ex39.cpp

//                                MFEM Example 39
//
// Compile with: make ex39
//
// Sample runs:  ex39
//               ex39 -ess "Southern Boundary"
//               ex39 -src Base
//
// Description:  This example code demonstrates the use of named attribute
//               sets in MFEM to specify material regions, boundary regions,
//               or source regions by name rather than attribute numbers. It
//               also demonstrates how new named attribute sets may be created
//               from arbitrary groupings of attribute numbers and used as a
//               convenient shorthand to refer to those groupings in other
//               portions of the application or through the command line.
//
//               The particular problem being solved here is nearly the same
//               as that in example 1 i.e. a simple finite element
//               discretization of the Laplace problem -Delta u = 1 with
//               homogeneous Dirichlet boundary conditions and, in this case,
//               an inhomogeneous diffusion coefficient. The diffusion
//               coefficient is given a small default value throughout the
//               domain which is increased by two separate amounts in two named
//               regions.
//
//               This example makes use of a specific input mesh, "compass.msh",
//               containing named domain and boundary regions generated by Gmsh
//               and stored in their "msh" format (version 2.2). This file
//               defines eight boundary regions corresponding to eight compass
//               headings; "ENE", "NNE", "NNW", "WSW", "SSW", "SSE", and "ESE".
//               It also defines nine domain regions; "Base", "N Even", "N Odd",
//               "W Even", "W Odd", "S Even", "S Odd", "E Even", and "E Odd".
//               These regions split the four compass pointers into two halves
//               each and also label the remaining elements as "Base". Starting
//               with these named regions we test the construction of named
//               sets as well as reading and writing these named groupings from
//               and to mesh files.
//
//               The example highlights the use of named attribute sets for
//               both subdomains and boundaries in different contexts as well
//               as basic methods to create named sets from existing attributes.

#include "mfem.hpp"
#include <fstream>
#include <iostream>

using namespace std;
using namespace mfem;

int main(int argc, char *argv[])
{
   // 1. Parse command-line options.
   const char *mesh_file = "../data/compass.msh";
   int order = 1;
   string source_name = "Rose Even";
   string ess_name = "Boundary";
   bool visualization = true;

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
                  "Mesh file to use.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree) or -1 for"
                  " isoparametric space.");
   args.AddOption(&source_name,"-src","--source-attr-name",
                  "Name of attribute set containing source.");
   args.AddOption(&ess_name,"-ess","--ess-attr-name",
                  "Name of attribute set containing essential BC.");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
   args.ParseCheck();

   // 2. Read the mesh from the given mesh file. We can handle triangular,
   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
   //    the same code.
   Mesh mesh(mesh_file, 1, 1);
   int dim = mesh.Dimension();

   // 3. Refine the mesh to increase the resolution. In this example we do
   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
   //    largest number that gives a final mesh with no more than 50,000
   //    elements.
   {
      int ref_levels =
         (int)floor(log(50000./mesh.GetNE())/log(2.)/dim);
      for (int l = 0; l < ref_levels; l++)
      {
         mesh.UniformRefinement();
      }
   }

   // 4a. Display attribute set names contained in the initial mesh
   AttributeSets &attr_sets = mesh.attribute_sets;
   AttributeSets &bdr_attr_sets = mesh.bdr_attribute_sets;
   {
      std::set<string> names = attr_sets.GetAttributeSetNames();
      cout << "Element Attribute Set Names: ";
      for (auto const &set_name : names)
      {
         cout << " \"" << set_name << "\"";
      }
      cout << endl;

      std::set<string> bdr_names = bdr_attr_sets.GetAttributeSetNames();
      cout << "Boundary Attribute Set Names: ";
      for (auto const &bdr_set_name : bdr_names)
      {
         cout << " \"" << bdr_set_name << "\"";
      }
      cout << endl;
   }

