libMesh::BoundaryProjectSolution Class Reference

This class implements projecting an arbitrary boundary function to the current mesh. More...

Public Member Functions
	BoundaryProjectSolution (const std::set< boundary_id_type > &b_in, const std::vector< unsigned int > &variables_in, const System &system_in, FunctionBase< Number > *f_in, FunctionBase< Gradient > *g_in, const Parameters &parameters_in, NumericVector< Number > &new_v_in)
	BoundaryProjectSolution (const BoundaryProjectSolution &in)
void	operator() (const ConstElemRange &range) const

Private Attributes
const std::set< boundary_id_type > &	b
const std::vector< unsigned int > &	variables
const System &	system
std::unique_ptr< FunctionBase< Number > >	f
std::unique_ptr< FunctionBase< Gradient > >	g
const Parameters &	parameters
NumericVector< Number > &	new_vector

Detailed Description

This class implements projecting an arbitrary boundary function to the current mesh.

This may be executed in parallel on multiple threads.

Definition at line 192 of file system_projection.C.

Constructor & Destructor Documentation

BoundaryProjectSolution() [1/2]

libMesh::BoundaryProjectSolution::BoundaryProjectSolution ( const std::set< boundary_id_type > &  b_in, const std::vector< unsigned int > &  variables_in, 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 204 of file system_projection.C.

References libMesh::libmesh_assert().

                                                             :
    b(b_in),
    variables(variables_in),
    system(system_in),
    f(f_in ? f_in->clone() : std::unique_ptr<FunctionBase<Number>>()),
    g(g_in ? g_in->clone() : std::unique_ptr<FunctionBase<Gradient>>()),
    parameters(parameters_in),
    new_vector(new_v_in)
  {
    libmesh_assert(f.get());
    f->init();
    if (g.get())
      g->init();
  }

BoundaryProjectSolution() [2/2]

libMesh::BoundaryProjectSolution::BoundaryProjectSolution ( const BoundaryProjectSolution &  in )

inline

Definition at line 225 of file system_projection.C.

References libMesh::libmesh_assert().

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

Member Function Documentation

operator()()

void libMesh::BoundaryProjectSolution::operator()

(

const ConstElemRange &

range

)

const

This method projects an arbitrary boundary 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 1473 of file system_projection.C.

References std::abs(), libMesh::Variable::active_on_subdomain(), libMesh::BoundaryInfo::boundary_ids(), libMesh::C_ONE, libMesh::C_ZERO, libMesh::DenseMatrix< T >::cholesky_solve(), libMesh::FEType::default_quadrature_rule(), dim, libMesh::DISCONTINUOUS, libMesh::DofMap::dof_indices(), libMesh::BoundaryInfo::edge_boundary_ids(), libMesh::FEType::family, libMesh::HERMITE, libMesh::index_range(), libMesh::libmesh_assert(), libMesh::make_range(), n_nodes, libMesh::DenseVector< T >::resize(), libMesh::DenseMatrix< T >::resize(), libMesh::SCALAR, libMesh::Threads::spin_mtx, libMesh::TOLERANCE, libMesh::Variable::type(), libMesh::DofMap::variable(), libMesh::DenseMatrix< T >::zero(), and libMesh::DenseVector< T >::zero().

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

  // 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();

  // Boundary info for the current mesh
  const BoundaryInfo & boundary_info =
    system.get_mesh().get_boundary_info();

  // 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 we've been requested to project
  for (auto v : make_range(variables.size()))
    {
      const unsigned int var = variables[v];

      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
      std::unique_ptr<FEBase> fe (FEBase::build(dim, fe_type));

      // Prepare variables for projection
      std::unique_ptr<QBase> qedgerule (fe_type.default_quadrature_rule(1));
      std::unique_ptr<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 = nullptr;

      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;

      // Container to catch IDs passed back from BoundaryInfo.
      std::vector<boundary_id_type> bc_ids;

      // Iterate over all the elements in the range
      for (const auto & elem : range)
        {
          // 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;

          const unsigned short n_nodes = elem->n_nodes();
          const unsigned short n_edges = elem->n_edges();
          const unsigned short n_sides = elem->n_sides();

          // Find out which nodes, edges and sides are on a requested
          // boundary:
          std::vector<bool> is_boundary_node(n_nodes, false),
            is_boundary_edge(n_edges, false),
            is_boundary_side(n_sides, false);

