libMesh::ProjectSolution Class Reference

List of all members.

Public Member Functions
	ProjectSolution (const System &system_in, FunctionBase< Number > *f_in, FunctionBase< Gradient > *g_in, const Parameters &parameters_in, NumericVector< Number > &new_v_in)
	ProjectSolution (const ProjectSolution &in)
void	operator() (const ConstElemRange &range) const
Private Attributes
const System &	system
AutoPtr< FunctionBase< Number > >	f
AutoPtr< FunctionBase< Gradient > >	g
const Parameters &	parameters
NumericVector< Number > &	new_vector

---

Detailed Description

This class implements projecting an arbitrary function to the current mesh. This may be exectued in parallel on multiple threads.

Definition at line 110 of file system_projection.C.

---

Constructor & Destructor Documentation

libMesh::ProjectSolution::ProjectSolution	(	const System &	system_in,
		FunctionBase< Number > *	f_in,
		FunctionBase< Gradient > *	g_in,
		const Parameters &	parameters_in,
		NumericVector< Number > &	new_v_in
	)			[inline]

Definition at line 121 of file system_projection.C.

References f, g, and libMesh::AutoPtr< Tp >::get().

                                                      :
    system(system_in),
    f(f_in ? f_in->clone() : AutoPtr<FunctionBase<Number> >(NULL)),
    g(g_in ? g_in->clone() : AutoPtr<FunctionBase<Gradient> >(NULL)),
    parameters(parameters_in),
    new_vector(new_v_in)
    {
      libmesh_assert(f.get());
      f->init();
      if (g.get())
        g->init();
    }

libMesh::ProjectSolution::ProjectSolution

(

const ProjectSolution &

in

)

[inline]

Definition at line 138 of file system_projection.C.

References f, g, and libMesh::AutoPtr< Tp >::get().

                                                :
    system(in.system),
    f(in.f.get() ? in.f->clone() : AutoPtr<FunctionBase<Number> >(NULL)),
    g(in.g.get() ? in.g->clone() : AutoPtr<FunctionBase<Gradient> >(NULL)),
    parameters(in.parameters),
    new_vector(in.new_vector)
    {
      libmesh_assert(f.get());
      f->init();
      if (g.get())
        g->init();
    }

---

Member Function Documentation

void libMesh::ProjectSolution::operator()

(

const ConstElemRange &

range

)

const

This method projects an arbitrary solution to the current mesh. The input function f gives the arbitrary solution, while the new_vector (which should already be correctly sized) gives the solution (to be computed) on the current mesh.

Definition at line 1250 of file system_projection.C.

References std::abs(), libMesh::Variable::active_on_subdomain(), libMesh::StoredRange< iterator_type, object_type >::begin(), libMesh::FEGenericBase< Real >::build(), libMeshEnums::C_ONE, libMeshEnums::C_ZERO, libMesh::DenseMatrix< T >::cholesky_solve(), libMesh::FunctionBase< Output >::component(), libMesh::FEType::default_quadrature_rule(), libMeshEnums::DISCONTINUOUS, libMesh::DofMap::dof_indices(), libMesh::FEInterface::dofs_on_edge(), libMesh::FEInterface::dofs_on_side(), libMesh::StoredRange< iterator_type, object_type >::end(), libMesh::FEType::family, libMesh::NumericVector< T >::first_local_index(), libMesh::System::get_dof_map(), libMesh::System::get_mesh(), libMeshEnums::HERMITE, libMesh::Elem::is_vertex(), libMesh::NumericVector< T >::last_local_index(), libMesh::MeshBase::mesh_dimension(), libMesh::FEInterface::n_dofs_at_node(), libMesh::Elem::n_edges(), libMesh::Elem::n_nodes(), libMesh::Elem::n_sides(), libMesh::System::n_vars(), libMesh::Elem::point(), libMesh::DenseMatrix< T >::resize(), libMesh::DenseVector< T >::resize(), libMeshEnums::SCALAR, libMesh::NumericVector< T >::set(), libMesh::Threads::spin_mtx, libMesh::Elem::subdomain_id(), system, libMesh::System::time, libMesh::TOLERANCE, libMesh::Elem::type(), libMesh::Variable::type(), libMesh::DofMap::variable(), libMesh::System::variable_scalar_number(), libMesh::DenseMatrix< T >::zero(), and libMesh::DenseVector< T >::zero().

