libMesh
vector_fe_ex4.C
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1 // The libMesh Finite Element Library.
2 // Copyright (C) 2002-2017 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
3 
4 // This library is free software; you can redistribute it and/or
5 // modify it under the terms of the GNU Lesser General Public
6 // License as published by the Free Software Foundation; either
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18 
19 
20 // <h1>Vector Finite Elements Example 4 - Nedelec Elements</h1>
21 // \author Paul Bauman
22 // \date 2013
23 //
24 // This example shows an example of using the Nedelec elements of the
25 // first type to solve a model problem in H(curl).
26 
27 // Basic include files
28 #include "libmesh/equation_systems.h"
29 #include "libmesh/getpot.h"
30 #include "libmesh/exodusII_io.h"
31 #include "libmesh/mesh.h"
32 #include "libmesh/mesh_generation.h"
33 #include "libmesh/exact_solution.h"
34 #include "libmesh/string_to_enum.h"
35 
36 // The systems and solvers we may use
37 #include "curl_curl_system.h"
38 #include "libmesh/diff_solver.h"
39 #include "libmesh/steady_solver.h"
40 
41 #include "solution_function.h"
42 
43 // Bring in everything from the libMesh namespace
44 using namespace libMesh;
45 
46 // The main program.
47 int main (int argc, char ** argv)
48 {
49  // Initialize libMesh.
50  LibMeshInit init (argc, argv);
51 
52  // This example requires a linear solver package.
53  libmesh_example_requires(libMesh::default_solver_package() != INVALID_SOLVER_PACKAGE,
54  "--enable-petsc, --enable-trilinos, or --enable-eigen");
55 
56  // Parse the input file
57  GetPot infile("vector_fe_ex4.in");
58 
59  // Read in parameters from the input file
60  const unsigned int grid_size = infile("grid_size", 2);
61 
62  // Skip higher-dimensional examples on a lower-dimensional libMesh build
63  libmesh_example_requires(3 <= LIBMESH_DIM, "2D/3D support");
64 
65  // Create a mesh, with dimension to be overridden later, on the
66  // default MPI communicator.
67  Mesh mesh(init.comm());
68 
69  // Use the MeshTools::Generation mesh generator to create a uniform
70  // grid on the square [-1,1]^D. We must use TRI6 elements for the
71  // Nedelec triangle elements.
72 
73  std::string elem_str =
74  command_line_value(std::string("element_type"),
75  std::string("HEX27"));
76 
77  if (elem_str != "HEX20" && elem_str != "HEX27")
78  libmesh_error_msg("You entered: " \
79  << elem_str \
80  << " but this example must be run with HEX20 or HEX27.");
81 
83  grid_size,
84  grid_size,
85  grid_size,
86  -1., 1,
87  -1., 1.,
88  -1., 1,
89  Utility::string_to_enum<ElemType>(elem_str));
90 
91 
92  // Print information about the mesh to the screen.
93  mesh.print_info();
94 
95  // Create an equation systems object.
96  EquationSystems equation_systems (mesh);
97 
98  // Declare the system "Navier-Stokes" and its variables.
99  CurlCurlSystem & system =
100  equation_systems.add_system<CurlCurlSystem> ("CurlCurl");
101 
102  // This example only implements the steady-state problem
103  system.time_solver =
104  UniquePtr<TimeSolver>(new SteadySolver(system));
105 
106  // Initialize the system
107  equation_systems.init();
108 
109  // And the nonlinear solver options
110  DiffSolver & solver = *(system.time_solver->diff_solver().get());
111  solver.quiet = infile("solver_quiet", true);
112  solver.verbose = !solver.quiet;
113  solver.max_nonlinear_iterations = infile("max_nonlinear_iterations", 15);
114  solver.relative_step_tolerance = infile("relative_step_tolerance", 1.e-3);
115  solver.relative_residual_tolerance = infile("relative_residual_tolerance", 1.0e-13);
116  solver.absolute_residual_tolerance = infile("absolute_residual_tolerance", 0.0);
117 
118  // And the linear solver options
119  solver.max_linear_iterations = infile("max_linear_iterations", 50000);
120  solver.initial_linear_tolerance = infile("initial_linear_tolerance", 1.e-10);
121 
122  // Print information about the system to the screen.
123  equation_systems.print_info();
124 
125  system.solve();
126 
127  ExactSolution exact_sol(equation_systems);
128 
129  SolutionFunction soln_func(system.variable_number("u"));
130  SolutionGradient soln_grad(system.variable_number("u"));
131 
132  // Build FunctionBase* containers to attach to the ExactSolution object.
133  std::vector<FunctionBase<Number> *> sols(1, &soln_func);
134  std::vector<FunctionBase<Gradient> *> grads(1, &soln_grad);
135 
136  exact_sol.attach_exact_values(sols);
137  exact_sol.attach_exact_derivs(grads);
138 
139  // Use higher quadrature order for more accurate error results
140  int extra_error_quadrature = infile("extra_error_quadrature", 2);
141  exact_sol.extra_quadrature_order(extra_error_quadrature);
142 
143  // Compute the error.