          // We also maintain a separate list of nodeset-based boundary nodes
          std::vector<bool> is_boundary_nodeset(n_nodes, false);

          for (unsigned char s=0; s != n_sides; ++s)
            {
              // First see if this side has been requested
              boundary_info.boundary_ids (elem, s, bc_ids);
              bool do_this_side = false;
              for (const auto & bc_id : bc_ids)
                if (b.count(bc_id))
                  {
                    do_this_side = true;
                    break;
                  }
              if (!do_this_side)
                continue;

              is_boundary_side[s] = true;

              // Then see what nodes and what edges are on it
              for (unsigned int n=0; n != n_nodes; ++n)
                if (elem->is_node_on_side(n,s))
                  is_boundary_node[n] = true;
              for (unsigned int e=0; e != n_edges; ++e)
                if (elem->is_edge_on_side(e,s))
                  is_boundary_edge[e] = true;
            }

            // We can also project on nodes, so we should also independently
            // check whether the nodes have been requested
            for (unsigned int n=0; n != n_nodes; ++n)
              {
                boundary_info.boundary_ids (elem->node_ptr(n), bc_ids);

                for (const auto & bc_id : bc_ids)
                  if (b.count(bc_id))
                    {
                      is_boundary_node[n] = true;
                      is_boundary_nodeset[n] = true;
                    }
              }

            // We can also project on edges, so we should also independently
            // check whether the edges have been requested
            for (unsigned short e=0; e != n_edges; ++e)
              {
                boundary_info.edge_boundary_ids (elem, e, bc_ids);

                for (const auto & bc_id : bc_ids)
                  if (b.count(bc_id))
                    is_boundary_edge[e] = true;
              }

          // 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 =
            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);

          // 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 boundary nodes, then
          // hold those fixed and project boundary edges, then hold
          // those fixed and project boundary faces,

          // Interpolate node values first
          unsigned int current_dof = 0;
          for (unsigned short n = 0; n != n_nodes; ++n)
            {
              // FIXME: this should go through the DofMap,
              // not duplicate dof_indices code badly!

              // This call takes into account elem->p_level() internally.
              const unsigned int nc =
                FEInterface::n_dofs_at_node (fe_type, elem, n);

              if ((!elem->is_vertex(n) || !is_boundary_node[n]) &&
                  !is_boundary_nodeset[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 LIBMESH_DIM > 1
                  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 LIBMESH_DIM > 2
                      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++;
                        }
#endif // LIBMESH_DIM > 2
                    }
#endif // LIBMESH_DIM > 1
                }
              // 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_msg("Unknown continuity " << cont);
            }

          // In 3D, project any edge values next
          if (dim > 2 && cont != DISCONTINUOUS)
            for (unsigned short e = 0; e != n_edges; ++e)
              {
                if (!is_boundary_edge[e])
                  continue;

                FEInterface::dofs_on_edge(elem, dim, fe_type, e,
                                          side_dofs);

                const unsigned int n_side_dofs =
                  cast_int<unsigned int>(side_dofs.size());

                // Some edge dofs are on nodes and already
                // fixed, others are free to calculate
                unsigned int free_dofs = 0;
                for (auto i : make_range(n_side_dofs))
                  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 != n_side_dofs; ++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 != n_side_dofs; ++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 short s = 0; s != n_sides; ++s)
              {
                if (!is_boundary_side[s])
                  continue;

                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 (auto i : index_range(side_dofs))
                  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();

                const unsigned int n_side_dofs =
                  cast_int<unsigned int>(side_dofs.size());

                // 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 != n_side_dofs; ++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 != n_side_dofs; ++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;
                  }
              }

          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++)
              if (dof_is_fixed[i] &&
                  (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

b

const std::set<boundary_id_type>& libMesh::BoundaryProjectSolution::b

private

Definition at line 195 of file system_projection.C.

f

std::unique_ptr<FunctionBase<Number> > libMesh::BoundaryProjectSolution::f

private

Definition at line 198 of file system_projection.C.

g

std::unique_ptr<FunctionBase<Gradient> > libMesh::BoundaryProjectSolution::g

private

Definition at line 199 of file system_projection.C.

new_vector

NumericVector<Number>& libMesh::BoundaryProjectSolution::new_vector

private

Definition at line 201 of file system_projection.C.

parameters

const Parameters& libMesh::BoundaryProjectSolution::parameters

private

Definition at line 200 of file system_projection.C.

system

const System& libMesh::BoundaryProjectSolution::system

private

Definition at line 197 of file system_projection.C.

variables

const std::vector<unsigned int>& libMesh::BoundaryProjectSolution::variables

private

Definition at line 196 of file system_projection.C.

---

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

• src/systems/system_projection.C