}
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