{
  // We need data to project
  libmesh_assert(f.get());

  // The number of variables in this system
  const unsigned int n_variables = system.n_vars();

  // The dimensionality of the current mesh
  const unsigned int dim = system.get_mesh().mesh_dimension();

  // The DofMap for this system
  const DofMap& dof_map = system.get_dof_map();

  // The element matrix and RHS for projections.
  // Note that Ke is always real-valued, whereas
  // Fe may be complex valued if complex number
  // support is enabled
  DenseMatrix<Real> Ke;
  DenseVector<Number> Fe;
  // The new element coefficients
  DenseVector<Number> Ue;


  // Loop over all the variables in the system
  for (unsigned int var=0; var<n_variables; var++)
    {
      const Variable& variable = dof_map.variable(var);

      const FEType& fe_type = variable.type();

      if (fe_type.family == SCALAR)
        continue;

      const unsigned int var_component =
        system.variable_scalar_number(var, 0);

      // Get FE objects of the appropriate type
      AutoPtr<FEBase> fe (FEBase::build(dim, fe_type));

      // Prepare variables for projection
      AutoPtr<QBase> qrule     (fe_type.default_quadrature_rule(dim));
      AutoPtr<QBase> qedgerule (fe_type.default_quadrature_rule(1));
      AutoPtr<QBase> qsiderule (fe_type.default_quadrature_rule(dim-1));

      // The values of the shape functions at the quadrature
      // points
      const std::vector<std::vector<Real> >& phi = fe->get_phi();

      // The gradients of the shape functions at the quadrature
      // points on the child element.
      const std::vector<std::vector<RealGradient> > *dphi = NULL;

      const FEContinuity cont = fe->get_continuity();

      if (cont == C_ONE)
        {
          // We'll need gradient data for a C1 projection
          libmesh_assert(g.get());

          const std::vector<std::vector<RealGradient> >&
            ref_dphi = fe->get_dphi();
          dphi = &ref_dphi;
        }

      // The Jacobian * quadrature weight at the quadrature points
      const std::vector<Real>& JxW =
        fe->get_JxW();

      // The XYZ locations of the quadrature points
      const std::vector<Point>& xyz_values =
        fe->get_xyz();

      // The global DOF indices
      std::vector<dof_id_type> dof_indices;
      // Side/edge DOF indices
      std::vector<unsigned int> side_dofs;

      // Iterate over all the elements in the range
      for (ConstElemRange::const_iterator elem_it=range.begin(); elem_it != range.end(); ++elem_it)
        {
          const Elem* elem = *elem_it;

          // Per-subdomain variables don't need to be projected on
          // elements where they're not active
          if (!variable.active_on_subdomain(elem->subdomain_id()))
            continue;

          // Update the DOF indices for this element based on
          // the current mesh
          dof_map.dof_indices (elem, dof_indices, var);

          // The number of DOFs on the element
          const unsigned int n_dofs = 
            libmesh_cast_int<unsigned int>(dof_indices.size());

          // Fixed vs. free DoFs on edge/face projections
          std::vector<char> dof_is_fixed(n_dofs, false); // bools
          std::vector<int> free_dof(n_dofs, 0);

          // The element type
          const ElemType elem_type = elem->type();

          // The number of nodes on the new element
          const unsigned int n_nodes = elem->n_nodes();

          // Zero the interpolated values
          Ue.resize (n_dofs); Ue.zero();

          // In general, we need a series of
          // projections to ensure a unique and continuous
          // solution.  We start by interpolating nodes, then
          // hold those fixed and project edges, then
          // hold those fixed and project faces, then
          // hold those fixed and project interiors

