libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError Class Reference

Class to compute the error contribution for a range of elements. More...

Public Member Functions
	EstimateError (const System &sys, const WeightedPatchRecoveryErrorEstimator &ee, ErrorVector &epc)
void	operator() (const ConstElemRange &range) const

Private Attributes
const System &	system
	Function to set the boolean patch_reuse in case the user wants to change the default behaviour of patch_recovery_error_estimator.
const WeightedPatchRecoveryErrorEstimator &	error_estimator
ErrorVector &	error_per_cell

Detailed Description

Class to compute the error contribution for a range of elements.

May be executed in parallel on separate threads.

Definition at line 93 of file weighted_patch_recovery_error_estimator.h.

Constructor & Destructor Documentation

EstimateError()

libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::EstimateError ( const System &  sys, const WeightedPatchRecoveryErrorEstimator &  ee, ErrorVector &  epc  )

inline

Definition at line 96 of file weighted_patch_recovery_error_estimator.h.

                                      :
      system(sys),
      error_estimator(ee),
      error_per_cell(epc)
    {}

Member Function Documentation

operator()()

void libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()

(

const ConstElemRange &

range

)

const

Definition at line 112 of file weighted_patch_recovery_error_estimator.C.

{
  // The current mesh
  const MeshBase & mesh = system.get_mesh();
 
  // The dimensionality of the mesh
  const unsigned int dim = mesh.mesh_dimension();
 
  // The number of variables in the system
  const unsigned int n_vars = system.n_vars();
 
  // The DofMap for this system
  const DofMap & dof_map = system.get_dof_map();
 
  //------------------------------------------------------------
  // Iterate over all the elements in the range.
  for (const auto & elem : range)
    {
      // We'll need an index into the error vector
      const dof_id_type e_id=elem->id();
 
      // We are going to build a patch containing the current element
      // and its neighbors on the local processor
      Patch patch(mesh.processor_id());
 
      // If we are reusing patches and the current element
      // already has an estimate associated with it, move on the
      // next element
      if (this->error_estimator.patch_reuse && error_per_cell[e_id] != 0)
        continue;
 
      // If we are not reusing patches or haven't built one containing this element, we build one
 
      // Use user specified patch size and growth strategy
      patch.build_around_element (elem, error_estimator.target_patch_size,
                                  error_estimator.patch_growth_strategy);
 
      // Declare a new_error_per_cell vector to hold error estimates
      // from each element in this patch, or one estimate if we are
      // not reusing patches since we will only be computing error for
      // one cell
      std::vector<Real> new_error_per_cell(1, 0.);
      if (this->error_estimator.patch_reuse)
        new_error_per_cell.resize(patch.size(), 0.);
 
      //------------------------------------------------------------
      // Process each variable in the system using the current patch
      for (unsigned int var=0; var<n_vars; var++)
        {
          const auto norm_type = error_estimator.error_norm.type(var);
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
#ifdef DEBUG
          bool is_valid_norm_type =
            norm_type == L2 ||
            norm_type == H1_SEMINORM ||
            norm_type == H2_SEMINORM ||
            norm_type == H1_X_SEMINORM ||
            norm_type == H1_Y_SEMINORM ||
            norm_type == H1_Z_SEMINORM ||
            norm_type == L_INF ||
            norm_type == W1_INF_SEMINORM ||
            norm_type == W2_INF_SEMINORM;
          libmesh_assert (is_valid_norm_type);
#endif // DEBUG
#else
          libmesh_assert (norm_type == L2 ||
                          norm_type == L_INF ||
                          norm_type == H1_SEMINORM ||
                          norm_type == H1_X_SEMINORM ||
                          norm_type == H1_Y_SEMINORM ||
                          norm_type == H1_Z_SEMINORM ||
                          norm_type == W1_INF_SEMINORM);
#endif
 
