curl_curl_system.C

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2019 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
 
#include "libmesh/getpot.h"
 
#include "curl_curl_system.h"
 
#include "libmesh/dof_map.h"
#include "libmesh/fe_base.h"
#include "libmesh/fe_interface.h"
#include "libmesh/fem_context.h"
#include "libmesh/mesh.h"
#include "libmesh/quadrature.h"
#include "libmesh/string_to_enum.h"
#include "libmesh/zero_function.h"
 
// Bring in everything from the libMesh namespace
using namespace libMesh;
 
CurlCurlSystem::CurlCurlSystem(EquationSystems & es,
                               const std::string & name_in,
                               const unsigned int number_in) :
  FEMSystem(es, name_in, number_in)
{}
 
void CurlCurlSystem::init_data ()
{
  // Check the input file for Reynolds number, application type,
  // approximation type
  GetPot infile("vector_fe_ex3.in");
 
  // Add the solution variable
  u_var = this->add_variable ("u", FIRST, NEDELEC_ONE);
 
  // The solution is evolving, with a first order time derivative
  this->time_evolving(u_var, 1);
 
  // Useful debugging options
  // Set verify_analytic_jacobians to 1e-6 to use
  this->verify_analytic_jacobians = infile("verify_analytic_jacobians", 0.);
  this->print_jacobians = infile("print_jacobians", false);
  this->print_element_jacobians = infile("print_element_jacobians", false);
 
  this->extra_quadrature_order = infile("extra_quadrature_order", 0);
 
  this->init_dirichlet_bcs();
 
  // Do the parent's initialization after variables and boundary constraints are defined
  FEMSystem::init_data();
}
 
void CurlCurlSystem::init_dirichlet_bcs()
{
  const boundary_id_type all_ids[4] = {0, 1, 2, 3};
  std::set<boundary_id_type> boundary_ids(all_ids, all_ids+4);
 
  std::vector<unsigned int> vars;
  vars.push_back(u_var);
 
  ZeroFunction<Real> func;
 
  // this->get_dof_map().add_dirichlet_boundary(libMesh::DirichletBoundary(boundary_ids, vars, &func));
}
 
void CurlCurlSystem::init_context(DiffContext & context)
{
  FEMContext & c = cast_ref<FEMContext &>(context);
 
  // Get finite element object
  FEGenericBase<RealGradient> * fe;
  c.get_element_fe<RealGradient>(u_var, fe);
 
  // We should prerequest all the data
  // we will need to build the linear system.
  fe->get_JxW();
  fe->get_phi();
  fe->get_curl_phi();
  fe->get_xyz();
 
  // Get finite element object
  FEGenericBase<RealGradient> * side_fe;
  c.get_side_fe<RealGradient>(u_var, side_fe);
 
  side_fe->get_JxW();
  side_fe->get_phi();
  side_fe->get_xyz();
}
 
 
bool CurlCurlSystem::element_time_derivative (bool request_jacobian,
                                              DiffContext & context)
{
  FEMContext & c = cast_ref<FEMContext &>(context);
 
  // Get finite element object
  FEGenericBase<RealGradient> * fe = nullptr;
  c.get_element_fe<RealGradient>(u_var, fe);
 
  // First we get some references to cell-specific data that
  // will be used to assemble the linear system.
 
  // Element Jacobian * quadrature weights for interior integration
  const std::vector<Real> & JxW = fe->get_JxW();
 
  // The velocity shape functions at interior quadrature points.
  const std::vector<std::vector<RealGradient>> & phi = fe->get_phi();
 
  // The velocity shape function gradients at interior
  // quadrature points.
  const std::vector<std::vector<RealGradient>> & curl_phi = fe->get_curl_phi();
 
  const std::vector<Point> & qpoint = fe->get_xyz();
 
  // The number of local degrees of freedom in each variable
  const unsigned int n_u_dofs = c.n_dof_indices(u_var);
 
  DenseSubMatrix<Number> & Kuu = c.get_elem_jacobian(u_var, u_var);
 