          // Interpolate node values first
          unsigned int current_dof = 0;
          for (unsigned int n=0; n!= n_nodes; ++n)
            {
              // FIXME: this should go through the DofMap,
              // not duplicate dof_indices code badly!
              const unsigned int nc =
                FEInterface::n_dofs_at_node (dim, fe_type, elem_type,
                                             n);
              if (!elem->is_vertex(n))
                {
                  current_dof += nc;
                  continue;
                }
              if (cont == DISCONTINUOUS)
                {
                  libmesh_assert_equal_to (nc, 0);
                }
              // Assume that C_ZERO elements have a single nodal
              // value shape function
              else if (cont == C_ZERO)
                {
                  libmesh_assert_equal_to (nc, 1);
                  Ue(current_dof) = f->component(var_component,
                                                 elem->point(n),
                                                 system.time);
                  dof_is_fixed[current_dof] = true;
                  current_dof++;
                }
              // The hermite element vertex shape functions are weird
              else if (fe_type.family == HERMITE)
                {
                  Ue(current_dof) = f->component(var_component,
                                                 elem->point(n),
                                                 system.time);
                  dof_is_fixed[current_dof] = true;
                  current_dof++;
                  Gradient grad = g->component(var_component,
                                               elem->point(n),
                                               system.time);
                  // x derivative
                  Ue(current_dof) = grad(0);
                  dof_is_fixed[current_dof] = true;
                  current_dof++;
                  if (dim > 1)
                    {
                      // We'll finite difference mixed derivatives
                      Point nxminus = elem->point(n),
                            nxplus = elem->point(n);
                      nxminus(0) -= TOLERANCE;
                      nxplus(0) += TOLERANCE;
                      Gradient gxminus = g->component(var_component,
                                                      nxminus,
                                                      system.time);
                      Gradient gxplus = g->component(var_component,
                                                     nxplus,
                                                     system.time);
                      // y derivative
                      Ue(current_dof) = grad(1);
                      dof_is_fixed[current_dof] = true;
                      current_dof++;
                      // xy derivative
                      Ue(current_dof) = (gxplus(1) - gxminus(1))
                                        / 2. / TOLERANCE;
                      dof_is_fixed[current_dof] = true;
                      current_dof++;

                      if (dim > 2)
                        {
                          // z derivative
                          Ue(current_dof) = grad(2);
                          dof_is_fixed[current_dof] = true;
                          current_dof++;
                          // xz derivative
                          Ue(current_dof) = (gxplus(2) - gxminus(2))
                                            / 2. / TOLERANCE;
                          dof_is_fixed[current_dof] = true;
                          current_dof++;
                          // We need new points for yz
                          Point nyminus = elem->point(n),
                                nyplus = elem->point(n);
                          nyminus(1) -= TOLERANCE;
                          nyplus(1) += TOLERANCE;
                          Gradient gyminus = g->component(var_component,
                                                          nyminus,
                                                          system.time);
                          Gradient gyplus = g->component(var_component,
                                                         nyplus,
                                                         system.time);
                          // xz derivative
                          Ue(current_dof) = (gyplus(2) - gyminus(2))
                                            / 2. / TOLERANCE;
                          dof_is_fixed[current_dof] = true;
                          current_dof++;
                          // Getting a 2nd order xyz is more tedious
                          Point nxmym = elem->point(n),
                                nxmyp = elem->point(n),
                                nxpym = elem->point(n),
                                nxpyp = elem->point(n);
                          nxmym(0) -= TOLERANCE;
                          nxmym(1) -= TOLERANCE;
                          nxmyp(0) -= TOLERANCE;
                          nxmyp(1) += TOLERANCE;
                          nxpym(0) += TOLERANCE;
                          nxpym(1) -= TOLERANCE;
                          nxpyp(0) += TOLERANCE;
                          nxpyp(1) += TOLERANCE;
                          Gradient gxmym = g->component(var_component,
                                                        nxmym,
                                                        system.time);
                          Gradient gxmyp = g->component(var_component,
                                                        nxmyp,
                                                        system.time);
                          Gradient gxpym = g->component(var_component,
                                                        nxpym,
                                                        system.time);
                          Gradient gxpyp = g->component(var_component,
                                                        nxpyp,
                                                        system.time);
                          Number gxzplus = (gxpyp(2) - gxmyp(2))
                                         / 2. / TOLERANCE;
                          Number gxzminus = (gxpym(2) - gxmym(2))
                                          / 2. / TOLERANCE;
                          // xyz derivative
                          Ue(current_dof) = (gxzplus - gxzminus)
                                            / 2. / TOLERANCE;
                          dof_is_fixed[current_dof] = true;
                          current_dof++;
                        }
                    }
                }
              // Assume that other C_ONE elements have a single nodal
              // value shape function and nodal gradient component
              // shape functions
              else if (cont == C_ONE)
                {
                  libmesh_assert_equal_to (nc, 1 + dim);
                  Ue(current_dof) = f->component(var_component,
                                                 elem->point(n),
                                                 system.time);
                  dof_is_fixed[current_dof] = true;
                  current_dof++;
                  Gradient grad = g->component(var_component,
                                               elem->point(n),
                                               system.time);
                  for (unsigned int i=0; i!= dim; ++i)
                    {
                      Ue(current_dof) = grad(i);
                      dof_is_fixed[current_dof] = true;
                      current_dof++;
                    }
                }
              else
                libmesh_error();
            }