#ifdef DEBUG
          if (var > 0)
            {
              // We can't mix L_inf and L_2 norms
              bool is_valid_norm_combo =
                ((norm_type == L2 ||
                  norm_type == H1_SEMINORM ||
                  norm_type == H1_X_SEMINORM ||
                  norm_type == H1_Y_SEMINORM ||
                  norm_type == H1_Z_SEMINORM ||
                  norm_type == H2_SEMINORM) &&
                 (error_estimator.error_norm.type(var-1) == L2 ||
                  error_estimator.error_norm.type(var-1) == H1_SEMINORM ||
                  error_estimator.error_norm.type(var-1) == H1_X_SEMINORM ||
                  error_estimator.error_norm.type(var-1) == H1_Y_SEMINORM ||
                  error_estimator.error_norm.type(var-1) == H1_Z_SEMINORM ||
                  error_estimator.error_norm.type(var-1) == H2_SEMINORM)) ||
                ((norm_type == L_INF ||
                  norm_type == W1_INF_SEMINORM ||
                  norm_type == W2_INF_SEMINORM) &&
                 (error_estimator.error_norm.type(var-1) == L_INF ||
                  error_estimator.error_norm.type(var-1) == W1_INF_SEMINORM ||
                  error_estimator.error_norm.type(var-1) == W2_INF_SEMINORM));
              libmesh_assert (is_valid_norm_combo);
            }
#endif // DEBUG
 
          // Possibly skip this variable
          if (error_estimator.error_norm.weight(var) == 0.0) continue;
 
          // The type of finite element to use for this variable
          const FEType & fe_type = dof_map.variable_type (var);
 
          const Order element_order = fe_type.order + elem->p_level();
 
          // Finite element object for use in this patch
          std::unique_ptr<FEBase> fe (FEBase::build (dim, fe_type));
 
          // Build an appropriate Gaussian quadrature rule
          std::unique_ptr<QBase> qrule =
            fe_type.default_quadrature_rule(dim, error_estimator._extra_order);
 
          // Tell the finite element about the quadrature rule.
          fe->attach_quadrature_rule (qrule.get());
 
          // Get Jacobian values, etc..
          const std::vector<Real> & JxW = fe->get_JxW();
          const std::vector<Point> & q_point = fe->get_xyz();
 
          // Get whatever phi/dphi/d2phi values we need.  Avoid
          // getting them unless the requested norm is actually going
          // to use them.
 
          const std::vector<std::vector<Real>> * phi = nullptr;
          // If we're using phi to assert the correct dof_indices
          // vector size later, then we'll need to get_phi whether we
          // plan to use it or not.
#ifdef NDEBUG
          if (norm_type == L2 ||
              norm_type == L_INF)
#endif
            phi = &(fe->get_phi());
 
          const std::vector<std::vector<RealGradient>> * dphi = nullptr;
          if (norm_type == H1_SEMINORM ||
              norm_type == H1_X_SEMINORM ||
              norm_type == H1_Y_SEMINORM ||
              norm_type == H1_Z_SEMINORM ||
              norm_type == W1_INF_SEMINORM)
            dphi = &(fe->get_dphi());
 
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
          const std::vector<std::vector<RealTensor>> * d2phi = nullptr;
          if (norm_type == H2_SEMINORM ||
              norm_type == W2_INF_SEMINORM)
            d2phi = &(fe->get_d2phi());
#endif
 
          // global DOF indices
          std::vector<dof_id_type> dof_indices;
 
          // Compute the appropriate size for the patch projection matrices
          // and vectors;
          unsigned int matsize = element_order + 1;
          if (dim > 1)
            {
              matsize *= (element_order + 2);
              matsize /= 2;
            }
          if (dim > 2)
            {
              matsize *= (element_order + 3);
              matsize /= 3;
            }
 
          DenseMatrix<Number> Kp(matsize,matsize);
          DenseVector<Number> F,    Fx,     Fy,     Fz,     Fxy,     Fxz,     Fyz;
          DenseVector<Number> Pu_h, Pu_x_h, Pu_y_h, Pu_z_h, Pu_xy_h, Pu_xz_h, Pu_yz_h;
          if (norm_type == L2 ||
              norm_type == L_INF)
            {
              F.resize(matsize); Pu_h.resize(matsize);
            }
          else if (norm_type == H1_SEMINORM ||
                   norm_type == W1_INF_SEMINORM ||
                   norm_type == H2_SEMINORM ||
                   norm_type == W2_INF_SEMINORM)
            {
              Fx.resize(matsize); Pu_x_h.resize(matsize); // stores xx in W2 cases
#if LIBMESH_DIM > 1
              Fy.resize(matsize); Pu_y_h.resize(matsize); // stores yy in W2 cases
#endif
#if LIBMESH_DIM > 2
              Fz.resize(matsize); Pu_z_h.resize(matsize); // stores zz in W2 cases
#endif
            }
          else if (norm_type == H1_X_SEMINORM)
            {
              Fx.resize(matsize); Pu_x_h.resize(matsize); // Only need to compute the x gradient for the x component seminorm
            }
          else if (norm_type == H1_Y_SEMINORM)
            {
              libmesh_assert(LIBMESH_DIM > 1);
              Fy.resize(matsize); Pu_y_h.resize(matsize); // Only need to compute the y gradient for the y component seminorm
            }
          else if (norm_type == H1_Z_SEMINORM)
            {
              libmesh_assert(LIBMESH_DIM > 2);
              Fz.resize(matsize); Pu_z_h.resize(matsize); // Only need to compute the z gradient for the z component seminorm
            }
 
