void RBSCMConstruction::evaluate_stability_constant()
{
START_LOG("evaluate_stability_constant()", "RBSCMConstruction");
// Get current index of C_J
const unsigned int j = rb_scm_eval->C_J.size()-1;
eigen_solver->set_position_of_spectrum(SMALLEST_REAL);
// We assume B is set in system assembly
// For coercive problems, B is set to the inner product matrix
// For non-coercive time-dependent problems, B is set to the mass matrix
// Set matrix A corresponding to mu_star
matrix_A->zero();
for(unsigned int q=0; q<get_rb_theta_expansion().get_n_A_terms(); q++)
{
add_scaled_symm_Aq(q, get_rb_theta_expansion().eval_A_theta(q,get_parameters()));
}
set_eigensolver_properties(-1);
solve();
unsigned int nconv = get_n_converged();
if (nconv != 0)
{
std::pair<Real, Real> eval = get_eigenpair(0);
// ensure that the eigenvalue is real
libmesh_assert_less (eval.second, TOLERANCE);
// Store the coercivity constant corresponding to mu_star
rb_scm_eval->set_C_J_stability_constraint(j,eval.first);
libMesh::out << std::endl << "Stability constant for C_J("<<j<<") = "
<< rb_scm_eval->get_C_J_stability_constraint(j) << std::endl << std::endl;
// Compute and store the vector y = (y_1, \ldots, y_Q) for the
// eigenvector currently stored in eigen_system.solution.
// We use this later to compute the SCM upper bounds.
Real norm_B2 = libmesh_real( B_inner_product(*solution, *solution) );
for(unsigned int q=0; q<get_rb_theta_expansion().get_n_A_terms(); q++)
{
Real norm_Aq2 = libmesh_real( Aq_inner_product(q, *solution, *solution) );
rb_scm_eval->set_SCM_UB_vector(j,q,norm_Aq2/norm_B2);
}
}
else
{
libMesh::err << "Error: Eigensolver did not converge in evaluate_stability_constant"
<< std::endl;
libmesh_error();
}
STOP_LOG("evaluate_stability_constant()", "RBSCMConstruction");
}
Real LaspackVector<T>::min () const
{
libmesh_assert (this->initialized());
if (!this->size())
return std::numeric_limits<Real>::max();
Real the_min = libmesh_real((*this)(0));
const numeric_index_type n = this->size();
for (numeric_index_type i=1; i<n; i++)
the_min = std::min (the_min, libmesh_real((*this)(i)));
return the_min;
}
Real RBEvaluation::eval_output_dual_norm(unsigned int n, const RBParameters& mu)
{
Number output_bound_sq = 0.;
unsigned int q=0;
for(unsigned int q_l1=0; q_l1<rb_theta_expansion->get_n_output_terms(n); q_l1++)
{
for(unsigned int q_l2=q_l1; q_l2<rb_theta_expansion->get_n_output_terms(n); q_l2++)
{
Real delta = (q_l1==q_l2) ? 1. : 2.;
output_bound_sq += delta * libmesh_real(
libmesh_conj(rb_theta_expansion->eval_output_theta(n,q_l1,mu))*
rb_theta_expansion->eval_output_theta(n,q_l2,mu) * output_dual_innerprods[n][q] );
q++;
}
}
return libmesh_real(std::sqrt( output_bound_sq ));
}
Real EigenSparseVector<T>::min () const
{
libmesh_assert (this->initialized());
if (!this->size())
return std::numeric_limits<Real>::max();
#ifdef LIBMESH_USE_COMPLEX_NUMBERS
Real the_min = libmesh_real((*this)(0));
const numeric_index_type n = this->size();
for (numeric_index_type i=1; i<n; i++)
the_min = std::min (the_min, libmesh_real((*this)(i)));
return the_min;
#else
return libmesh_real(_vec.minCoeff());
#endif
}
RBParameters RBConstructionBase<Base>::get_params_from_training_set(unsigned int index)
{
libmesh_assert(training_parameters_initialized);
libmesh_assert( (this->get_first_local_training_index() <= index) &&
(index < this->get_last_local_training_index()) );
RBParameters params;
std::map< std::string, NumericVector<Number>* >::const_iterator it = training_parameters.begin();
std::map< std::string, NumericVector<Number>* >::const_iterator it_end = training_parameters.end();
for( ; it != it_end; ++it)
{
std::string param_name = it->first;
Real param_value = libmesh_real( ( *(it->second) )(index) );
params.set_value(param_name, param_value);
}
return params;
}
void NonlinearNeoHookeCurrentConfig::init_for_qp(VectorValue<Gradient> & grad_u, unsigned int qp) {
this->current_qp = qp;
F.zero();
S.zero();
{
RealTensor invF;
invF.zero();
for (unsigned int i = 0; i < 3; ++i)
for (unsigned int j = 0; j < 3; ++j) {
invF(i, j) += libmesh_real(grad_u(i)(j));
}
F.add(inv(invF));
libmesh_assert_greater (F.det(), -TOLERANCE);
}
if (this->calculate_linearized_stiffness) {
this->calculate_tangent();
}
this->calculate_stress();
}
bool FEMPhysics::eulerian_residual (bool request_jacobian,
DiffContext &/*c*/)
{
// Only calculate a mesh movement residual if it's necessary
if (!_mesh_sys)
return request_jacobian;
libmesh_not_implemented();
#if 0
FEMContext &context = libmesh_cast_ref<FEMContext&>(c);
// This function only supports fully coupled mesh motion for now
libmesh_assert_equal_to (_mesh_sys, this);
unsigned int n_qpoints = (context.get_element_qrule())->n_points();
const unsigned int n_x_dofs = (_mesh_x_var == libMesh::invalid_uint) ?
0 : context.dof_indices_var[_mesh_x_var].size();
const unsigned int n_y_dofs = (_mesh_y_var == libMesh::invalid_uint) ?
0 : context.dof_indices_var[_mesh_y_var].size();
const unsigned int n_z_dofs = (_mesh_z_var == libMesh::invalid_uint) ?
