376 lines
14 KiB
C++
376 lines
14 KiB
C++
// MFEM Example 39
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//
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// Compile with: make ex39
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//
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// Sample runs: ex39
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// ex39 -ess "Southern Boundary"
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// ex39 -src Base
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//
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// Device sample runs:
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// ex39 -fa -d cuda
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//
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// Description: This example code demonstrates the use of named attribute
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// sets in MFEM to specify material regions, boundary regions,
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// or source regions by name rather than attribute numbers. It
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// also demonstrates how new named attribute sets may be created
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// from arbitrary groupings of attribute number and used as a
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// convenient shorthand to refer to those groupings in other
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// portions of the application or through the command line.
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//
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// The particular problem being solved here is nearly the same
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// as that in example 1 i.e. a simple finite element
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// discretization of the Laplace problem -Delta u = 1 with
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// homogeneous Dirichlet boundary conditions and, in this case,
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// an inhomogeneous diffusion coefficient. The diffusion
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// coefficient is given a small default value throughout the
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// domain which is increased by two separate amounts in two named
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// regions.
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//
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// The example highlights the use of named attribute sets for
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// both subdomains and boundaries in different contexts as well
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// as basic methods to create named sets from existing attributes.
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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/compass.msh";
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int order = 1;
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string source_name = "Rose Even";
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string ess_name = "Boundary";
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bool static_cond = false;
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bool pa = false;
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bool fa = false;
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const char *device_config = "cpu";
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bool visualization = true;
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bool algebraic_ceed = 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(&source_name,"-src","--source-attr-name",
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"Name of attribute set containing source.");
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args.AddOption(&ess_name,"-ess","--ess-attr-name",
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"Name of attribute set containing essential BC.");
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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(&fa, "-fa", "--full-assembly", "-no-fa",
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"--no-full-assembly", "Enable Full 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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#ifdef MFEM_USE_CEED
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args.AddOption(&algebraic_ceed, "-a", "--algebraic",
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"-no-a", "--no-algebraic",
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"Use algebraic Ceed solver");
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#endif
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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(mesh_file, 1, 1);
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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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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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// Display attribute set names contained in the initial mesh
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{
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std::set<string> names;
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mesh.GetAttributeSetNames(names);
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cout << "Element Attribute Set Names: ";
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for (auto const &set_name : names)
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{
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cout << " \"" << set_name << "\"";
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}
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cout << endl;
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std::set<string> bdr_names;
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mesh.GetBdrAttributeSetNames(bdr_names);
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cout << "Boundary Attribute Set Names: ";
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for (auto const &bdr_set_name : bdr_names)
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{
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cout << " \"" << bdr_set_name << "\"";
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}
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cout << endl;
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}
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// Define new regions based on existing attribute sets
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{
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Array<int> & Na = mesh.GetAttributeSet("N Even");
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Array<int> & Nb = mesh.GetAttributeSet("N Odd");
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Array<int> & Sa = mesh.GetAttributeSet("S Even");
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Array<int> & Sb = mesh.GetAttributeSet("S Odd");
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Array<int> & Ea = mesh.GetAttributeSet("E Even");
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Array<int> & Eb = mesh.GetAttributeSet("E Odd");
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Array<int> & Wa = mesh.GetAttributeSet("W Even");
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Array<int> & Wb = mesh.GetAttributeSet("W Odd");
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// Create a new set spanning the North point
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mesh.SetAttributeSet("North", Na);
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mesh.AddToAttributeSet("North", Nb);
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// Create a new set spanning the South point
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mesh.SetAttributeSet("South", Sa);
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mesh.AddToAttributeSet("South", Sb);
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// Create a new set spanning the East point
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mesh.SetAttributeSet("East", Ea);
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mesh.AddToAttributeSet("East", Eb);
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// Create a new set spanning the West point
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mesh.SetAttributeSet("West", Wa);
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mesh.AddToAttributeSet("West", Wb);
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// Create a new set consisting of the "a" sides of the compass rose
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mesh.SetAttributeSet("Rose Even", Na);
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mesh.AddToAttributeSet("Rose Even", Sa);
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mesh.AddToAttributeSet("Rose Even", Ea);
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mesh.AddToAttributeSet("Rose Even", Wa);
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// Create a new set consisting of the "b" sides of the compass rose
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mesh.SetAttributeSet("Rose Odd", Nb);
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mesh.AddToAttributeSet("Rose Odd", Sb);
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mesh.AddToAttributeSet("Rose Odd", Eb);
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mesh.AddToAttributeSet("Rose Odd", Wb);
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// Create a new set consisting of the full compass rose
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Array<int> & Ra = mesh.GetAttributeSet("Rose Even");
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Array<int> & Rb = mesh.GetAttributeSet("Rose Odd");
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mesh.SetAttributeSet("Rose", Ra);
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mesh.AddToAttributeSet("Rose", Rb);
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}