#if LIBMESH_DIM > 1
          if (norm_type == H2_SEMINORM ||
              norm_type == W2_INF_SEMINORM)
            {
              Fxy.resize(matsize); Pu_xy_h.resize(matsize);
#if LIBMESH_DIM > 2
              Fxz.resize(matsize); Pu_xz_h.resize(matsize);
              Fyz.resize(matsize); Pu_yz_h.resize(matsize);
#endif
            }
#endif
 
 
          //------------------------------------------------------
          // Loop over each element in the patch and compute their
          // contribution to the patch gradient projection.
          for (const auto & e_p : patch)
            {
              // Reinitialize the finite element data for this element
              fe->reinit (e_p);
 
              // Get the global DOF indices for the current variable
              // in the current element
              dof_map.dof_indices (e_p, dof_indices, var);
              libmesh_assert (dof_indices.size() == phi->size());
 
              const unsigned int n_dofs =
                cast_int<unsigned int>(dof_indices.size());
              const unsigned int n_qp   = qrule->n_points();
 
              // Compute the weighted projection components from this cell.
              // \int_{Omega_e} \psi_i \psi_j = \int_{Omega_e} w * du_h/dx_k \psi_i
              for (unsigned int qp=0; qp<n_qp; qp++)
                {
                  // Construct the shape function values for the patch projection
                  std::vector<Real> psi(specpoly(dim, element_order, q_point[qp], matsize));
 
                  const unsigned int psi_size = cast_int<unsigned int>(psi.size());
 
                  // Patch matrix contribution
                  const unsigned int m = Kp.m(), n = Kp.n();
                  for (unsigned int i=0; i<m; i++)
                    for (unsigned int j=0; j<n; j++)
                      Kp(i,j) += JxW[qp]*psi[i]*psi[j];
 
                  if (norm_type == L2 ||
                      norm_type == L_INF)
                    {
                      // Compute the solution on the current patch element
                      // the quadrature point
                      Number u_h = libMesh::zero;
 
                      for (unsigned int i=0; i<n_dofs; i++)
                        u_h += (*phi)[i][qp]*system.current_solution (dof_indices[i]);
 
                      // Patch RHS contributions
                      for (unsigned int i=0; i != psi_size; i++)
                        F(i) = JxW[qp]*u_h*psi[i];
 
                    }
                  else if (norm_type == H1_SEMINORM ||
                           norm_type == W1_INF_SEMINORM)
                    {
                      // Compute the gradient on the current patch element
                      // at the quadrature point
                      Gradient grad_u_h;
 
                      for (std::size_t i=0; i<n_dofs; i++)
                        grad_u_h.add_scaled ((*dphi)[i][qp],
                                             system.current_solution(dof_indices[i]));
 
 
 
                      // Patch RHS contributions
                      for (unsigned int i=0; i != psi_size; i++)
                        {
                          Fx(i) += JxW[qp]*grad_u_h(0)*psi[i];
#if LIBMESH_DIM > 1
                          Fy(i) += JxW[qp]*grad_u_h(1)*psi[i];
#endif
#if LIBMESH_DIM > 2
                          Fz(i) += JxW[qp]*grad_u_h(2)*psi[i];
#endif
                        }
                    }
                  else if (norm_type == H1_X_SEMINORM)
                    {
                      // Compute the gradient on the current patch element
                      // at the quadrature point
                      Gradient grad_u_h;
 
                      for (unsigned int i=0; i<n_dofs; i++)
                        grad_u_h.add_scaled ((*dphi)[i][qp],
                                             system.current_solution(dof_indices[i]));
 
 
 
                      // Patch RHS contributions
                      for (unsigned int i=0; i != psi_size; i++)
                        {
                          Fx(i) += JxW[qp]*grad_u_h(0)*psi[i];
                        }
                    }
#if LIBMESH_DIM > 1
                  else if (norm_type == H1_Y_SEMINORM)
                    {
                      // Compute the gradient on the current patch element
                      // at the quadrature point
                      Gradient grad_u_h;
 
                      for (unsigned int i=0; i<n_dofs; i++)
                        grad_u_h.add_scaled ((*dphi)[i][qp],
                                             system.current_solution(dof_indices[i]));
 