          // In 3D, project any edge values next
          if (dim > 2 && cont != DISCONTINUOUS)
            for (unsigned int e=0; e != elem->n_edges(); ++e)
              {
                FEInterface::dofs_on_edge(elem, dim, fe_type, e,
                                          side_dofs);

                // Some edge dofs are on nodes and already
                // fixed, others are free to calculate
                unsigned int free_dofs = 0;
                for (unsigned int i=0; i != side_dofs.size(); ++i)
                  if (!dof_is_fixed[side_dofs[i]])
                    free_dof[free_dofs++] = i;

                // There may be nothing to project
                if (!free_dofs)
                  continue;

                Ke.resize (free_dofs, free_dofs); Ke.zero();
                Fe.resize (free_dofs); Fe.zero();
                // The new edge coefficients
                DenseVector<Number> Uedge(free_dofs);

                // Initialize FE data on the edge
                fe->attach_quadrature_rule (qedgerule.get());
                fe->edge_reinit (elem, e);
                const unsigned int n_qp = qedgerule->n_points();

                // Loop over the quadrature points
                for (unsigned int qp=0; qp<n_qp; qp++)
                  {
                    // solution at the quadrature point
                    Number fineval = f->component(var_component,
                                                  xyz_values[qp],
                                                  system.time);
                    // solution grad at the quadrature point
                    Gradient finegrad;
                    if (cont == C_ONE)
                      finegrad = g->component(var_component,
                                              xyz_values[qp],
                                              system.time);

                    // Form edge projection matrix
                    for (unsigned int sidei=0, freei=0;
                         sidei != side_dofs.size(); ++sidei)
                      {
                        unsigned int i = side_dofs[sidei];
                        // fixed DoFs aren't test functions
                        if (dof_is_fixed[i])
                          continue;
                        for (unsigned int sidej=0, freej=0;
                             sidej != side_dofs.size(); ++sidej)
                          {
                            unsigned int j = side_dofs[sidej];
                            if (dof_is_fixed[j])
                              Fe(freei) -= phi[i][qp] * phi[j][qp] *
                                           JxW[qp] * Ue(j);
                            else
                              Ke(freei,freej) += phi[i][qp] *
                                                 phi[j][qp] * JxW[qp];
                            if (cont == C_ONE)
                              {
                                if (dof_is_fixed[j])
                                  Fe(freei) -= ((*dphi)[i][qp] *
                                                (*dphi)[j][qp]) *
                                                JxW[qp] * Ue(j);
                                else
                                  Ke(freei,freej) += ((*dphi)[i][qp] *
                                                      (*dphi)[j][qp])
                                                      * JxW[qp];
                              }
                            if (!dof_is_fixed[j])
                              freej++;
                          }
                        Fe(freei) += phi[i][qp] * fineval * JxW[qp];
                        if (cont == C_ONE)
                          Fe(freei) += (finegrad * (*dphi)[i][qp]) *
                                       JxW[qp];
                        freei++;
                      }
                  }

                Ke.cholesky_solve(Fe, Uedge);