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// Define new boundary regions based on existing boundary attribute sets
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{
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Array<int> & NNE = mesh.GetBdrAttributeSet("NNE");
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Array<int> & NNW = mesh.GetBdrAttributeSet("NNW");
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Array<int> & ENE = mesh.GetBdrAttributeSet("ENE");
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Array<int> & ESE = mesh.GetBdrAttributeSet("ESE");
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Array<int> & SSE = mesh.GetBdrAttributeSet("SSE");
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Array<int> & SSW = mesh.GetBdrAttributeSet("SSW");
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Array<int> & WNW = mesh.GetBdrAttributeSet("WNW");
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Array<int> & WSW = mesh.GetBdrAttributeSet("WSW");
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mesh.SetBdrAttributeSet("Northern Boundary", NNE);
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mesh.AddToBdrAttributeSet("Northern Boundary", NNW);
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mesh.SetBdrAttributeSet("Southern Boundary", SSE);
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mesh.AddToBdrAttributeSet("Southern Boundary", SSW);
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mesh.SetBdrAttributeSet("Eastern Boundary", ENE);
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mesh.AddToBdrAttributeSet("Eastern Boundary", ESE);
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mesh.SetBdrAttributeSet("Western Boundary", WNW);
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mesh.AddToBdrAttributeSet("Western Boundary", WSW);
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mesh.SetBdrAttributeSet("Boundary",
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mesh.GetBdrAttributeSet("Northern Boundary"));
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mesh.AddToBdrAttributeSet("Boundary",
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mesh.GetBdrAttributeSet("Southern Boundary"));
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mesh.AddToBdrAttributeSet("Boundary",
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mesh.GetBdrAttributeSet("Eastern Boundary"));
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mesh.AddToBdrAttributeSet("Boundary",
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mesh.GetBdrAttributeSet("Western Boundary"));
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}
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// 5. 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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bool delete_fec;
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if (order > 0)
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{
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fec = new H1_FECollection(order, dim);
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delete_fec = true;
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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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delete_fec = false;
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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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delete_fec = true;
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}
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FiniteElementSpace fespace(&mesh, fec);
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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 regions corresponding to the boundary attributes
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// contained in the set named "ess_name" 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_marker;
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mesh.BdrAttrToMarker(mesh.GetBdrAttributeSet(ess_name),
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ess_bdr_marker);
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fespace.GetEssentialTrueDofs(ess_bdr_marker, 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_s,phi_i) where phi_i
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// are the basis functions in fespace and 1_s is an indicator function
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// equal to 1 on the region defined by the named set "source_name" and
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// zero elsewhere.
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Array<int> source_marker;
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mesh.AttrToMarker(mesh.GetAttributeSet(source_name), source_marker);
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LinearForm b(&fespace);
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ConstantCoefficient one(1.0);
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b.AddDomainIntegrator(new DomainLFIntegrator(one), source_marker);
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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
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// Diffusion domain integrator.
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BilinearForm a(&fespace);
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if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
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if (fa)
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{
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a.SetAssemblyLevel(AssemblyLevel::FULL);
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// Sort the matrix column indices when running on GPU or with OpenMP (i.e.
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// when Device::IsEnabled() returns true). This makes the results
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// bit-for-bit deterministic at the cost of somewhat longer run time.
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a.EnableSparseMatrixSorting(Device::IsEnabled());
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}
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ConstantCoefficient defaultCoef(1.0e-6);
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ConstantCoefficient baseCoef(1.0);
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ConstantCoefficient roseCoef(2.0);
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Array<int> base_marker;
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Array<int> rose_marker;
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mesh.AttrToMarker(mesh.GetAttributeSet("Base"), base_marker);
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mesh.AttrToMarker(mesh.GetAttributeSet("Rose Even"), rose_marker);
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a.AddDomainIntegrator(new DiffusionIntegrator(defaultCoef));
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a.AddDomainIntegrator(new DiffusionIntegrator(baseCoef), base_marker);
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a.AddDomainIntegrator(new DiffusionIntegrator(roseCoef), rose_marker);
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// 10. 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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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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// 11. Solve the linear system A X = B.
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if (!pa)
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{
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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, 800, 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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}
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else
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{
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if (UsesTensorBasis(fespace))
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{
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if (algebraic_ceed)
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{
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ceed::AlgebraicSolver M(a, ess_tdof_list);
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PCG(*A, M, B, X, 1, 800, 1e-12, 0.0);
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}
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else
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{
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OperatorJacobiSmoother M(a, ess_tdof_list);
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PCG(*A, M, B, X, 1, 800, 1e-12, 0.0);
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}
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}
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else
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{
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CG(*A, B, X, 1, 800, 1e-12, 0.0);
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}
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}
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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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// 13. 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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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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// 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 << "solution\n" << mesh << x << "keys Rjmm" << flush;
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}
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// 15. Free the used memory.
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if (delete_fec)
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{
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delete fec;
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}
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return 0;
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}
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