 
 
                      // Patch RHS contributions
                      for (unsigned int i=0; i != psi_size; i++)
                        {
                          Fy(i) += JxW[qp]*grad_u_h(1)*psi[i];
                        }
                    }
#endif // LIBMESH_DIM > 1
#if LIBMESH_DIM > 2
                  else if (norm_type == H1_Z_SEMINORM)
                    {
                      // Compute the gradient on the current patch element
                      // at the quadrature point
                      Gradient grad_u_h;
 
                      for (unsigned int i=0; i<n_dofs; i++)
                        grad_u_h.add_scaled ((*dphi)[i][qp],
                                             system.current_solution(dof_indices[i]));
 
 
 
                      // Patch RHS contributions
                      for (unsigned int i=0; i != psi_size; i++)
                        {
                          Fz(i) += JxW[qp]*grad_u_h(2)*psi[i];
                        }
                    }
#endif // LIBMESH_DIM > 2
                  else if (norm_type == H2_SEMINORM ||
                           norm_type == W2_INF_SEMINORM)
                    {
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
                      // Compute the hessian on the current patch element
                      // at the quadrature point
                      Tensor hess_u_h;
 
                      for (unsigned int i=0; i<n_dofs; i++)
                        hess_u_h.add_scaled ((*d2phi)[i][qp],
                                             system.current_solution(dof_indices[i]));
 
 
 
                      // Patch RHS contributions
                      for (unsigned int i=0; i != psi_size; i++)
                        {
                          Fx(i)  += JxW[qp]*hess_u_h(0,0)*psi[i];
#if LIBMESH_DIM > 1
                          Fy(i)  += JxW[qp]*hess_u_h(1,1)*psi[i];
                          Fxy(i) += JxW[qp]*hess_u_h(0,1)*psi[i];
#endif
#if LIBMESH_DIM > 2
                          Fz(i)  += JxW[qp]*hess_u_h(2,2)*psi[i];
                          Fxz(i) += JxW[qp]*hess_u_h(0,2)*psi[i];
                          Fyz(i) += JxW[qp]*hess_u_h(1,2)*psi[i];
#endif
                        }
#else
                      libmesh_error_msg("ERROR:  --enable-second-derivatives is required \nfor _sobolev_order == 2!");
#endif
                    }
                  else
                    libmesh_error_msg("Unsupported error norm type == " << Utility::enum_to_string(norm_type));
                } // end quadrature loop
            } // end patch loop
 
 
 
          //--------------------------------------------------
          // Now we have fully assembled the projection system
          // for this patch.  Project the gradient components.
          // MAY NEED TO USE PARTIAL PIVOTING!
          if (norm_type == L2 ||
              norm_type == L_INF)
            {
              Kp.lu_solve(F, Pu_h);
            }
          else if (norm_type == H1_SEMINORM ||
                   norm_type == W1_INF_SEMINORM ||
                   norm_type == H2_SEMINORM ||
                   norm_type == W2_INF_SEMINORM)
            {
              Kp.lu_solve (Fx, Pu_x_h);
#if LIBMESH_DIM > 1
              Kp.lu_solve (Fy, Pu_y_h);
#endif
#if LIBMESH_DIM > 2
              Kp.lu_solve (Fz, Pu_z_h);
#endif
            }
          else if (norm_type == H1_X_SEMINORM)
            {
              Kp.lu_solve (Fx, Pu_x_h);
            }
          else if (norm_type == H1_Y_SEMINORM)
            {
              Kp.lu_solve (Fy, Pu_y_h);
            }
          else if (norm_type == H1_Z_SEMINORM)
            {
              Kp.lu_solve (Fz, Pu_z_h);
            }
 
#if LIBMESH_DIM > 1
          if (norm_type == H2_SEMINORM ||
              norm_type == W2_INF_SEMINORM)
            {
              Kp.lu_solve(Fxy, Pu_xy_h);
#if LIBMESH_DIM > 2
              Kp.lu_solve(Fxz, Pu_xz_h);
              Kp.lu_solve(Fyz, Pu_yz_h);
#endif
            }
#endif
 