   // 4b. Define new regions based on existing attribute sets
   {
      Array<int> & Na = attr_sets.GetAttributeSet("N Even");
      Array<int> & Nb = attr_sets.GetAttributeSet("N Odd");
      Array<int> & Sa = attr_sets.GetAttributeSet("S Even");
      Array<int> & Sb = attr_sets.GetAttributeSet("S Odd");
      Array<int> & Ea = attr_sets.GetAttributeSet("E Even");
      Array<int> & Eb = attr_sets.GetAttributeSet("E Odd");
      Array<int> & Wa = attr_sets.GetAttributeSet("W Even");
      Array<int> & Wb = attr_sets.GetAttributeSet("W Odd");

      // Create a new set spanning the North point
      attr_sets.SetAttributeSet("North", Na);
      attr_sets.AddToAttributeSet("North", Nb);

      // Create a new set spanning the South point
      attr_sets.SetAttributeSet("South", Sa);
      attr_sets.AddToAttributeSet("South", Sb);

      // Create a new set spanning the East point
      attr_sets.SetAttributeSet("East", Ea);
      attr_sets.AddToAttributeSet("East", Eb);

      // Create a new set spanning the West point
      attr_sets.SetAttributeSet("West", Wa);
      attr_sets.AddToAttributeSet("West", Wb);

      // Create a new set consisting of the "a" sides of the compass rose
      attr_sets.SetAttributeSet("Rose Even", Na);
      attr_sets.AddToAttributeSet("Rose Even", Sa);
      attr_sets.AddToAttributeSet("Rose Even", Ea);
      attr_sets.AddToAttributeSet("Rose Even", Wa);

      // Create a new set consisting of the "b" sides of the compass rose
      attr_sets.SetAttributeSet("Rose Odd", Nb);
      attr_sets.AddToAttributeSet("Rose Odd", Sb);
      attr_sets.AddToAttributeSet("Rose Odd", Eb);
      attr_sets.AddToAttributeSet("Rose Odd", Wb);

      // Create a new set consisting of the full compass rose
      Array<int> & Ra = attr_sets.GetAttributeSet("Rose Even");
      Array<int> & Rb = attr_sets.GetAttributeSet("Rose Odd");
      attr_sets.SetAttributeSet("Rose", Ra);
      attr_sets.AddToAttributeSet("Rose", Rb);
   }
   // 4c. Define new boundary regions based on existing boundary attribute sets
   {
      Array<int> & NNE = bdr_attr_sets.GetAttributeSet("NNE");
      Array<int> & NNW = bdr_attr_sets.GetAttributeSet("NNW");
      Array<int> & ENE = bdr_attr_sets.GetAttributeSet("ENE");
      Array<int> & ESE = bdr_attr_sets.GetAttributeSet("ESE");
      Array<int> & SSE = bdr_attr_sets.GetAttributeSet("SSE");
      Array<int> & SSW = bdr_attr_sets.GetAttributeSet("SSW");
      Array<int> & WNW = bdr_attr_sets.GetAttributeSet("WNW");
      Array<int> & WSW = bdr_attr_sets.GetAttributeSet("WSW");

      bdr_attr_sets.SetAttributeSet("Northern Boundary", NNE);
      bdr_attr_sets.AddToAttributeSet("Northern Boundary", NNW);

      bdr_attr_sets.SetAttributeSet("Southern Boundary", SSE);
      bdr_attr_sets.AddToAttributeSet("Southern Boundary", SSW);

      bdr_attr_sets.SetAttributeSet("Eastern Boundary", ENE);
      bdr_attr_sets.AddToAttributeSet("Eastern Boundary", ESE);

      bdr_attr_sets.SetAttributeSet("Western Boundary", WNW);
      bdr_attr_sets.AddToAttributeSet("Western Boundary", WSW);

      bdr_attr_sets.SetAttributeSet("Boundary",
                                    bdr_attr_sets.GetAttributeSet
                                    ("Northern Boundary"));
      bdr_attr_sets.AddToAttributeSet("Boundary",
                                      bdr_attr_sets.GetAttributeSet
                                      ("Southern Boundary"));
      bdr_attr_sets.AddToAttributeSet("Boundary",
                                      bdr_attr_sets.GetAttributeSet
                                      ("Eastern Boundary"));
      bdr_attr_sets.AddToAttributeSet("Boundary",
                                      bdr_attr_sets.GetAttributeSet
                                      ("Western Boundary"));
   }