144  exact_sol.compute_error("CurlCurl", "u");
145 
146  // Print out the error values
147  libMesh::out << "L2-Error is: "
148  << exact_sol.l2_error("CurlCurl", "u")
149  << std::endl;
150  libMesh::out << "HCurl semi-norm error is: "
151  << exact_sol.error_norm("CurlCurl", "u", HCURL_SEMINORM)
152  << std::endl;
153  libMesh::out << "HCurl-Error is: "
154  << exact_sol.hcurl_error("CurlCurl", "u")
155  << std::endl;
156 
157 #ifdef LIBMESH_HAVE_EXODUS_API
158 
159  // We write the file in the ExodusII format.
160  ExodusII_IO(mesh).write_equation_systems("out.e", equation_systems);
161 
162 #endif // #ifdef LIBMESH_HAVE_EXODUS_API
163 
164  // All done.
165  return 0;
166 }
This class handles the computation of the L2 and/or H1 error for the Systems in the EquationSystems o...
UniquePtr< TimeSolver > time_solver
A pointer to the solver object we&#39;re going to use.
Definition: diff_system.h:221
This is the EquationSystems class.
int main(int argc, char **argv)
Definition: vector_fe_ex4.C:47
bool quiet
The DiffSolver should not print anything to libMesh::out unless quiet is set to false; default is tru...
Definition: diff_solver.h:162
The ExodusII_IO class implements reading meshes in the ExodusII file format from Sandia National Labs...
Definition: exodusII_io.h:52
unsigned int max_nonlinear_iterations
The DiffSolver should exit in failure if max_nonlinear_iterations is exceeded and continue_after_max_...
Definition: diff_solver.h:156
Real absolute_residual_tolerance
The DiffSolver should exit after the residual is reduced to either less than absolute_residual_tolera...
Definition: diff_solver.h:191
void attach_exact_values(const std::vector< FunctionBase< Number > * > &f)
Clone and attach arbitrary functors which compute the exact values of the EquationSystems&#39; solutions ...
MeshBase & mesh
void extra_quadrature_order(const int extraorder)
Increases or decreases the order of the quadrature rule used for numerical integration.
The LibMeshInit class, when constructed, initializes the dependent libraries (e.g.
Definition: libmesh.h:62
The libMesh namespace provides an interface to certain functionality in the library.
Real initial_linear_tolerance
Any required linear solves will at first be done with this tolerance; the DiffSolver may tighten the ...
Definition: diff_solver.h:210
Real error_norm(const std::string &sys_name, const std::string &unknown_name, const FEMNormType &norm)
void compute_error(const std::string &sys_name, const std::string &unknown_name)
Computes and stores the error in the solution value e = u-u_h, the gradient grad(e) = grad(u) - grad(...
std::unique_ptr< T > UniquePtr
Definition: auto_ptr.h:46
PetscDiffSolver & solver
SolverPackage default_solver_package()
Definition: libmesh.C:995
This is a generic class that defines a solver to handle ImplicitSystem classes, including NonlinearIm...
Definition: diff_solver.h:70
unsigned short int variable_number(const std::string &var) const
Definition: system.C:1263
virtual void solve() libmesh_override
Invokes the solver associated with the system.
Definition: fem_system.C:1056
T command_line_value(const std::string &, T)
Definition: libmesh.C:932
void print_info(std::ostream &os=libMesh::out) const
Prints information about the equation systems, by default to libMesh::out.
unsigned int max_linear_iterations
Each linear solver step should exit after max_linear_iterations is exceeded.
Definition: diff_solver.h:148
void init(triangulateio &t)
Initializes the fields of t to NULL/0 as necessary.
virtual System & add_system(const std::string &system_type, const std::string &name)
Add the system of type system_type named name to the systems array.
This class implements a TimeSolver which does a single solve of the steady state problem.
Definition: steady_solver.h:47
const Parallel::Communicator & comm() const
Definition: libmesh.h:81
void attach_exact_derivs(const std::vector< FunctionBase< Gradient > * > &g)
Clone and attach arbitrary functors which compute the exact gradients of the EquationSystems&#39; solutio...
FEMSystem, TimeSolver and NewtonSolver will handle most tasks, but we must specify element residuals...
virtual void write_equation_systems(const std::string &, const EquationSystems &, const std::set< std::string > *system_names=libmesh_nullptr)
This method implements writing a mesh with data to a specified file where the data is taken from the ...
Definition: mesh_output.C:31
Real hcurl_error(const std::string &sys_name, const std::string &unknown_name)
bool verbose
The DiffSolver may print a lot more to libMesh::out if verbose is set to true; default is false...
Definition: diff_solver.h:168
OStreamProxy out
virtual void init()
Initialize all the systems.
Real l2_error(const std::string &sys_name, const std::string &unknown_name)
The Mesh class is a thin wrapper, around the ReplicatedMesh class by default.
Definition: mesh.h:50
void print_info(std::ostream &os=libMesh::out) const
Prints relevant information about the mesh.
Definition: mesh_base.C:448
void build_cube(UnstructuredMesh &mesh, const unsigned int nx=0, const unsigned int ny=0, const unsigned int nz=0, const Real xmin=0., const Real xmax=1., const Real ymin=0., const Real ymax=1., const Real zmin=0., const Real zmax=1., const ElemType type=INVALID_ELEM, const bool gauss_lobatto_grid=false)
Builds a (elements) cube.
Real relative_residual_tolerance
Definition: diff_solver.h:192