0 : context.dof_indices_var[_mesh_z_var].size();
const unsigned int mesh_xyz_var = n_x_dofs ? _mesh_x_var :
(n_y_dofs ? _mesh_y_var :
(n_z_dofs ? _mesh_z_var :
libMesh::invalid_uint));
// If we're our own _mesh_sys, we'd better be in charge of
// at least one coordinate, and we'd better have the same
// FE type for all coordinates we are in charge of
libmesh_assert_not_equal_to (mesh_xyz_var, libMesh::invalid_uint);
libmesh_assert(!n_x_dofs || context.element_fe_var[_mesh_x_var] ==
context.element_fe_var[mesh_xyz_var]);
libmesh_assert(!n_y_dofs || context.element_fe_var[_mesh_y_var] ==
context.element_fe_var[mesh_xyz_var]);
libmesh_assert(!n_z_dofs || context.element_fe_var[_mesh_z_var] ==
context.element_fe_var[mesh_xyz_var]);
const std::vector<std::vector<Real> > &psi =
context.element_fe_var[mesh_xyz_var]->get_phi();
for (unsigned int var = 0; var != context.n_vars(); ++var)
{
// Mesh motion only affects time-evolving variables
if (this->is_time_evolving(var))
continue;
// The mesh coordinate variables themselves are Lagrangian,
// not Eulerian, and no convective term is desired.
if (/*_mesh_sys == this && */
(var == _mesh_x_var ||
var == _mesh_y_var ||
var == _mesh_z_var))
continue;
// Some of this code currently relies on the assumption that
// we can pull mesh coordinate data from our own system
if (_mesh_sys != this)
libmesh_not_implemented();
// This residual should only be called by unsteady solvers:
// if the mesh is steady, there's no mesh convection term!
UnsteadySolver *unsteady;
if (this->time_solver->is_steady())
return request_jacobian;
else
unsteady = libmesh_cast_ptr<UnsteadySolver*>(this->time_solver.get());
const std::vector<Real> &JxW =
context.element_fe_var[var]->get_JxW();
const std::vector<std::vector<Real> > &phi =
context.element_fe_var[var]->get_phi();
const std::vector<std::vector<RealGradient> > &dphi =
context.element_fe_var[var]->get_dphi();
const unsigned int n_u_dofs = context.dof_indices_var[var].size();
DenseSubVector<Number> &Fu = *context.elem_subresiduals[var];
DenseSubMatrix<Number> &Kuu = *context.elem_subjacobians[var][var];
DenseSubMatrix<Number> *Kux = n_x_dofs ?
context.elem_subjacobians[var][_mesh_x_var] : NULL;
DenseSubMatrix<Number> *Kuy = n_y_dofs ?
context.elem_subjacobians[var][_mesh_y_var] : NULL;
DenseSubMatrix<Number> *Kuz = n_z_dofs ?
context.elem_subjacobians[var][_mesh_z_var] : NULL;
std::vector<Real> delta_x(n_x_dofs, 0.);
std::vector<Real> delta_y(n_y_dofs, 0.);
std::vector<Real> delta_z(n_z_dofs, 0.);
for (unsigned int i = 0; i != n_x_dofs; ++i)
{
unsigned int j = context.dof_indices_var[_mesh_x_var][i];
delta_x[i] = libmesh_real(this->current_solution(j)) -
libmesh_real(unsteady->old_nonlinear_solution(j));
}
for (unsigned int i = 0; i != n_y_dofs; ++i)
{
unsigned int j = context.dof_indices_var[_mesh_y_var][i];
delta_y[i] = libmesh_real(this->current_solution(j)) -
libmesh_real(unsteady->old_nonlinear_solution(j));
}
for (unsigned int i = 0; i != n_z_dofs; ++i)
{
unsigned int j = context.dof_indices_var[_mesh_z_var][i];
delta_z[i] = libmesh_real(this->current_solution(j)) -
libmesh_real(unsteady->old_nonlinear_solution(j));
}
for (unsigned int qp = 0; qp != n_qpoints; ++qp)
{
Gradient grad_u = context.interior_gradient(var, qp);
RealGradient convection(0.);
for (unsigned int i = 0; i != n_x_dofs; ++i)
convection(0) += delta_x[i] * psi[i][qp];
for (unsigned int i = 0; i != n_y_dofs; ++i)
convection(1) += delta_y[i] * psi[i][qp];
for (unsigned int i = 0; i != n_z_dofs; ++i)
convection(2) += delta_z[i] * psi[i][qp];
for (unsigned int i = 0; i != n_u_dofs; ++i)
{
Number JxWxPhiI = JxW[qp] * phi[i][qp];
Fu(i) += (convection * grad_u) * JxWxPhiI;
if (request_jacobian)
{
Number JxWxPhiI = JxW[qp] * phi[i][qp];
for (unsigned int j = 0; j != n_u_dofs; ++j)
Kuu(i,j) += JxWxPhiI * (convection * dphi[j][qp]);
Number JxWxPhiIoverDT = JxWxPhiI/this->deltat;
Number JxWxPhiIxDUDXoverDT = JxWxPhiIoverDT * grad_u(0);
for (unsigned int j = 0; j != n_x_dofs; ++j)
(*Kux)(i,j) += JxWxPhiIxDUDXoverDT * psi[j][qp];
Number JxWxPhiIxDUDYoverDT = JxWxPhiIoverDT * grad_u(1);
for (unsigned int j = 0; j != n_y_dofs; ++j)
(*Kuy)(i,j) += JxWxPhiIxDUDYoverDT * psi[j][qp];
Number JxWxPhiIxDUDZoverDT = JxWxPhiIoverDT * grad_u(2);
for (unsigned int j = 0; j != n_z_dofs; ++j)
(*Kuz)(i,j) += JxWxPhiIxDUDZoverDT * psi[j][qp];
}
}
}
}
#endif // 0
return request_jacobian;
}
void FEMSystem::numerical_jacobian (TimeSolverResPtr res,
FEMContext &context)
{
// Logging is done by numerical_elem_jacobian
// or numerical_side_jacobian
