286 lines
12 KiB
C++
286 lines
12 KiB
C++
// 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 Poisson 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;
|
|
}
|