          // If we are reusing patches, reuse the current patch to loop
          // over all elements in the current patch, otherwise build a new
          // patch containing just the current element and loop over it
          // Note that C++ will not allow patch_re_end to be a const here
          Patch::const_iterator patch_re_it;
          Patch::const_iterator patch_re_end;
 
          // Declare a new patch
          Patch patch_re(mesh.processor_id());
 
          if (this->error_estimator.patch_reuse)
            {
              // Just get the iterators from the current patch
              patch_re_it  = patch.begin();
              patch_re_end = patch.end();
            }
          else
            {
              // Use a target patch size of just 0, this will contain
              // just the current element
              patch_re.build_around_element (elem, 0,
                                             error_estimator.patch_growth_strategy);
 
              // Get the iterators from this newly constructed patch
              patch_re_it = patch_re.begin();
              patch_re_end = patch_re.end();
            }
 
          // If we are reusing patches, loop over all the elements
          // in the current patch and develop an estimate
          // for all the elements by computing  || w * (P u_h - u_h)|| or ||w *(P grad_u_h - grad_u_h)||
          // or ||w * (P hess_u_h - hess_u_h)|| according to the requested
          // seminorm, otherwise just compute it for the current element
 
          // Get an FEMContext for this system, this will help us in
          // obtaining the weights from the user code.
          // We don't use full elem_jacobian or subjacobians here.
          FEMContext femcontext(system, nullptr,
                                /* allocate_local_matrices = */ false);
          error_estimator.weight_functions[var]->init_context(femcontext);
 
          // Loop over every element in the patch
          for (unsigned int e = 0 ; patch_re_it != patch_re_end; ++patch_re_it, ++e)
            {
              // Build the Finite Element for the current element
 
              // The pth element in the patch
              const Elem * e_p = *patch_re_it;
 
              // We'll need an index into the error vector for this element
              const dof_id_type e_p_id = e_p->id();
 
              // Initialize the FEMContext
              femcontext.pre_fe_reinit(system, e_p);
 
              // We will update the new_error_per_cell vector with element_error if the
              // error_per_cell[e_p_id] entry is non-zero, otherwise update it
              // with 0. i.e. leave it unchanged
 
              // No need to compute the estimate if we are reusing patches and already have one
              if (this->error_estimator.patch_reuse && error_per_cell[e_p_id] != 0.)
                continue;
 
              // Reinitialize the finite element data for this element
              fe->reinit (e_p);
 
              // Get the global DOF indices for the current variable
              // in the current element
              dof_map.dof_indices (e_p, dof_indices, var);
              libmesh_assert (dof_indices.size() == phi->size());
 
              // The number of dofs for this variable on this element
              const unsigned int n_dofs =
                cast_int<unsigned int>(dof_indices.size());
 
              // Variable to hold the error on the current element
              Real element_error = 0;
 
              const Order qorder = fe_type.order + e_p->p_level();
 
              // A quadrature rule for this element
              QGrid samprule (dim, qorder);
 
              if (norm_type == W1_INF_SEMINORM ||
                  norm_type == W2_INF_SEMINORM)
                fe->attach_quadrature_rule (&samprule);
 
              // The number of points we will sample over
              const unsigned int n_sp =
                cast_int<unsigned int>(JxW.size());
 
              // Loop over every sample point for the current element
              for (unsigned int sp=0; sp<n_sp; sp++)
                {
                  // Compute the solution at the current sample point
 
                  std::vector<Number> temperr(6,0.0); // x,y,z or xx,yy,zz,xy,xz,yz
 
                  if (norm_type == L2 ||
                      norm_type == L_INF)
                    {
                      // Compute the value at the current sample point
                      Number u_h = libMesh::zero;
 
                      for (unsigned int i=0; i<n_dofs; i++)
                        u_h += (*phi)[i][sp]*system.current_solution (dof_indices[i]);
 
                      // Compute the phi values at the current sample point
                      std::vector<Real> psi(specpoly(dim, element_order, q_point[sp], matsize));
                      for (unsigned int i=0; i<matsize; i++)
                        {
                          temperr[0] += psi[i]*Pu_h(i);
                        }
 
                      temperr[0] -= u_h;
                    }
                  else if (norm_type == H1_SEMINORM ||
                           norm_type == W1_INF_SEMINORM)
                    {
                      // Compute the gradient at the current sample point
                      Gradient grad_u_h;
 
                      for (unsigned int i=0; i<n_dofs; i++)
                        grad_u_h.add_scaled ((*dphi)[i][sp],
                                             system.current_solution(dof_indices[i]));
 