DenseVector<Number> original_residual(context.elem_residual);
DenseVector<Number> backwards_residual(context.elem_residual);
DenseMatrix<Number> numerical_jacobian(context.elem_jacobian);
#ifdef DEBUG
DenseMatrix<Number> old_jacobian(context.elem_jacobian);
#endif
Real numerical_point_h = 0.;
if (_mesh_sys == this)
numerical_point_h = numerical_jacobian_h * context.elem->hmin();
for (unsigned int j = 0; j != context.dof_indices.size(); ++j)
{
// Take the "minus" side of a central differenced first derivative
Number original_solution = context.elem_solution(j);
context.elem_solution(j) -= numerical_jacobian_h;
// Make sure to catch any moving mesh terms
// FIXME - this could be less ugly
Real *coord = NULL;
if (_mesh_sys == this)
{
if (_mesh_x_var != libMesh::invalid_uint)
for (unsigned int k = 0;
k != context.dof_indices_var[_mesh_x_var].size(); ++k)
if (context.dof_indices_var[_mesh_x_var][k] ==
context.dof_indices[j])
coord = &(const_cast<Elem*>(context.elem)->point(k)(0));
if (_mesh_y_var != libMesh::invalid_uint)
for (unsigned int k = 0;
k != context.dof_indices_var[_mesh_y_var].size(); ++k)
if (context.dof_indices_var[_mesh_y_var][k] ==
context.dof_indices[j])
coord = &(const_cast<Elem*>(context.elem)->point(k)(1));
if (_mesh_z_var != libMesh::invalid_uint)
for (unsigned int k = 0;
k != context.dof_indices_var[_mesh_z_var].size(); ++k)
if (context.dof_indices_var[_mesh_z_var][k] ==
context.dof_indices[j])
coord = &(const_cast<Elem*>(context.elem)->point(k)(2));
}
if (coord)
{
// We have enough information to scale the perturbations
// here appropriately
context.elem_solution(j) = original_solution - numerical_point_h;
*coord = libmesh_real(context.elem_solution(j));
}
context.elem_residual.zero();
((*time_solver).*(res))(false, context);
#ifdef DEBUG
libmesh_assert_equal_to (old_jacobian, context.elem_jacobian);
#endif
backwards_residual = context.elem_residual;
// Take the "plus" side of a central differenced first derivative
context.elem_solution(j) = original_solution + numerical_jacobian_h;
if (coord)
{
context.elem_solution(j) = original_solution + numerical_point_h;
*coord = libmesh_real(context.elem_solution(j));
}
context.elem_residual.zero();
((*time_solver).*(res))(false, context);
#ifdef DEBUG
libmesh_assert_equal_to (old_jacobian, context.elem_jacobian);
#endif
context.elem_solution(j) = original_solution;
if (coord)
{
*coord = libmesh_real(context.elem_solution(j));
for (unsigned int i = 0; i != context.dof_indices.size(); ++i)
{
numerical_jacobian(i,j) =
(context.elem_residual(i) - backwards_residual(i)) /
2. / numerical_point_h;
}
}
else
{
for (unsigned int i = 0; i != context.dof_indices.size(); ++i)
{
numerical_jacobian(i,j) =
(context.elem_residual(i) - backwards_residual(i)) /
2. / numerical_jacobian_h;
}
}
}
context.elem_residual = original_residual;
context.elem_jacobian = numerical_jacobian;
}
Real RBEvaluation::compute_residual_dual_norm(const unsigned int N)
{
START_LOG("compute_residual_dual_norm()", "RBEvaluation");
const RBParameters& mu = get_parameters();
// Use the stored representor inner product values
// to evaluate the residual norm
Number residual_norm_sq = 0.;
unsigned int q=0;
for(unsigned int q_f1=0; q_f1<rb_theta_expansion->get_n_F_terms(); q_f1++)
{
for(unsigned int q_f2=q_f1; q_f2<rb_theta_expansion->get_n_F_terms(); q_f2++)
{
Real delta = (q_f1==q_f2) ? 1. : 2.;
residual_norm_sq += delta * libmesh_real(
rb_theta_expansion->eval_F_theta(q_f1, mu)
* libmesh_conj(rb_theta_expansion->eval_F_theta(q_f2, mu)) * Fq_representor_innerprods[q] );
q++;
}
}
for(unsigned int q_f=0; q_f<rb_theta_expansion->get_n_F_terms(); q_f++)
{
for(unsigned int q_a=0; q_a<rb_theta_expansion->get_n_A_terms(); q_a++)
{
for(unsigned int i=0; i<N; i++)
{
Real delta = 2.;
residual_norm_sq +=
delta * libmesh_real( rb_theta_expansion->eval_F_theta(q_f, mu) *
libmesh_conj(rb_theta_expansion->eval_A_theta(q_a, mu)) *
libmesh_conj(RB_solution(i)) * Fq_Aq_representor_innerprods[q_f][q_a][i] );
}
}
}
q=0;
for(unsigned int q_a1=0; q_a1<rb_theta_expansion->get_n_A_terms(); q_a1++)
{
for(unsigned int q_a2=q_a1; q_a2<rb_theta_expansion->get_n_A_terms(); q_a2++)
{
Real delta = (q_a1==q_a2) ? 1. : 2.;
for(unsigned int i=0; i<N; i++)
{
for(unsigned int j=0; j<N; j++)
{
residual_norm_sq +=
delta * libmesh_real( libmesh_conj(rb_theta_expansion->eval_A_theta(q_a1, mu)) *
rb_theta_expansion->eval_A_theta(q_a2, mu) *
libmesh_conj(RB_solution(i)) * RB_solution(j) * Aq_Aq_representor_innerprods[q][i][j] );
}
}
q++;
}
}
if(libmesh_real(residual_norm_sq) < 0.)