                // Transfer new edge solutions to element
                for (unsigned int i=0; i != free_dofs; ++i)
                  {
                    Number &ui = Ue(side_dofs[free_dof[i]]);
                    libmesh_assert(std::abs(ui) < TOLERANCE ||
                           std::abs(ui - Uedge(i)) < TOLERANCE);
                    ui = Uedge(i);
                    dof_is_fixed[side_dofs[free_dof[i]]] = true;
                  }
              }

          // Project any side values (edges in 2D, faces in 3D)
          if (dim > 1 && cont != DISCONTINUOUS)
            for (unsigned int s=0; s != elem->n_sides(); ++s)
              {
                FEInterface::dofs_on_side(elem, dim, fe_type, s,
                                          side_dofs);

                // Some side dofs are on nodes/edges and already
                // fixed, others are free to calculate
                unsigned int free_dofs = 0;
                for (unsigned int i=0; i != side_dofs.size(); ++i)
                  if (!dof_is_fixed[side_dofs[i]])
                    free_dof[free_dofs++] = i;

                // There may be nothing to project
                if (!free_dofs)
                  continue;

                Ke.resize (free_dofs, free_dofs); Ke.zero();
                Fe.resize (free_dofs); Fe.zero();
                // The new side coefficients
                DenseVector<Number> Uside(free_dofs);

                // Initialize FE data on the side
                fe->attach_quadrature_rule (qsiderule.get());
                fe->reinit (elem, s);
                const unsigned int n_qp = qsiderule->n_points();

                // Loop over the quadrature points
                for (unsigned int qp=0; qp<n_qp; qp++)
                  {
                    // solution at the quadrature point
                    Number fineval = f->component(var_component,
                                                  xyz_values[qp],
                                                  system.time);
                    // solution grad at the quadrature point
                    Gradient finegrad;
                    if (cont == C_ONE)
                      finegrad = g->component(var_component,
                                              xyz_values[qp],
                                              system.time);

                    // Form side projection matrix
                    for (unsigned int sidei=0, freei=0;
                         sidei != side_dofs.size(); ++sidei)
                      {
                        unsigned int i = side_dofs[sidei];
                        // fixed DoFs aren't test functions
                        if (dof_is_fixed[i])
                          continue;
                        for (unsigned int sidej=0, freej=0;
                             sidej != side_dofs.size(); ++sidej)
                          {
                            unsigned int j = side_dofs[sidej];
                            if (dof_is_fixed[j])
                              Fe(freei) -= phi[i][qp] * phi[j][qp] *
                                           JxW[qp] * Ue(j);
                            else
                              Ke(freei,freej) += phi[i][qp] *
                                                 phi[j][qp] * JxW[qp];
                            if (cont == C_ONE)
                              {
                                if (dof_is_fixed[j])
                                  Fe(freei) -= ((*dphi)[i][qp] *
                                                (*dphi)[j][qp]) *
                                               JxW[qp] * Ue(j);
                                else
                                  Ke(freei,freej) += ((*dphi)[i][qp] *
                                                      (*dphi)[j][qp])
                                                     * JxW[qp];
                              }
                            if (!dof_is_fixed[j])
                              freej++;
                          }
                        Fe(freei) += (fineval * phi[i][qp]) * JxW[qp];
                        if (cont == C_ONE)
                          Fe(freei) += (finegrad * (*dphi)[i][qp]) *
                                       JxW[qp];
                        freei++;
                      }
                  }

                Ke.cholesky_solve(Fe, Uside);

                // Transfer new side solutions to element
                for (unsigned int i=0; i != free_dofs; ++i)
                  {
                    Number &ui = Ue(side_dofs[free_dof[i]]);
                    libmesh_assert(std::abs(ui) < TOLERANCE ||
                           std::abs(ui - Uside(i)) < TOLERANCE);
                    ui = Uside(i);
                    dof_is_fixed[side_dofs[free_dof[i]]] = true;
                  }
              }

          // Project the interior values, finally

          // Some interior dofs are on nodes/edges/sides and
          // already fixed, others are free to calculate
          unsigned int free_dofs = 0;
          for (unsigned int i=0; i != n_dofs; ++i)
            if (!dof_is_fixed[i])
              free_dof[free_dofs++] = i;

