libMesh
Functions
vector_fe_ex3.C File Reference

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Functions

int main (int argc, char **argv)
 

Function Documentation

int main ( int  argc,
char **  argv 
)

Definition at line 47 of file vector_fe_ex3.C.

References libMesh::DiffSolver::absolute_residual_tolerance, libMesh::EquationSystems::add_system(), libMesh::ExactSolution::attach_exact_derivs(), libMesh::ExactSolution::attach_exact_values(), libMesh::MeshTools::Generation::build_square(), libMesh::LibMeshInit::comm(), libMesh::command_line_value(), libMesh::ExactSolution::compute_error(), libMesh::default_solver_package(), libMesh::ExactSolution::error_norm(), libMesh::ExactSolution::extra_quadrature_order(), libMesh::ExactSolution::hcurl_error(), libMesh::HCURL_SEMINORM, libMesh::TriangleWrapper::init(), libMesh::EquationSystems::init(), libMesh::DiffSolver::initial_linear_tolerance, libMesh::INVALID_SOLVER_PACKAGE, libMesh::ExactSolution::l2_error(), libMesh::DiffSolver::max_linear_iterations, libMesh::DiffSolver::max_nonlinear_iterations, mesh, libMesh::out, libMesh::EquationSystems::print_info(), libMesh::MeshBase::print_info(), libMesh::DiffSolver::quiet, libMesh::DiffSolver::relative_residual_tolerance, libMesh::DiffSolver::relative_step_tolerance, libMesh::FEMSystem::solve(), libMesh::solver, libMesh::DifferentiableSystem::time_solver, libMesh::System::variable_number(), libMesh::DiffSolver::verbose, and libMesh::MeshOutput< MT >::write_equation_systems().

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_ex3.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  std::string elem_str =
73  command_line_value(std::string("element_type"),
74  std::string("TRI6"));
75 
76  if (elem_str != "TRI6" && elem_str != "QUAD8" && elem_str != "QUAD9")
77  libmesh_error_msg("You selected: " \
78  << elem_str \
79  << " but this example must be run with TRI6, QUAD8, or QUAD9.");
80 
82  grid_size,
83  grid_size,
84  -1., 1.,
85  -1., 1.,
86  Utility::string_to_enum<ElemType>(elem_str));
87 
88 
89  // Print information about the mesh to the screen.
90  mesh.print_info();
91 
92  // Create an equation systems object.
93  EquationSystems equation_systems (mesh);
94 
95  // Declare the system "Navier-Stokes" and its variables.
96  CurlCurlSystem & system =
97  equation_systems.add_system<CurlCurlSystem> ("CurlCurl");
98 
99  // This example only implements the steady-state problem
100  system.time_solver =
101  UniquePtr<TimeSolver>(new SteadySolver(system));
102 
103  // Initialize the system
104  equation_systems.init();
105 
106  // And the nonlinear solver options
107  DiffSolver & solver = *(system.time_solver->diff_solver().get());
108  solver.quiet = infile("solver_quiet", true);
109  solver.verbose = !solver.quiet;
110  solver.max_nonlinear_iterations = infile("max_nonlinear_iterations", 15);
111  solver.relative_step_tolerance = infile("relative_step_tolerance", 1.e-3);
112  solver.relative_residual_tolerance = infile("relative_residual_tolerance", 1.0e-13);
113  solver.absolute_residual_tolerance = infile("absolute_residual_tolerance", 0.0);
114 
115  // And the linear solver options
116  solver.max_linear_iterations = infile("max_linear_iterations", 50000);
117  solver.initial_linear_tolerance = infile("initial_linear_tolerance", 1.e-10);
118 
119  // Print information about the system to the screen.
120  equation_systems.print_info();
121 
122  system.solve();
123 
124  ExactSolution exact_sol(equation_systems);
125 
126  SolutionFunction soln_func(system.variable_number("u"));
127  SolutionGradient soln_grad(system.variable_number("u"));
128 
129  // Build FunctionBase* containers to attach to the ExactSolution object.
130  std::vector<FunctionBase<Number> *> sols(1, &soln_func);
131  std::vector<FunctionBase<Gradient> *> grads(1, &soln_grad);
132 
133  exact_sol.attach_exact_values(sols);
134  exact_sol.attach_exact_derivs(grads);
135 
136  // Use higher quadrature order for more accurate error results
137  int extra_error_quadrature = infile("extra_error_quadrature", 2);
138  exact_sol.extra_quadrature_order(extra_error_quadrature);
139 
140  // Compute the error.
141  exact_sol.compute_error("CurlCurl", "u");
142 
143  // Print out the error values
144  libMesh::out << "L2-Error is: "
145  << exact_sol.l2_error("CurlCurl", "u")
146  << std::endl;
147  libMesh::out << "HCurl semi-norm error is: "
148  << exact_sol.error_norm("CurlCurl", "u", HCURL_SEMINORM)
149  << std::endl;
150  libMesh::out << "HCurl-Error is: "
151  << exact_sol.hcurl_error("CurlCurl", "u")
152  << std::endl;
153 
154 #ifdef LIBMESH_HAVE_EXODUS_API
155 
156  // We write the file in the ExodusII format.
157  ExodusII_IO(mesh).write_equation_systems("out.e", equation_systems);
158 
159 #endif // #ifdef LIBMESH_HAVE_EXODUS_API
160 
161  // All done.
162  return 0;
163 }
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.
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
MeshBase & mesh
void build_square(UnstructuredMesh &mesh, const unsigned int nx, const unsigned int ny, const Real xmin=0., const Real xmax=1., const Real ymin=0., const Real ymax=1., const ElemType type=INVALID_ELEM, const bool gauss_lobatto_grid=false)
A specialized build_cube() for 2D meshes.
The LibMeshInit class, when constructed, initializes the dependent libraries (e.g.
Definition: libmesh.h:62
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
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
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.
This class implements a TimeSolver which does a single solve of the steady state problem.
Definition: steady_solver.h:47
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
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
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
Real relative_residual_tolerance
Definition: diff_solver.h:192