{
// libMesh::out << "Warning: Square of residual norm is negative "
// << "in RBSystem::compute_residual_dual_norm()" << std::endl;
// Sometimes this is negative due to rounding error,
// but when this occurs the error is on the order of 1.e-10,
// so shouldn't affect error bound much...
residual_norm_sq = std::abs(residual_norm_sq);
}
STOP_LOG("compute_residual_dual_norm()", "RBEvaluation");
return std::sqrt( libmesh_real(residual_norm_sq) );
}
// This function solves the tangent system:
// [ G_u G_{lambda} ][(du/ds)_new ] = [ 0 ]
// [ Theta*(du/ds)_old (dlambda/ds)_old ][(dlambda/ds)_new ] [-N_s]
// The solution is given by:
// .) Let G_u y = G_lambda, then
// .) 2nd row yields:
// (dlambda/ds)_new = 1.0 / ( (dlambda/ds)_old - Theta*(du/ds)_old*y )
// .) 1st row yields
// (du_ds)_new = -(dlambda/ds)_new * y
void ContinuationSystem::solve_tangent()
{
// We shouldn't call this unless the current tangent already makes sense.
libmesh_assert (tangent_initialized);
// Set pointer to underlying Newton solver
if (!newton_solver)
newton_solver =
libmesh_cast_ptr<NewtonSolver*> (this->time_solver->diff_solver().get());
// Assemble the system matrix AND rhs, with rhs = G_{\lambda}
this->rhs_mode = G_Lambda;
// Assemble Residual and Jacobian
this->assembly(true, // Residual
true); // Jacobian
// Not sure if this is really necessary
rhs->close();
// Solve G_u*y = G_{\lambda}
std::pair<unsigned int, Real> rval =
linear_solver->solve(*matrix,
*y,
*rhs,
1.e-12, // relative linear tolerance
2*newton_solver->max_linear_iterations); // max linear iterations
// FIXME: If this doesn't converge at all, the new tangent vector is
// going to be really bad...
if (!quiet)
libMesh::out << "G_u*y = G_{lambda} solver converged at step "
<< rval.first
<< " linear tolerance = "
<< rval.second
<< "."
<< std::endl;
// Save old solution and parameter tangents for possible use in higher-order
// predictor schemes.
previous_dlambda_ds = dlambda_ds;
*previous_du_ds = *du_ds;
// 1.) Previous, probably wrong, technique!
// // Solve for the updated d(lambda)/ds
// // denom = N_{lambda} - (du_ds)^t y
// // = d(lambda)/ds - (du_ds)^t y
// Real denom = dlambda_ds - du_ds->dot(*y);
// //libMesh::out << "denom=" << denom << std::endl;
// libmesh_assert_not_equal_to (denom, 0.0);
// dlambda_ds = 1.0 / denom;
// if (!quiet)
// libMesh::out << "dlambda_ds=" << dlambda_ds << std::endl;
// // Compute the updated value of du/ds = -_dlambda_ds * y
// du_ds->zero();
// du_ds->add(-dlambda_ds, *y);
// du_ds->close();
// 2.) From Brian Carnes' paper...
// According to Carnes, y comes from solving G_u * y = -G_{\lambda}
y->scale(-1.);
const Real ynorm = y->l2_norm();
dlambda_ds = 1. / std::sqrt(1. + Theta_LOCA*Theta_LOCA*Theta*ynorm*ynorm);
// Determine the correct sign for dlambda_ds.
// We will use delta_u to temporarily compute this sign.
*delta_u = *solution;
delta_u->add(-1., *previous_u);
delta_u->close();
const Real sgn_dlambda_ds =
libmesh_real(Theta_LOCA*Theta_LOCA*Theta*y->dot(*delta_u) +
(*continuation_parameter-old_continuation_parameter));
if (sgn_dlambda_ds < 0.)
{
if (!quiet)
libMesh::out << "dlambda_ds is negative." << std::endl;
dlambda_ds *= -1.;
}
// Finally, set the new tangent vector, du/ds = dlambda/ds * y.
du_ds->zero();
du_ds->add(dlambda_ds, *y);
du_ds->close();
if (!quiet)
{
libMesh::out << "d(lambda)/ds = " << dlambda_ds << std::endl;
libMesh::out << "||du_ds|| = " << du_ds->l2_norm() << std::endl;
}
// Our next solve expects y ~ -du/dlambda, so scale it back by -1 again now.
y->scale(-1.);
y->close();
}
// This is most of the "guts" of this class. This is where we implement
// our custom Newton iterations and perform most of the solves.
void ContinuationSystem::continuation_solve()
{
// Be sure the user has set the continuation parameter pointer
if (!continuation_parameter)
{
libMesh::err << "You must set the continuation_parameter pointer "
<< "to a member variable of the derived class, preferably in the "
<< "Derived class's init_data function. This is how the ContinuationSystem "
<< "updates the continuation parameter."
<< std::endl;
libmesh_error();
}
// Use extra precision for all the numbers printed in this function.
unsigned int old_precision = libMesh::out.precision();
libMesh::out.precision(16);
libMesh::out.setf(std::ios_base::scientific);
// We can't start solving the augmented PDE system unless the tangent
// vectors have been initialized. This only needs to occur once.
if (!tangent_initialized)
initialize_tangent();
// Save the old value of -du/dlambda. This will be used after the Newton iterations
// to compute the angle between previous tangent vectors. This cosine of this angle is
//
// tau := abs( (du/d(lambda)_i , du/d(lambda)_{i-1}) / (||du/d(lambda)_i|| * ||du/d(lambda)_{i-1}||) )
//
// The scaling factor tau (which should vary between 0 and 1) is used to shrink the step-size ds
// when we are approaching a turning point. Note that it can only shrink the step size.