  DenseSubVector<Number> & Fu = c.get_elem_residual(u_var);
 
  // Now we will build the element Jacobian and residual.
  // Constructing the residual requires the solution and its
  // gradient from the previous timestep.  This must be
  // calculated at each quadrature point by summing the
  // solution degree-of-freedom values by the appropriate
  // weight functions.
  const unsigned int n_qpoints = c.get_element_qrule().n_points();
 
  // Loop over quadrature points
  for (unsigned int qp=0; qp != n_qpoints; qp++)
    {
      Gradient u;
      Gradient curl_u;
 
      c.interior_value(u_var, qp, u);
 
      c.interior_curl(u_var, qp, curl_u);
 
      // Value of the forcing function at this quadrature point
      RealGradient f = this->forcing(qpoint[qp]);
 
      // First, an i-loop over the degrees of freedom.
      for (unsigned int i=0; i != n_u_dofs; i++)
        {
          Fu(i) += (curl_u*curl_phi[i][qp] + u*phi[i][qp] - f*phi[i][qp])*JxW[qp];
 
          // Matrix contributions for the uu and vv couplings.
          if (request_jacobian)
            for (unsigned int j=0; j != n_u_dofs; j++)
              Kuu(i,j) += (curl_phi[j][qp]*curl_phi[i][qp] +
                           phi[j][qp]*phi[i][qp])*JxW[qp];
        }
    } // end of the quadrature point qp-loop
 
  return request_jacobian;
}
 
 
bool CurlCurlSystem::side_time_derivative (bool request_jacobian,
                                           DiffContext & context)
{
  FEMContext & c = cast_ref<FEMContext &>(context);
 
  // Get finite element object
  FEGenericBase<RealGradient> * side_fe = nullptr;
  c.get_side_fe<RealGradient>(u_var, side_fe);
 
  // First we get some references to cell-specific data that
  // will be used to assemble the linear system.
 
  // Element Jacobian * quadrature weights for interior integration
  const std::vector<Real> & JxW = side_fe->get_JxW();
 
  // The velocity shape functions at interior quadrature points.
  const std::vector<std::vector<RealGradient>> & phi = side_fe->get_phi();
 
  // The number of local degrees of freedom in each variable
  const unsigned int n_u_dofs = c.n_dof_indices(u_var);
 
  const std::vector<Point> & normals = side_fe->get_normals();
 
  const std::vector<Point> & qpoint = side_fe->get_xyz();
 
  // The penalty value.  \frac{1}{\epsilon}
  // in the discussion above.
  const Real penalty = 1.e10;
 
  DenseSubMatrix<Number> & Kuu = c.get_elem_jacobian(u_var, u_var);
  DenseSubVector<Number> & Fu = c.get_elem_residual(u_var);
 
  const unsigned int n_qpoints = c.get_side_qrule().n_points();
 
  for (unsigned int qp=0; qp != n_qpoints; qp++)
    {
      Gradient u;
      c.side_value(u_var, qp, u);
 
      RealGradient N(normals[qp](0), normals[qp](1));
 
      Gradient u_exact = this->exact_solution(qpoint[qp]);
 
      Gradient Ncu = (u - u_exact).cross(N);
 
      for (unsigned int i=0; i != n_u_dofs; i++)
        {
          Fu(i) += penalty*Ncu*(phi[i][qp].cross(N))*JxW[qp];
 
          if (request_jacobian)
            for (unsigned int j=0; j != n_u_dofs; j++)
              Kuu(i,j) += penalty*(phi[j][qp].cross(N))*(phi[i][qp].cross(N))*JxW[qp];
        }
    }
 
  return request_jacobian;
}
 
RealGradient CurlCurlSystem::forcing(const Point & p)
{
  Real x = p(0); Real y = p(1);
 
  return soln.forcing(x, y);
}
 
RealGradient CurlCurlSystem::exact_solution(const Point & p)
{
  Real x = p(0); Real y = p(1);
 
  return soln(x, y);
}