447 lines
13 KiB
C++
447 lines
13 KiB
C++
// MFEM Example 1
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//
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// Compile with: make AddScwarz
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//
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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/one-hex.mesh";
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int order = 1;
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int sdim = 1;
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bool static_cond = false;
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bool pa = false;
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const char *device_config = "cpu";
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bool visualization = true;
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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(&sdim, "-d", "--dimension", "Dimension");
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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(&pa, "-pa", "--partial-assembly", "-no-pa",
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"--no-partial-assembly", "Enable Partial Assembly.");
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args.AddOption(&device_config, "-d", "--device",
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"Device configuration string, see Device::Configure().");
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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. Enable hardware devices such as GPUs, and programming models such as
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// CUDA, OCCA, RAJA and OpenMP based on command line options.
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Device device(device_config);
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device.Print();
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// 3. 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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Mesh * mesh;
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// Define a simple square mesh
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if (sdim == 2)
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{
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mesh = new Mesh(1, 1, Element::QUADRILATERAL, true,1.0, 1.0,false);
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}
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else
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{
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mesh = new Mesh(1, 1, 1, Element::HEXAHEDRON, true,1.0, 1.0,1.0, false);
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}
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int dim = mesh->Dimension();
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// 4. 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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// int ref_levels =
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// (int)floor(log(50000./mesh->GetNE())/log(2.)/dim);
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int ref_levels = 1;
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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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// mesh->PrintInfo(cout);
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int nrelem = mesh->GetNE();
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int nrvert = mesh->GetNV();
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int nredge = mesh->GetNEdges();
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int nrface = mesh->GetNFaces();
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// 5. Define a finite element space on the mesh.
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FiniteElementCollection *fec = new H1_FECollection(order, dim);
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FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
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// cout << "Element to dof table " << endl;
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// fespace->GetElementToDofTable().Print();
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// Array<int>edge_dofs;
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// Array<int>edge_vert;
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// for (int i=0; i< nredge; i++ )
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// {
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// // fespace->GetEdgeDofs(i,edge_dofs);
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// mesh->GetEdgeVertices(i,edge_vert);
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// cout << "edge no " << i << " vertices :" ; edge_vert.Print();
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// }
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// Array<int>face_dofs;
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// Array<int>face_vert;
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// for (int i=0; i< nrface; i++ )
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// {
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// // fespace->GetFaceDofs(i,face_dofs);
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// mesh->GetFaceVertices(i,face_vert);
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// // cout << " face no " << i << " dofs :" ; face_dofs.Print();
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// cout << "face no " << i << " vertices :" ; face_vert.Print();
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// }
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// Array<int>elem_vert;
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// for (int i=0; i< nrelem; i++ )
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// {
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// // fespace->GetFaceDofs(i,face_dofs);
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// mesh->GetElementVertices(i,elem_vert);
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// // cout << " face no " << i << " dofs :" ; face_dofs.Print();
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// cout << "elem no " << i << " vertices :" ; elem_vert.Print();
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// }
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// construct a list of indices for each patch/vertex (that is not essential)
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// // Get essential
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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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// fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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// }
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// cout<< "essential boundary dofs: " ; ess_tdof_list.Print();
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Array<Array<int>> patch(nrvert);
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// Initialize each patch by an array consisting of the vertex its self
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// Numbering of vertices starts from 0
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for (int i=0; i<nrvert; i++)
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{
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Array<int> vert(1);
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vert=i;
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patch[i] = vert;
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}
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// Loop through all the edges and find the the vertices they contribute to
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Array<int>edge_vert;
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Array<int>edge_int_dofs;
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for (int i=0; i< nredge; i++ )
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{
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mesh->GetEdgeVertices(i,edge_vert);
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int nv = edge_vert.Size();
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fespace->GetEdgeInteriorDofs(i,edge_int_dofs);
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for (int j=0; j<nv ; j++)
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{
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int k = edge_vert[j];
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patch[k].Append(edge_int_dofs);
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}
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}
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// Loop through all the faces and find the the vertices they contribute to
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Array<int>face_vert;
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Array<int>face_int_dofs;
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for (int i=0; i< nrface; i++ )
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{
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mesh->GetFaceVertices(i,face_vert);
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int nv = face_vert.Size();
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fespace->GetFaceInteriorDofs(i,face_int_dofs);
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for (int j=0; j<nv ; j++)
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{
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int k = face_vert[j];
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patch[k].Append(face_int_dofs);
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}
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}
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// Loop through all the elements and find the the vertices they contribute to
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Array<int>elem_vert;
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Array<int>elem_int_dofs;
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for (int i=0; i< nrelem; i++ )
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{
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mesh->GetElementVertices(i,elem_vert);
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int nv = elem_vert.Size();
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fespace->GetElementInteriorDofs(i,elem_int_dofs);
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for (int j=0; j<nv ; j++)
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{
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int k = elem_vert[j];
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patch[k].Append(elem_int_dofs);
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}
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}
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for (int i=0; i<nrvert; i++)
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{
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cout << "Patch no: " << i << " dofs " ;
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patch[i].Print();
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}
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// Build a sparse matrix out of this map to extract the patch submatrix
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Array<SparseMatrix *> Pid(nrvert);
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Array<int> dofoffset(nrvert);
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dofoffset = 0;
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for (int i=0; i<nrvert; i++)
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{
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int height = fespace->GetVSize();
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int width = patch[i].Size();
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Pid[i] = new SparseMatrix(height,width);
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Pid[i]->Set(i,dofoffset[i],1.0); // Fill in the vertex dof (1 column for each vertex)