*y_old = *y;
// Set pointer to underlying Newton solver
if (!newton_solver)
newton_solver = libmesh_cast_ptr<NewtonSolver*> (this->time_solver->diff_solver().get());
// A pair for catching return values from linear system solves.
std::pair<unsigned int, Real> rval;
// Convergence flag for the entire arcstep
bool arcstep_converged = false;
// Begin loop over arcstep reductions.
for (unsigned int ns=0; ns<n_arclength_reductions; ++ns)
{
if (!quiet)
{
libMesh::out << "Current arclength stepsize, ds_current=" << ds_current << std::endl;
libMesh::out << "Current parameter value, lambda=" << *continuation_parameter << std::endl;
}
// Upon exit from the nonlinear loop, the newton_converged flag
// will tell us the convergence status of Newton's method.
bool newton_converged = false;
// The nonlinear residual before *any* nonlinear steps have been taken.
Real nonlinear_residual_firststep = 0.;
// The nonlinear residual from the current "k" Newton step, before the Newton step
Real nonlinear_residual_beforestep = 0.;
// The nonlinear residual from the current "k" Newton step, after the Newton step
Real nonlinear_residual_afterstep = 0.;
// The linear solver tolerance, can be updated dynamically at each Newton step.
Real current_linear_tolerance = 0.;
// The nonlinear loop
for (newton_step=0; newton_step<newton_solver->max_nonlinear_iterations; ++newton_step)
{
libMesh::out << "\n === Starting Newton step " << newton_step << " ===" << std::endl;
// Set the linear system solver tolerance
// // 1.) Set the current linear tolerance based as a multiple of the current residual of the system.
// const Real residual_multiple = 1.e-4;
// Real current_linear_tolerance = residual_multiple*nonlinear_residual_beforestep;
// // But if the current residual isn't small, don't let the solver exit with zero iterations!
// if (current_linear_tolerance > 1.)
// current_linear_tolerance = residual_multiple;
// 2.) Set the current linear tolerance based on the method based on technique of Eisenstat & Walker.
if (newton_step==0)
{
// At first step, only try reducing the residual by a small amount
current_linear_tolerance = initial_newton_tolerance;//0.01;
}
else
{
// The new tolerance is based on the ratio of the most recent tolerances
const Real alp=0.5*(1.+std::sqrt(5.));
const Real gam=0.9;
libmesh_assert_not_equal_to (nonlinear_residual_beforestep, 0.0);
libmesh_assert_not_equal_to (nonlinear_residual_afterstep, 0.0);
current_linear_tolerance = std::min(gam*std::pow(nonlinear_residual_afterstep/nonlinear_residual_beforestep, alp),
current_linear_tolerance*current_linear_tolerance
);
// Don't let it get ridiculously small!!
if (current_linear_tolerance < 1.e-12)
current_linear_tolerance = 1.e-12;
}
if (!quiet)
libMesh::out << "Using current_linear_tolerance=" << current_linear_tolerance << std::endl;
// Assemble the residual (and Jacobian).
rhs_mode = Residual;
assembly(true, // Residual
true); // Jacobian
rhs->close();
// Save the current nonlinear residual. We don't need to recompute the residual unless
// this is the first step, since it was already computed as part of the convergence check
// at the end of the last loop iteration.
if (newton_step==0)
{
nonlinear_residual_beforestep = rhs->l2_norm();
// Store the residual before any steps have been taken. This will *not*
// be updated at each step, and can be used to see if any progress has
// been made from the initial residual at later steps.
nonlinear_residual_firststep = nonlinear_residual_beforestep;
const Real old_norm_u = solution->l2_norm();
libMesh::out << " (before step) ||R||_{L2} = " << nonlinear_residual_beforestep << std::endl;
libMesh::out << " (before step) ||R||_{L2}/||u|| = " << nonlinear_residual_beforestep / old_norm_u << std::endl;
// In rare cases (very small arcsteps), it's possible that the residual is
// already below our absolute linear tolerance.
if (nonlinear_residual_beforestep < solution_tolerance)
{
if (!quiet)
libMesh::out << "Initial guess satisfied linear tolerance, exiting with zero Newton iterations!" << std::endl;
// Since we go straight from here to the solve of the next tangent, we
// have to close the matrix before it can be assembled again.
matrix->close();
newton_converged=true;
break; // out of Newton iterations, with newton_converged=true
}
}
else
{
nonlinear_residual_beforestep = nonlinear_residual_afterstep;
}
// Solve the linear system G_u*z = G
// Initial guess?
z->zero(); // It seems to be extremely important to zero z here, otherwise the solver quits early.
z->close();
// It's possible that we have selected the current_linear_tolerance so large that
// a guess of z=zero yields a linear system residual |Az + R| small enough that the
// linear solver exits in zero iterations. If this happens, we will reduce the
// current_linear_tolerance until the linear solver does at least 1 iteration.
do
{
rval =
linear_solver->solve(*matrix,
*z,
*rhs,
//1.e-12,
current_linear_tolerance,
newton_solver->max_linear_iterations); // max linear iterations
if (rval.first==0)
{
if (newton_step==0)
{
libMesh::out << "Repeating initial solve with smaller linear tolerance!" << std::endl;
current_linear_tolerance *= initial_newton_tolerance; // reduce the linear tolerance to force the solver to do some work
}
else
{
// We shouldn't get here ... it means the linear solver did no work on a Newton
// step other than the first one. If this happens, we need to think more about our
// tolerance selection.
libmesh_error();
}
}
} while (rval.first==0);
if (!quiet)
libMesh::out << " G_u*z = G solver converged at step "
<< rval.first
<< " linear tolerance = "
<< rval.second
<< "."
<< std::endl;
// Sometimes (I am not sure why) the linear solver exits after zero iterations.