                      // Compute the phi values at the current sample point
                      std::vector<Real> psi(specpoly(dim, element_order, q_point[sp], matsize));
 
                      for (unsigned int i=0; i<matsize; i++)
                        {
                          temperr[0] += psi[i]*Pu_x_h(i);
#if LIBMESH_DIM > 1
                          temperr[1] += psi[i]*Pu_y_h(i);
#endif
#if LIBMESH_DIM > 2
                          temperr[2] += psi[i]*Pu_z_h(i);
#endif
                        }
                      temperr[0] -= grad_u_h(0);
#if LIBMESH_DIM > 1
                      temperr[1] -= grad_u_h(1);
#endif
#if LIBMESH_DIM > 2
                      temperr[2] -= grad_u_h(2);
#endif
                    }
                  else if (norm_type == H1_X_SEMINORM)
                    {
                      // Compute the gradient at the current sample point
                      Gradient grad_u_h;
 
                      for (unsigned int i=0; i<n_dofs; i++)
                        grad_u_h.add_scaled ((*dphi)[i][sp],
                                             system.current_solution(dof_indices[i]));
 
                      // Compute the phi values at the current sample point
                      std::vector<Real> psi(specpoly(dim, element_order, q_point[sp], matsize));
                      for (unsigned int i=0; i<matsize; i++)
                        {
                          temperr[0] += psi[i]*Pu_x_h(i);
                        }
 
                      temperr[0] -= grad_u_h(0);
                    }
#if LIBMESH_DIM > 1
                  else if (norm_type == H1_Y_SEMINORM)
                    {
                      // Compute the gradient at the current sample point
                      Gradient grad_u_h;
 
                      for (unsigned int i=0; i<n_dofs; i++)
                        grad_u_h.add_scaled ((*dphi)[i][sp],
                                             system.current_solution(dof_indices[i]));
 
                      // Compute the phi values at the current sample point
                      std::vector<Real> psi(specpoly(dim, element_order, q_point[sp], matsize));
                      for (unsigned int i=0; i<matsize; i++)
                        {
                          temperr[1] += psi[i]*Pu_y_h(i);
                        }
 
                      temperr[1] -= grad_u_h(1);
                    }
#endif // LIBMESH_DIM > 1
#if LIBMESH_DIM > 2
                  else if (norm_type == H1_Z_SEMINORM)
                    {
                      // Compute the gradient at the current sample point
                      Gradient grad_u_h;
 
                      for (unsigned int i=0; i<n_dofs; i++)
                        grad_u_h.add_scaled ((*dphi)[i][sp],
                                             system.current_solution(dof_indices[i]));
 
                      // Compute the phi values at the current sample point
                      std::vector<Real> psi(specpoly(dim, element_order, q_point[sp], matsize));
                      for (unsigned int i=0; i<matsize; i++)
                        {
                          temperr[2] += psi[i]*Pu_z_h(i);
                        }
 
                      temperr[2] -= grad_u_h(2);
                    }
#endif // LIBMESH_DIM > 2
                  else if (norm_type == H2_SEMINORM ||
                           norm_type == W2_INF_SEMINORM)
                    {
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
                      // Compute the Hessian at the current sample point
                      Tensor hess_u_h;
 
                      for (unsigned int i=0; i<n_dofs; i++)
                        hess_u_h.add_scaled ((*d2phi)[i][sp],
                                             system.current_solution(dof_indices[i]));
 
                      // Compute the phi values at the current sample point
                      std::vector<Real> psi(specpoly(dim, element_order, q_point[sp], matsize));
                      for (unsigned int i=0; i<matsize; i++)
                        {
                          temperr[0] += psi[i]*Pu_x_h(i);
#if LIBMESH_DIM > 1
                          temperr[1] += psi[i]*Pu_y_h(i);
                          temperr[3] += psi[i]*Pu_xy_h(i);
#endif
#if LIBMESH_DIM > 2
                          temperr[2] += psi[i]*Pu_z_h(i);
                          temperr[4] += psi[i]*Pu_xz_h(i);
                          temperr[5] += psi[i]*Pu_yz_h(i);
#endif
                        }
 
                      temperr[0] -= hess_u_h(0,0);
#if LIBMESH_DIM > 1
                      temperr[1] -= hess_u_h(1,1);
                      temperr[3] -= hess_u_h(0,1);
#endif
#if LIBMESH_DIM > 2
                      temperr[2] -= hess_u_h(2,2);
                      temperr[4] -= hess_u_h(0,2);
                      temperr[5] -= hess_u_h(1,2);
#endif
#else
                      libmesh_error_msg("ERROR:  --enable-second-derivatives is required \nfor _sobolev_order == 2!");
#endif
                    }
 
