vector_fe_ex2.C

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2026 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
 
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
 
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
 
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 
 
 
// <h1>FEMSystem Example 1 - Unsteady Navier-Stokes Equations with
// FEMSystem</h1>
// \author Paul Bauman
// \date 2012
//
// This example shows how the transient nonlinear problem from
// systems_of_equations_ex2 can be solved using the
// DifferentiableSystem class framework
 
// Basic include files
#include "libmesh/equation_systems.h"
#include "libmesh/getpot.h"
#include "libmesh/exodusII_io.h"
#include "libmesh/mesh.h"
#include "libmesh/mesh_generation.h"
#include "libmesh/exact_solution.h"
#include "libmesh/ucd_io.h"
#include "libmesh/enum_solver_package.h"
 
// The systems and solvers we may use
#include "laplace_system.h"
#include "libmesh/diff_solver.h"
#include "libmesh/steady_solver.h"
 
// C++ includes
#include <memory>
 
// Bring in everything from the libMesh namespace
using namespace libMesh;
 
// The main program.
int main (int argc, char** argv)
{
  // Initialize libMesh.
  LibMeshInit init (argc, argv);
 
  // This example requires a linear solver package.
  libmesh_example_requires(libMesh::default_solver_package() != INVALID_SOLVER_PACKAGE,
                           "--enable-petsc, --enable-trilinos, or --enable-eigen");
 
  // Parse the input file
  GetPot infile("vector_fe_ex2.in");
 
  // But allow the command line to override it.
  infile.parse_command_line(argc, argv);
 
  // Read in parameters from the input file
  const unsigned int grid_size = infile("grid_size", 2);
 
  // Skip higher-dimensional examples on a lower-dimensional libMesh build
  libmesh_example_requires(3 <= LIBMESH_DIM, "2D/3D support");
 
  // We use Dirichlet boundary conditions here
#ifndef LIBMESH_ENABLE_DIRICHLET
  libmesh_example_requires(false, "--enable-dirichlet");
#endif
 
  // Create a mesh, with dimension to be overridden later, on the
  // default MPI communicator.
  Mesh mesh(init.comm());
 
  // Use the MeshTools::Generation mesh generator to create a uniform
  // grid on the square [-1,1]^D.  We instruct the mesh generator
  // to build a mesh of 8x8 Quad9 elements in 2D, or Hex27
  // elements in 3D.  Building these higher-order elements allows
  // us to use higher-order approximation, as in example 3.
  MeshTools::Generation::build_cube (mesh,
                                     grid_size,
                                     grid_size,
                                     grid_size,
                                     -1., 1.,
                                     -1., 1.,
                                     -1., 1.,
                                     HEX8);
 
  // Print information about the mesh to the screen.
  mesh.print_info();
 
  // Create an equation systems object.
  EquationSystems equation_systems (mesh);
 
  // Declare the system "Laplace" and its variables.
  LaplaceSystem & system =
    equation_systems.add_system<LaplaceSystem> ("Laplace");
 
  // This example only implements the steady-state problem
  system.time_solver = std::make_unique<SteadySolver>(system);
 
  // Initialize the system
  equation_systems.init();
 
  // And the nonlinear solver options
  DiffSolver & solver = *(system.time_solver->diff_solver().get());
  solver.quiet = infile("solver_quiet", true);
  solver.verbose = !solver.quiet;
  solver.max_nonlinear_iterations = infile("max_nonlinear_iterations", 15);
  solver.relative_step_tolerance = infile("relative_step_tolerance", 1.e-3);
  solver.relative_residual_tolerance = infile("relative_residual_tolerance", 0.0);
  solver.absolute_residual_tolerance = infile("absolute_residual_tolerance", 0.0);
 
  // And the linear solver options
  solver.max_linear_iterations = infile("max_linear_iterations", 50000);
  solver.initial_linear_tolerance = infile("initial_linear_tolerance", 1.e-3);
 
  // Print information about the system to the screen.
  equation_systems.print_info();
 
  system.solve();
 
  ExactSolution exact_sol(equation_systems);
 
  SolutionFunction soln_func(system.variable_number("u"));
  SolutionGradient soln_grad(system.variable_number("u"));
 
  // Build FunctionBase* containers to attach to the ExactSolution object.
  std::vector<FunctionBase<Number> *> sols(1, &soln_func);
  std::vector<FunctionBase<Gradient> *> grads(1, &soln_grad);
 
  exact_sol.attach_exact_values(sols);
  exact_sol.attach_exact_derivs(grads);
 
  // Use higher quadrature order for more accurate error results
  int extra_error_quadrature = infile("extra_error_quadrature", 2);
  exact_sol.extra_quadrature_order(extra_error_quadrature);
 
  // Compute the error.
  exact_sol.compute_error("Laplace", "u");
 
  // Print out the error values
  libMesh::out << "L2-Error is: "
               << exact_sol.l2_error("Laplace", "u")
               << std::endl;
  libMesh::out << "H1-Error is: "
               << exact_sol.h1_error("Laplace", "u")
               << std::endl;
 
#ifdef LIBMESH_HAVE_EXODUS_API
 
  // We write the file in the ExodusII format.
  ExodusII_IO(mesh).write_equation_systems("out.e", equation_systems);
 
#endif // #ifdef LIBMESH_HAVE_EXODUS_API
 
  UCDIO(mesh).write_equation_systems("out.inp", equation_systems);
 
  // All done.
  return 0;
}