// Perhaps it is hitting PETSc's divergence tolerance dtol??? If this occurs,
// we should break out of the Newton iteration loop because nothing further is
// going to happen... Of course if the tolerance is already small enough after
// zero iterations (how can this happen?!) we should not quit.
if ((rval.first == 0) && (rval.second > current_linear_tolerance*nonlinear_residual_beforestep))
{
if (!quiet)
libMesh::out << "Linear solver exited in zero iterations!" << std::endl;
// Try to find out the reason for convergence/divergence
linear_solver->print_converged_reason();
break; // out of Newton iterations
}
// Note: need to scale z by -1 since our code always solves Jx=R
// instead of Jx=-R.
z->scale(-1.);
z->close();
// Assemble the G_Lambda vector, skip residual.
rhs_mode = G_Lambda;
// Assemble both rhs and Jacobian
assembly(true, // Residual
false); // Jacobian
// Not sure if this is really necessary
rhs->close();
const Real yrhsnorm=rhs->l2_norm();
if (yrhsnorm == 0.0)
{
libMesh::out << "||G_Lambda|| = 0" << std::endl;
libmesh_error();
}
// We select a tolerance for the y-system which is based on the inexact Newton
// tolerance but scaled by an extra term proportional to the RHS (which is not -> 0 in this case)
const Real ysystemtol=current_linear_tolerance*(nonlinear_residual_beforestep/yrhsnorm);
if (!quiet)
libMesh::out << "ysystemtol=" << ysystemtol << std::endl;
// Solve G_u*y = G_{\lambda}
// FIXME: Initial guess? This is really a solve for -du/dlambda so we could try
// initializing it with the latest approximation to that... du/dlambda ~ du/ds * ds/dlambda
//*y = *solution;
//y->add(-1., *previous_u);
//y->scale(-1. / (*continuation_parameter - old_continuation_parameter)); // Be careful of divide by zero...
//y->close();
// const unsigned int max_attempts=1;
// unsigned int attempt=0;
// do
// {
// if (!quiet)
// libMesh::out << "Trying to solve tangent system, attempt " << attempt << std::endl;
rval =
linear_solver->solve(*matrix,
*y,
*rhs,
//1.e-12,
ysystemtol,
newton_solver->max_linear_iterations); // max linear iterations
if (!quiet)
libMesh::out << " G_u*y = G_{lambda} solver converged at step "
<< rval.first
<< ", linear tolerance = "
<< rval.second
<< "."
<< std::endl;
// Sometimes (I am not sure why) the linear solver exits after zero iterations.
// Perhaps it is hitting PETSc's divergence tolerance dtol??? If this occurs,
// we should break out of the Newton iteration loop because nothing further is
// going to happen...
if ((rval.first == 0) && (rval.second > ysystemtol))
{
if (!quiet)
libMesh::out << "Linear solver exited in zero iterations!" << std::endl;
break; // out of Newton iterations
}
// ++attempt;
// } while ((attempt<max_attempts) && (rval.first==newton_solver->max_linear_iterations));
// Compute N, the residual of the arclength constraint eqn.
// Note 1: N(u,lambda,s) := (u-u_{old}, du_ds) + (lambda-lambda_{old}, dlambda_ds) - _ds
// We temporarily use the delta_u vector as a temporary vector for this calculation.
*delta_u = *solution;
delta_u->add(-1., *previous_u);
// First part of the arclength constraint
const Number N1 = Theta_LOCA*Theta_LOCA*Theta*delta_u->dot(*du_ds);
const Number N2 = ((*continuation_parameter) - old_continuation_parameter)*dlambda_ds;
const Number N3 = ds_current;
if (!quiet)
{
libMesh::out << " N1=" << N1 << std::endl;
libMesh::out << " N2=" << N2 << std::endl;
libMesh::out << " N3=" << N3 << std::endl;
}
// The arclength constraint value
const Number N = N1+N2-N3;
if (!quiet)
libMesh::out << " N=" << N << std::endl;
const Number duds_dot_z = du_ds->dot(*z);
const Number duds_dot_y = du_ds->dot(*y);
//libMesh::out << "duds_dot_z=" << duds_dot_z << std::endl;
//libMesh::out << "duds_dot_y=" << duds_dot_y << std::endl;
//libMesh::out << "dlambda_ds=" << dlambda_ds << std::endl;
const Number delta_lambda_numerator = -(N + Theta_LOCA*Theta_LOCA*Theta*duds_dot_z);
const Number delta_lambda_denominator = (dlambda_ds - Theta_LOCA*Theta_LOCA*Theta*duds_dot_y);
libmesh_assert_not_equal_to (delta_lambda_denominator, 0.0);
// Now, we are ready to compute the step delta_lambda
const Number delta_lambda_comp = delta_lambda_numerator /
delta_lambda_denominator;
// Lambda is real-valued
const Real delta_lambda = libmesh_real(delta_lambda_comp);
// Knowing delta_lambda, we are ready to update delta_u
// delta_u = z - delta_lambda*y
delta_u->zero();
delta_u->add(1., *z);
delta_u->add(-delta_lambda, *y);
delta_u->close();
// Update the system solution and the continuation parameter.
solution->add(1., *delta_u);
solution->close();
*continuation_parameter += delta_lambda;
// Did the Newton step actually reduce the residual?
rhs_mode = Residual;
assembly(true, // Residual
false); // Jacobian
rhs->close();
nonlinear_residual_afterstep = rhs->l2_norm();
// In a "normal" Newton step, ||du||/||R|| > 1 since the most recent
// step is where you "just were" and the current residual is where
// you are now. It can occur that ||du||/||R|| < 1, but these are
// likely not good cases to attempt backtracking (?).
const Real norm_du_norm_R = delta_u->l2_norm() / nonlinear_residual_afterstep;
if (!quiet)
libMesh::out << " norm_du_norm_R=" << norm_du_norm_R << std::endl;
// Factor to decrease the stepsize by for backtracking
Real newton_stepfactor = 1.;
const bool attempt_backtracking =
(nonlinear_residual_afterstep > solution_tolerance)
&& (nonlinear_residual_afterstep > nonlinear_residual_beforestep)
&& (n_backtrack_steps>0)
&& (norm_du_norm_R > 1.)
