244 lines
9.1 KiB
C++
244 lines
9.1 KiB
C++
// MFEM Example 6
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//
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// Compile with: make ex6
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//
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// Sample runs: ex6 -m ../data/square-disc.mesh -o 1
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// ex6 -m ../data/square-disc.mesh -o 2
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// ex6 -m ../data/square-disc-nurbs.mesh -o 2
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// ex6 -m ../data/star.mesh -o 3
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// ex6 -m ../data/escher.mesh -o 1
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// ex6 -m ../data/fichera.mesh -o 2
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// ex6 -m ../data/disc-nurbs.mesh -o 2
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// ex6 -m ../data/ball-nurbs.mesh
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// ex6 -m ../data/pipe-nurbs.mesh
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// ex6 -m ../data/star-surf.mesh -o 2
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// ex6 -m ../data/square-disc-surf.mesh -o 2
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// ex6 -m ../data/amr-quad.mesh
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//
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// Description: This is a version of Example 1 with a simple adaptive mesh
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// refinement loop. The problem being solved is again the Laplace
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// equation -Delta u = 1 with homogeneous Dirichlet boundary
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// conditions. The problem is solved on a sequence of meshes which
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// are locally refined in a conforming (triangles, tetrahedrons)
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// or non-conforming (quadrilateral, hexahedrons) manner according
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// to a simple ZZ error estimator.
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//
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// The example demonstrates MFEM's capability to work with both
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// conforming and nonconforming refinements, in 2D and 3D, on
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// linear, curved and surface meshes. Interpolation of functions
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// from coarse to fine meshes, as well as persistent GLVis
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// visualization are also illustrated.
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//
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// We recommend viewing Example 1 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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using namespace std;
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using namespace mfem;
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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/star.mesh";
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int order = 1;
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bool visualization = 1;
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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).");
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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.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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ifstream imesh(mesh_file);
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if (!imesh)
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{
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cerr << "\nCan not open mesh file: " << mesh_file << '\n' << endl;
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return 2;
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}
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Mesh mesh(imesh, 1, 1);
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imesh.close();
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int dim = mesh.Dimension();
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int sdim = mesh.SpaceDimension();
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// 3. Since a NURBS mesh can currently only be refined uniformly, we need to
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// convert it to a piecewise-polynomial curved mesh. First we refine the
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// NURBS mesh a bit more and then project the curvature to quadratic Nodes.
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if (mesh.NURBSext)
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{
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for (int i = 0; i < 2; i++)
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{
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mesh.UniformRefinement();
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}
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mesh.SetCurvature(2);
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}
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// 4. Define a finite element space on the mesh. The polynomial order is
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// one (linear) by default, but this can be changed on the command line.
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H1_FECollection fec(order, dim);
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FiniteElementSpace fespace(&mesh, &fec);
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// 5. As in Example 1, we set up bilinear and linear forms corresponding to
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// the Laplace problem -\Delta u = 1. We don't assemble the discrete
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// problem yet, this will be done in the main loop.
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BilinearForm a(&fespace);
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LinearForm b(&fespace);
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ConstantCoefficient one(1.0);
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ConstantCoefficient zero(0.0);
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a.AddDomainIntegrator(new DiffusionIntegrator(one));
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b.AddDomainIntegrator(new DomainLFIntegrator(one));
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// 6. The solution vector x and the associated finite element grid function
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// will be maintained over the AMR iterations. We initialize it to zero.
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GridFunction x(&fespace);
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x = 0;
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// 7. All boundary attributes will be used for essential (Dirichlet) BC.
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MFEM_VERIFY(mesh.bdr_attributes.Size() > 0,
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"Boundary attributes required in the mesh.");
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Array<int> ess_bdr(mesh.bdr_attributes.Max());
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ess_bdr = 1;
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// 8. Connect to GLVis.