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dofoffset[i]++;
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}
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// Fill the sparse matrix with the edge dof indices (1 column for each dof)
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for (int i=0; i< nredge; i++ )
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{
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mesh->GetEdgeVertices(i,edge_vert);
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int nv = edge_vert.Size();
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fespace->GetEdgeInteriorDofs(i,edge_int_dofs);
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int ne = edge_int_dofs.Size();
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for (int j=0; j<nv ; j++)
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{
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int k = edge_vert[j];
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for (int l=0; l < ne; l++)
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{
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int m = edge_int_dofs[l];
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Pid[k]->Set(m,dofoffset[k],1.0);
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dofoffset[k]++;
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}
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}
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}
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// Fill the sparse matrix with the face dof indices (1 column for each dof)
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for (int i=0; i< nrface; i++ )
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{
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mesh->GetEdgeVertices(i,face_vert);
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int nv = face_vert.Size();
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fespace->GetFaceInteriorDofs(i,face_int_dofs);
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int nf = face_int_dofs.Size();
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for (int j=0; j<nv ; j++)
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{
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int k = face_vert[j];
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for (int l=0; l < nf; l++)
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{
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int m = face_int_dofs[l];
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Pid[k]->Set(m,dofoffset[k],1.0);
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dofoffset[k]++;
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}
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}
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}
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// Fill the sparse matrix with the element (middle) dof indices (1 column for each dof)
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for (int i=0; i< nrelem; i++ )
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{
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mesh->GetElementVertices(i,elem_vert);
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int nv = elem_vert.Size();
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fespace->GetElementInteriorDofs(i,elem_int_dofs);
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int nel = elem_int_dofs.Size();
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for (int j=0; j<nv ; j++)
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{
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int k = elem_vert[j];
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for (int l=0; l < nel; l++)
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{
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int m = elem_int_dofs[l];
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Pid[k]->Set(m,dofoffset[k],1.0);
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dofoffset[k]++;
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}
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}
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}
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Pid[0]->Finalize();
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Pid[0]->PrintMatlab(cout);
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// SparseMatrix * S = new SparseMatrix(5,5);
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// // S->PrintMatlab(std::cout);
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// S->Set(1,1,1.0);
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// S->Finalize();
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// // S->Print(cout);
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// S->PrintMatlab(cout);
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// cout << "Edges to vertex table " << endl;
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// mesh->GetEdgeVertexTable()->Print();
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// if (sdim == 3)
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// {
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// cout << "Faces to edges table " << endl;
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// mesh->GetFaceEdgeTable()->Print(); // is this really Face to Vertex table?
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// }
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// Custom vertex patch partitioning partitioning
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// Array<int> vertex_dofs;
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// for (int i=0; i< nrelems; i++ )
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// {
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// fespace->GetElementVertices(i,vertex_dofs);
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// std::cout << "Element "<< i+1 << " Vertex dofs: " ; vertex_dofs.Print();
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// }
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// This is local numbering of nodes
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// for (int i=0; i< nrelems; i++ )
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// {
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// cout << "Element " << i+1 << " Number of vertices: " <<
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// mesh->GetElement(i)->GetNVertices() << endl;
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// const int ne = mesh->GetElement(i)->GetNEdges();
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// for (int j=0; j< ne; j++ )
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// {
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// const int *ev = mesh->GetElement(i)->GetEdgeVertices(j);
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// cout << "Edge " << j << " vertices " << ev[0] << ", "<< ev[1] << endl;
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// }
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// }
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// Array<int> vertex_dofs;
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// fespace->GetElementToDofTable().Print();
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// for (int i=0; i< nrelems; i++ )
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// {
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// std::cout << "Vertex dofs " << endl;
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// fespace->GetElementVertices(i,vertex_dofs);
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// vertex_dofs.Print();
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// }
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// Array<int> vertex_dofs;
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// Array<int> interior_dofs;
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// for (int i=0; i< nrelems; i++ )
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// {
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// std::cout << "Element " << i+1 << endl;
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// fespace->GetElementVertices(i,vertex_dofs);
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// std::cout << "Vertex dofs " << endl;
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// vertex_dofs.Print();
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// fespace->GetElementInteriorDofs(i,interior_dofs);
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// std::cout << "Interior dofs " << endl;
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// interior_dofs.Print();
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// }
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// std::cout << "Number of global unknowns: " << fespace->GetVSize() << endl;
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// std::cout << "Number of vertex dofs " << fespace->GetNVDofs() << endl;
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// std::cout << "Number of edge dofs " << fespace->GetNEDofs() << endl;
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// std::cout << "Number of face dofs " << fespace->GetNFDofs() << endl;
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// std::cout << "Number of total dofs " << fespace->GetNDofs() << endl;
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// cout << "Number of finite element unknowns: "
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// << fespace->GetTrueVSize() << endl;
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// // 6. 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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// fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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// }
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// 7. 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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// ConstantCoefficient one(1.0);
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// b->AddDomainIntegrator(new DomainLFIntegrator(one));
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// b->Assemble();
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// 8. 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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// 9. 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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// if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
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// a->AddDomainIntegrator(new DiffusionIntegrator(one));
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// a->Assemble();
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// OperatorPtr 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 << "Size of linear system: " << A->Height() << endl;
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// A->PrintMatlab(cout);
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// #ifndef MFEM_USE_SUITESPARSE
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// // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
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// GSSmoother M((SparseMatrix&)(*A));
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// PCG(*A, M, B, X, 1, 200, 1e-12, 0.0);
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// #else
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// // 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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// // 12. Recover the solution as a finite element grid function.
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// a->RecoverFEMSolution(X, *b, x);
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// 14. 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 << "mesh\n" << *mesh << flush;
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}
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// // 15. 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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