;
// If residual is not reduced, do Newton back tracking.
if (attempt_backtracking)
{
if (!quiet)
libMesh::out << "Newton step did not reduce residual." << std::endl;
// back off the previous step.
solution->add(-1., *delta_u);
solution->close();
*continuation_parameter -= delta_lambda;
// Backtracking: start cutting the Newton stepsize by halves until
// the new residual is actually smaller...
for (unsigned int backtrack_step=0; backtrack_step<n_backtrack_steps; ++backtrack_step)
{
newton_stepfactor *= 0.5;
if (!quiet)
libMesh::out << "Shrinking step size by " << newton_stepfactor << std::endl;
// Take fractional step
solution->add(newton_stepfactor, *delta_u);
solution->close();
*continuation_parameter += newton_stepfactor*delta_lambda;
rhs_mode = Residual;
assembly(true, // Residual
false); // Jacobian
rhs->close();
nonlinear_residual_afterstep = rhs->l2_norm();
if (!quiet)
libMesh::out << "At shrink step "
<< backtrack_step
<< ", nonlinear_residual_afterstep="
<< nonlinear_residual_afterstep
<< std::endl;
if (nonlinear_residual_afterstep < nonlinear_residual_beforestep)
{
if (!quiet)
libMesh::out << "Backtracking succeeded!" << std::endl;
break; // out of backtracking loop
}
else
{
// Back off that step
solution->add(-newton_stepfactor, *delta_u);
solution->close();
*continuation_parameter -= newton_stepfactor*delta_lambda;
}
// Save a copy of the solution from before the Newton step.
//AutoPtr<NumericVector<Number> > prior_iterate = solution->clone();
}
} // end if (attempte_backtracking)
// If we tried backtracking but the residual is still not reduced, print message.
if ((attempt_backtracking) && (nonlinear_residual_afterstep > nonlinear_residual_beforestep))
{
//libMesh::err << "Backtracking failed." << std::endl;
libMesh::out << "Backtracking failed." << std::endl;
// 1.) Quit, exit program.
//libmesh_error();
// 2.) Continue with last newton_stepfactor
if (newton_step<3)
{
solution->add(newton_stepfactor, *delta_u);
solution->close();
*continuation_parameter += newton_stepfactor*delta_lambda;
if (!quiet)
libMesh::out << "Backtracking could not reduce residual ... continuing anyway!" << std::endl;
}
// 3.) Break out of Newton iteration loop with newton_converged = false,
// reduce the arclength stepsize, and try again.
else
{
break; // out of Newton iteration loop, with newton_converged=false
}
}
// Another type of convergence check: suppose the residual has not been reduced
// from its initial value after half of the allowed Newton steps have occurred.
// In our experience, this typically means that it isn't going to converge and
// we could probably save time by dropping out of the Newton iteration loop and
// trying a smaller arcstep.
if (this->newton_progress_check)
{
if ((nonlinear_residual_afterstep > nonlinear_residual_firststep) &&
(newton_step+1 > static_cast<unsigned int>(0.5*newton_solver->max_nonlinear_iterations)))
{
libMesh::out << "Progress check failed: the current residual: "
<< nonlinear_residual_afterstep
<< ", is\n"
<< "larger than the initial residual, and half of the allowed\n"
<< "number of Newton iterations have elapsed.\n"
<< "Exiting Newton iterations with converged==false." << std::endl;
break; // out of Newton iteration loop, newton_converged = false
}
}
// Safety check: Check the current continuation parameter against user-provided min-allowable parameter value
if (*continuation_parameter < min_continuation_parameter)
{
libMesh::out << "Continuation parameter fell below min-allowable value." << std::endl;
// libmesh_error();
break; // out of Newton iteration loop, newton_converged = false
}
// Safety check: Check the current continuation parameter against user-provided max-allowable parameter value
if ( (max_continuation_parameter != 0.0) &&
(*continuation_parameter > max_continuation_parameter) )
{
libMesh::out << "Current continuation parameter value: "
<< *continuation_parameter
<< " exceeded max-allowable value."
<< std::endl;
// libmesh_error();
break; // out of Newton iteration loop, newton_converged = false
}
// Check the convergence of the parameter and the solution. If they are small
// enough, we can break out of the Newton iteration loop.
const Real norm_delta_u = delta_u->l2_norm();
const Real norm_u = solution->l2_norm();
libMesh::out << " delta_lambda = " << delta_lambda << std::endl;
libMesh::out << " newton_stepfactor*delta_lambda = " << newton_stepfactor*delta_lambda << std::endl;
libMesh::out << " lambda_current = " << *continuation_parameter << std::endl;
libMesh::out << " ||delta_u|| = " << norm_delta_u << std::endl;
libMesh::out << " ||delta_u||/||u|| = " << norm_delta_u / norm_u << std::endl;
// Evaluate the residual at the current Newton iterate. We don't want to detect
// convergence due to a small Newton step when the residual is still not small.
rhs_mode = Residual;
assembly(true, // Residual
false); // Jacobian
rhs->close();
const Real norm_residual = rhs->l2_norm();
libMesh::out << " ||R||_{L2} = " << norm_residual << std::endl;
libMesh::out << " ||R||_{L2}/||u|| = " << norm_residual / norm_u << std::endl;
// FIXME: The norm_delta_u tolerance (at least) should be relative.
// It doesn't make sense to converge a solution whose size is ~ 10^5 to
// a tolerance of 1.e-6. Oh, and we should also probably check the
// (relative) size of the residual as well, instead of just the step.
if ((std::abs(delta_lambda) < continuation_parameter_tolerance) &&
//(norm_delta_u < solution_tolerance) && // This is a *very* strict criterion we can probably skip
(norm_residual < solution_tolerance))
{
if (!quiet)
libMesh::out << "Newton iterations converged!" << std::endl;
newton_converged = true;
break; // out of Newton iterations
}
} // end nonlinear loop
if (!newton_converged)
{
libMesh::out << "Newton iterations of augmented system did not converge!" << std::endl;
// Reduce ds_current, recompute the solution and parameter, and continue to next
// arcstep, if there is one.
ds_current *= 0.5;
// Go back to previous solution and parameter value.