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char vishost[] = "localhost";
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int visport = 19916;
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socketstream sol_sock;
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if (visualization)
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{
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sol_sock.open(vishost, visport);
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}
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// 9. The main AMR loop. In each iteration we solve the problem on the
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// current mesh, visualize the solution, estimate the error on all
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// elements, refine the worst elements and update all objects to work
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// with the new mesh.
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const int max_dofs = 50000;
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for (int it = 0; ; it++)
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{
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int cdofs = fespace.GetTrueVSize();
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cout << "\nIteration " << it << endl;
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cout << "Number of unknowns: " << cdofs << endl;
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// 10. Assemble the stiffness matrix and the right-hand side. Note that
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// MFEM doesn't care at this point if the mesh is nonconforming (i.e.,
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// contains hanging nodes). The FE space is considered 'cut' along
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// hanging edges/faces.
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a.Assemble();
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b.Assemble();
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// 11. Set Dirichlet boundary values in the GridFunction x.
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// Determine the list of Dirichlet true DOFs in the linear system.
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Array<int> ess_tdof_list;
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x.ProjectBdrCoefficient(zero, ess_bdr);
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fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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// 12. Create the linear system: eliminate boundary conditions, constrain
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// hanging nodes and possibly apply other transformations. The system
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// will be solved for true (unconstrained) DOFs only.
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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, 1);
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#ifndef MFEM_USE_SUITESPARSE
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// 13. Define a simple symmetric Gauss-Seidel preconditioner and use it to
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// solve the linear system with PCG.
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GSSmoother M(A);
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PCG(A, M, B, X, 2, 200, 1e-12, 0.0);
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#else
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// 13. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the
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// the linear 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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// 14. After solving the linear system, reconstruct the solution as a finite
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// element grid function. Constrained nodes are interpolated from true
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// DOFs (it may therefore happen that dim(x) >= dim(X)).
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a.RecoverFEMSolution(X, b, x);
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// 15. Send solution by socket to the GLVis server.
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if (visualization && sol_sock.good())
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{
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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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if (cdofs > max_dofs)
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{
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break;
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}
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// 16. Estimate element errors using the Zienkiewicz-Zhu error estimator.
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// The bilinear form integrator must have the 'ComputeElementFlux'
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// method defined.
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Vector errors(mesh.GetNE());
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Array<int> aniso_flags;
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{
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DiffusionIntegrator flux_integrator(one);
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FiniteElementSpace flux_fespace(&mesh, &fec, sdim);
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GridFunction flux(&flux_fespace);
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ZZErrorEstimator(flux_integrator, x, flux, errors, &aniso_flags);
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}
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// 17. Make a list of elements whose error is larger than a fraction (0.7)
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// of the maximum element error. These elements will be refined.
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Array<Refinement> ref_list;
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const double frac = 0.7;
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// the 'errors' are squared, so we need to square the fraction
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double threshold = (frac*frac) * errors.Max();
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for (int i = 0; i < errors.Size(); i++)
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{
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if (errors[i] >= threshold)
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{
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ref_list.Append(Refinement(i, aniso_flags[i]));
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}
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}
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// 18. Refine the selected elements. Since we are going to transfer the
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// grid function x from the coarse mesh to the new fine mesh in the
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// next step, we need to request the "two-level state" of the mesh.
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mesh.UseTwoLevelState(1);
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mesh.GeneralRefinement(ref_list);
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// 19. Update the space to reflect the new state of the mesh. Also,
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// interpolate the solution x so that it lies in the new space but
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// represents the same function. This saves solver iterations since
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// we'll have a good initial guess of x in the next step.
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// The interpolation algorithm needs the mesh to hold some information
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// about the previous state, which is why the call UseTwoLevelState
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// above is required.
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fespace.UpdateAndInterpolate(&x);
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// Note: If interpolation was not needed, we could just use the following
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// two calls to update the space and the grid function. (No need to
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// call UseTwoLevelState in this case.)
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// fespace.Update();
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// x.Update();
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// 20. Inform also the bilinear and linear forms that the space has
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// changed.
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a.Update();
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b.Update();
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}
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return 0;
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}
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