                  // Get the weight from the user code
                  Number weight = (*error_estimator.weight_functions[var])(femcontext, q_point[sp], system.time);
 
                  // Add up relevant terms.  We can easily optimize the
                  // LIBMESH_DIM < 3 cases a little bit with the exception
                  // of the W2 cases
 
                  if (norm_type == L_INF)
                    element_error = std::max(element_error, std::abs(weight*temperr[0]));
                  else if (norm_type == W1_INF_SEMINORM)
                    for (unsigned int i=0; i != LIBMESH_DIM; ++i)
                      element_error = std::max(element_error, std::abs(weight*temperr[i]));
                  else if (norm_type == W2_INF_SEMINORM)
                    for (unsigned int i=0; i != 6; ++i)
                      element_error = std::max(element_error, std::abs(weight*temperr[i]));
                  else if (norm_type == L2)
                    element_error += JxW[sp]*TensorTools::norm_sq(weight*temperr[0]);
                  else if (norm_type == H1_SEMINORM)
                    for (unsigned int i=0; i != LIBMESH_DIM; ++i)
                      element_error += JxW[sp]*TensorTools::norm_sq(weight*temperr[i]);
                  else if (norm_type == H1_X_SEMINORM)
                    element_error += JxW[sp]*TensorTools::norm_sq(weight*temperr[0]);
                  else if (norm_type == H1_Y_SEMINORM)
                    element_error += JxW[sp]*TensorTools::norm_sq(weight*temperr[1]);
                  else if (norm_type == H1_Z_SEMINORM)
                    element_error += JxW[sp]*TensorTools::norm_sq(weight*temperr[2]);
                  else if (norm_type == H2_SEMINORM)
                    {
                      for (unsigned int i=0; i != LIBMESH_DIM; ++i)
                        element_error += JxW[sp]*TensorTools::norm_sq(weight*temperr[i]);
                      // Off diagonal terms enter into the Hessian norm twice
                      for (unsigned int i=3; i != 6; ++i)
                        element_error += JxW[sp]*2*TensorTools::norm_sq(weight*temperr[i]);
                    }
 
                } // End loop over sample points
 
              if (norm_type == L_INF ||
                  norm_type == W1_INF_SEMINORM ||
                  norm_type == W2_INF_SEMINORM)
                new_error_per_cell[e] += error_estimator.error_norm.weight(var) * element_error;
              else if (norm_type == L2 ||
                       norm_type == H1_SEMINORM ||
                       norm_type == H1_X_SEMINORM ||
                       norm_type == H1_Y_SEMINORM ||
                       norm_type == H1_Z_SEMINORM ||
                       norm_type == H2_SEMINORM)
                new_error_per_cell[e] += error_estimator.error_norm.weight_sq(var) * element_error;
              else
                libmesh_error_msg("Unsupported error norm type == " << Utility::enum_to_string(norm_type));
            }  // End (re) loop over patch elements
 
        } // end variables loop
 
      // Now that we have the contributions from each variable,
      // we have take square roots of the entries we
      // added to error_per_cell to get an error norm
      // If we are reusing patches, once again reuse the current patch to loop
      // over all elements in the current patch, otherwise build a new
      // patch containing just the current element and loop over it
      Patch::const_iterator patch_re_it;
      Patch::const_iterator patch_re_end;
 
      // Build a new patch if necessary
      Patch current_elem_patch(mesh.processor_id());
 
      if (this->error_estimator.patch_reuse)
        {
          // Just get the iterators from the current patch
          patch_re_it  = patch.begin();
          patch_re_end = patch.end();
        }
      else
        {
          // Use a target patch size of just 0, this will contain
          // just the current element.
          current_elem_patch.build_around_element (elem, 0,
                                                   error_estimator.patch_growth_strategy);
 
          // Get the iterators from this newly constructed patch
          patch_re_it = current_elem_patch.begin();
          patch_re_end = current_elem_patch.end();
        }
 
      // Loop over every element in the patch we just constructed
      for (unsigned int i = 0 ; patch_re_it != patch_re_end; ++patch_re_it, ++i)
        {
          // The pth element in the patch
          const Elem * e_p = *patch_re_it;
 