          // There may be nothing to project
          if (free_dofs)
            {

          Ke.resize (free_dofs, free_dofs); Ke.zero();
          Fe.resize (free_dofs); Fe.zero();
          // The new interior coefficients
          DenseVector<Number> Uint(free_dofs);

          // Initialize FE data
          fe->attach_quadrature_rule (qrule.get());
          fe->reinit (elem);
          const unsigned int n_qp = qrule->n_points();

          // Loop over the quadrature points
          for (unsigned int qp=0; qp<n_qp; qp++)
            {
              // solution at the quadrature point
              Number fineval = f->component(var_component,
                                            xyz_values[qp],
                                            system.time);
              // solution grad at the quadrature point
              Gradient finegrad;
              if (cont == C_ONE)
                finegrad = g->component(var_component,
                                        xyz_values[qp],
                                        system.time);

              // Form interior projection matrix
              for (unsigned int i=0, freei=0; i != n_dofs; ++i)
                {
                  // fixed DoFs aren't test functions
                  if (dof_is_fixed[i])
                    continue;
                  for (unsigned int j=0, freej=0; j != n_dofs; ++j)
                    {
                      if (dof_is_fixed[j])
                        Fe(freei) -= phi[i][qp] * phi[j][qp] * JxW[qp]
                                     * Ue(j);
                      else
                        Ke(freei,freej) += phi[i][qp] * phi[j][qp] *
                                           JxW[qp];
                      if (cont == C_ONE)
                        {
                          if (dof_is_fixed[j])
                            Fe(freei) -= ((*dphi)[i][qp] *
                                         (*dphi)[j][qp]) * JxW[qp] *
                                         Ue(j);
                          else
                            Ke(freei,freej) += ((*dphi)[i][qp] *
                                                (*dphi)[j][qp]) *
                                               JxW[qp];
                        }
                      if (!dof_is_fixed[j])
                        freej++;
                    }
                  Fe(freei) += phi[i][qp] * fineval * JxW[qp];
                  if (cont == C_ONE)
                    Fe(freei) += (finegrad * (*dphi)[i][qp]) * JxW[qp];
                  freei++;
                }
            }
          Ke.cholesky_solve(Fe, Uint);

          // Transfer new interior solutions to element
          for (unsigned int i=0; i != free_dofs; ++i)
            {
              Number &ui = Ue(free_dof[i]);
              libmesh_assert(std::abs(ui) < TOLERANCE ||
                     std::abs(ui - Uint(i)) < TOLERANCE);
              ui = Uint(i);
              dof_is_fixed[free_dof[i]] = true;
            }

            } // if there are free interior dofs

          // Make sure every DoF got reached!
          for (unsigned int i=0; i != n_dofs; ++i)
            libmesh_assert(dof_is_fixed[i]);

          const dof_id_type
            first = new_vector.first_local_index(),
            last  = new_vector.last_local_index();

          // Lock the new_vector since it is shared among threads.
          {
            Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);

            for (unsigned int i = 0; i < n_dofs; i++)
              // We may be projecting a new zero value onto
              // an old nonzero approximation - RHS
              // if (Ue(i) != 0.)
              if ((dof_indices[i] >= first) &&
                  (dof_indices[i] <  last))
                {
                  new_vector.set(dof_indices[i], Ue(i));
                }
          }
        }  // end elem loop
    } // end variables loop
}

---

Member Data Documentation

AutoPtr<FunctionBase<Number> > libMesh::ProjectSolution::f [private]

Definition at line 115 of file system_projection.C.

Referenced by ProjectSolution().

AutoPtr<FunctionBase<Gradient> > libMesh::ProjectSolution::g [private]

Definition at line 116 of file system_projection.C.

Referenced by ProjectSolution().

NumericVector<Number>& libMesh::ProjectSolution::new_vector [private]

Definition at line 118 of file system_projection.C.

const Parameters& libMesh::ProjectSolution::parameters [private]

Definition at line 117 of file system_projection.C.

const System& libMesh::ProjectSolution::system [private]

Definition at line 113 of file system_projection.C.

Referenced by operator()().

---

The documentation for this class was generated from the following file:

• system_projection.C