   // 5. Define a finite element space on the mesh. Here we use continuous
   //    Lagrange finite elements of the specified order.
   H1_FECollection fec(order, mesh.Dimension());
   FiniteElementSpace fespace(&mesh, &fec);
   cout << "Number of finite element unknowns: "
        << fespace.GetTrueVSize() << endl;

   // 6. Determine the list of true (i.e. conforming) essential boundary dofs.
   //    In this example, the boundary conditions are defined by marking all
   //    the boundary regions corresponding to the boundary attributes
   //    contained in the set named "ess_name" as essential (Dirichlet) and
   //    converting them to a list of true dofs.
   Array<int> ess_tdof_list;
   if (bdr_attr_sets.AttributeSetExists(ess_name))
   {
      Array<int> ess_bdr_marker = bdr_attr_sets.GetAttributeSetMarker(ess_name);
      fespace.GetEssentialTrueDofs(ess_bdr_marker, ess_tdof_list);
   }

   // 7. Set up the linear form b(.) which corresponds to the right-hand side of
   //    the FEM linear system, which in this case is (1_s,phi_i) where phi_i
   //    are the basis functions in fespace and 1_s is an indicator function
   //    equal to 1 on the region defined by the named set "source_name" and
   //    zero elsewhere.
   Array<int> source_marker = attr_sets.GetAttributeSetMarker(source_name);

   LinearForm b(&fespace);
   ConstantCoefficient one(1.0);
   b.AddDomainIntegrator(new DomainLFIntegrator(one), source_marker);
   b.Assemble();

   // 8. Define the solution vector x as a finite element grid function
   //    corresponding to fespace. Initialize x with initial guess of zero,
   //    which satisfies the boundary conditions.
   GridFunction x(&fespace);
   x = 0.0;

   // 9. Set up the bilinear form a(.,.) on the finite element space
   //    corresponding to the Laplacian operator -Delta, by adding the
   //    Diffusion domain integrator.
   BilinearForm a(&fespace);

   ConstantCoefficient defaultCoef(1.0e-6);
   ConstantCoefficient baseCoef(1.0);
   ConstantCoefficient roseCoef(2.0);

   Array<int> base_marker = attr_sets.GetAttributeSetMarker("Base");
   Array<int> rose_marker = attr_sets.GetAttributeSetMarker("Rose Even");

   // Impose a very small diffusion coefficient across the entire mesh
   a.AddDomainIntegrator(new DiffusionIntegrator(defaultCoef));

   // Impose an additional, stronger diffusion coefficient in select regions
   a.AddDomainIntegrator(new DiffusionIntegrator(baseCoef), base_marker);
   a.AddDomainIntegrator(new DiffusionIntegrator(roseCoef), rose_marker);

   // 10. Assemble the bilinear form and the corresponding linear system,
   //     applying any necessary transformations.
   a.Assemble();

   SparseMatrix A;
   Vector B, X;
   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);

   cout << "Size of linear system: " << A.Height() << endl;

   // 11. Solve the system using PCG with symmetric Gauss-Seidel preconditioner.
   GSSmoother M(A);
   PCG(A, M, B, X, 1, 800, 1e-12, 0.0);

   // 12. Recover the solution as a finite element grid function.
   a.RecoverFEMSolution(X, b, x);

   // 13. Save the refined mesh and the solution. This output can be viewed
   //     later using GLVis: "glvis -m refined.mesh -g sol.gf".
   mesh.Save("refined.mesh");
   x.Save("sol.gf");

   // 14. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
      int  visport   = 19916;
      socketstream sol_sock(vishost, visport);
      sol_sock.precision(8);
      sol_sock << "solution\n" << mesh << x << "keys Rjmm" << flush;
   }

   return 0;
}