          // We'll need an index into the error vector
          const dof_id_type e_p_id = e_p->id();
 
          // Update the error_per_cell vector for this element
          if (error_estimator.error_norm.type(0) == L2 ||
              error_estimator.error_norm.type(0) == H1_SEMINORM ||
              error_estimator.error_norm.type(0) == H1_X_SEMINORM ||
              error_estimator.error_norm.type(0) == H1_Y_SEMINORM ||
              error_estimator.error_norm.type(0) == H1_Z_SEMINORM ||
              error_estimator.error_norm.type(0) == H2_SEMINORM)
            {
              Threads::spin_mutex::scoped_lock acquire(Threads::spin_mtx);
              if (!error_per_cell[e_p_id])
                error_per_cell[e_p_id] = static_cast<ErrorVectorReal>
                  (std::sqrt(new_error_per_cell[i]));
            }
          else
            {
              libmesh_assert (error_estimator.error_norm.type(0) == L_INF ||
                              error_estimator.error_norm.type(0) == W1_INF_SEMINORM ||
                              error_estimator.error_norm.type(0) == W2_INF_SEMINORM);
              Threads::spin_mutex::scoped_lock acquire(Threads::spin_mtx);
              if (!error_per_cell[e_p_id])
                error_per_cell[e_p_id] = static_cast<ErrorVectorReal>
                  (new_error_per_cell[i]);
            }
 
        } // End loop over every element in patch
 
 
    } // end element loop
 
} // End () operator definition

References libMesh::PatchRecoveryErrorEstimator::_extra_order, libMesh::TypeTensor< T >::add_scaled(), libMesh::TypeVector< T >::add_scaled(), libMesh::FEGenericBase< OutputType >::build(), libMesh::Patch::build_around_element(), libMesh::System::current_solution(), libMesh::FEType::default_quadrature_rule(), dim, libMesh::DofMap::dof_indices(), libMesh::Utility::enum_to_string(), error_estimator, libMesh::ErrorEstimator::error_norm, error_per_cell, libMesh::ErrorVectorReal, libMesh::System::get_dof_map(), libMesh::System::get_mesh(), libMesh::H1_SEMINORM, libMesh::H1_X_SEMINORM, libMesh::H1_Y_SEMINORM, libMesh::H1_Z_SEMINORM, libMesh::H2_SEMINORM, libMesh::DofObject::id(), libMesh::L2, libMesh::L_INF, libMesh::libmesh_assert(), libMesh::DenseMatrix< T >::lu_solve(), libMesh::DenseMatrixBase< T >::m(), mesh, libMesh::MeshBase::mesh_dimension(), libMesh::DenseMatrixBase< T >::n(), n_vars, libMesh::System::n_vars(), libMesh::TensorTools::norm_sq(), libMesh::FEType::order, libMesh::Elem::p_level(), libMesh::PatchRecoveryErrorEstimator::patch_growth_strategy, libMesh::PatchRecoveryErrorEstimator::patch_reuse, libMesh::FEMContext::pre_fe_reinit(), libMesh::Real, libMesh::DenseVector< T >::resize(), libMesh::PatchRecoveryErrorEstimator::specpoly(), libMesh::Threads::spin_mtx, system, libMesh::PatchRecoveryErrorEstimator::target_patch_size, libMesh::System::time, libMesh::SystemNorm::type(), libMesh::DofMap::variable_type(), libMesh::W1_INF_SEMINORM, libMesh::W2_INF_SEMINORM, libMesh::SystemNorm::weight(), libMesh::WeightedPatchRecoveryErrorEstimator::weight_functions, libMesh::SystemNorm::weight_sq(), and libMesh::zero.

Member Data Documentation

error_estimator

const WeightedPatchRecoveryErrorEstimator& libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::error_estimator

private

Definition at line 114 of file weighted_patch_recovery_error_estimator.h.

Referenced by operator()().

error_per_cell

ErrorVector& libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::error_per_cell

private

Definition at line 115 of file weighted_patch_recovery_error_estimator.h.

Referenced by operator()().

system

const System& libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::system

private

Function to set the boolean patch_reuse in case the user wants to change the default behaviour of patch_recovery_error_estimator.

Definition at line 113 of file weighted_patch_recovery_error_estimator.h.

Referenced by operator()().

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

• include/error_estimation/weighted_patch_recovery_error_estimator.h
• src/error_estimation/weighted_patch_recovery_error_estimator.C