*solution = *previous_u;
*continuation_parameter = old_continuation_parameter;
// Compute new predictor with smaller ds
apply_predictor();
}
else
{
// Set step convergence and break out
arcstep_converged=true;
break; // out of arclength reduction loop
}
} // end loop over arclength reductions
// Check for convergence of the whole arcstep. If not converged at this
// point, we have no choice but to quit.
if (!arcstep_converged)
{
libMesh::out << "Arcstep failed to converge after max number of reductions! Exiting..." << std::endl;
libmesh_error();
}
// Print converged solution control parameter and max value.
libMesh::out << "lambda_current=" << *continuation_parameter << std::endl;
//libMesh::out << "u_max=" << solution->max() << std::endl;
// Reset old stream precision and flags.
libMesh::out.precision(old_precision);
libMesh::out.unsetf(std::ios_base::scientific);
// Note: we don't want to go on to the next guess yet, since the user may
// want to post-process this data. It's up to the user to call advance_arcstep()
// when they are ready to go on.
}
void RBConstructionBase<Base>::initialize_training_parameters(const RBParameters& mu_min,
const RBParameters& mu_max,
unsigned int n_training_samples,
std::map<std::string,bool> log_param_scale,
bool deterministic)
{
// Print out some info about the training set initialization
libMesh::out << "Initializing training parameters with "
<< (deterministic ? "deterministic " : "random " )
<< "training set..." << std::endl;
{
std::map<std::string,bool>::iterator it = log_param_scale.begin();
std::map<std::string,bool>::const_iterator it_end = log_param_scale.end();
for(; it != it_end; ++it)
{
libMesh::out << "Parameter " << it->first
<< ": log scaling = " << it->second << std::endl;
}
}
libMesh::out << std::endl;
if(deterministic)
{
generate_training_parameters_deterministic(this->comm(),
log_param_scale,
training_parameters,
n_training_samples,
mu_min,
mu_max,
serial_training_set);
}
else
{
// Generate random training samples for all parameters
generate_training_parameters_random(this->comm(),
log_param_scale,
training_parameters,
n_training_samples,
mu_min,
mu_max,
this->training_parameters_random_seed,
serial_training_set);
}
// For each parameter that only allows discrete values, we "snap" to the nearest
// allowable discrete value
if(get_n_discrete_params() > 0)
{
std::map< std::string, NumericVector<Number>* >::iterator it = training_parameters.begin();
std::map< std::string, NumericVector<Number>* >::const_iterator it_end = training_parameters.end();
for( ; it != it_end; ++it)
{
std::string param_name = it->first;
if(is_discrete_parameter(param_name))
{
std::vector<Real> discrete_values =
get_discrete_parameter_values().find(param_name)->second;
NumericVector<Number>* training_vector = it->second;
for(numeric_index_type index=training_vector->first_local_index();
index<training_vector->last_local_index();
index++)
{
Real value = libmesh_real((*training_vector)(index));
Real nearest_discrete_value = get_closest_value(value, discrete_values);
training_vector->set(index, nearest_discrete_value);
}
}
}
}
training_parameters_initialized = true;
}
void AdjointRefinementEstimator::estimate_error (const System& _system,
ErrorVector& error_per_cell,
const NumericVector<Number>* solution_vector,
bool /*estimate_parent_error*/)
{
// We have to break the rules here, because we can't refine a const System
System& system = const_cast<System&>(_system);
// An EquationSystems reference will be convenient.
EquationSystems& es = system.get_equation_systems();
// The current mesh
MeshBase& mesh = es.get_mesh();
// Resize the error_per_cell vector to be
// the number of elements, initialized to 0.
error_per_cell.clear();
error_per_cell.resize (mesh.max_elem_id(), 0.);
// We'll want to back up all coarse grid vectors
std::map<std::string, NumericVector<Number> *> coarse_vectors;
for (System::vectors_iterator vec = system.vectors_begin(); vec !=
system.vectors_end(); ++vec)
{
// The (string) name of this vector
const std::string& var_name = vec->first;
coarse_vectors[var_name] = vec->second->clone().release();
}
// Back up the coarse solution and coarse local solution
NumericVector<Number> * coarse_solution =
system.solution->clone().release();
NumericVector<Number> * coarse_local_solution =
system.current_local_solution->clone().release();
// And make copies of the projected solution
NumericVector<Number> * projected_solution;
// And we'll need to temporarily change solution projection settings
bool old_projection_setting;
old_projection_setting = system.project_solution_on_reinit();
// Make sure the solution is projected when we refine the mesh
system.project_solution_on_reinit() = true;
// And it'll be best to avoid any repartitioning
AutoPtr<Partitioner> old_partitioner = mesh.partitioner();
mesh.partitioner().reset(NULL);
// And we can't allow any renumbering
const bool old_renumbering_setting = mesh.allow_renumbering();
mesh.allow_renumbering(false);
// Use a non-standard solution vector if necessary
if (solution_vector && solution_vector != system.solution.get())
{
NumericVector<Number> *newsol =
const_cast<NumericVector<Number>*> (solution_vector);
newsol->swap(*system.solution);
system.update();
}
#ifndef NDEBUG
// n_coarse_elem is only used in an assertion later so
// avoid declaring it unless asserts are active.
const dof_id_type n_coarse_elem = mesh.n_elem();
#endif
// Uniformly refine the mesh
MeshRefinement mesh_refinement(mesh);
libmesh_assert (number_h_refinements > 0 || number_p_refinements > 0);
// FIXME: this may break if there is more than one System
// on this mesh but estimate_error was still called instead of
// estimate_errors
for (unsigned int i = 0; i != number_h_refinements; ++i)
{
mesh_refinement.uniformly_refine(1);
es.reinit();
}
for (unsigned int i = 0; i != number_p_refinements; ++i)
{
mesh_refinement.uniformly_p_refine(1);
es.reinit();
}
// Copy the projected coarse grid solutions, which will be
// overwritten by solve()
projected_solution = NumericVector<Number>::build(mesh.comm()).release();
projected_solution->init(system.solution->size(), true, SERIAL);
system.solution->localize(*projected_solution,
system.get_dof_map().get_send_list());
// Rebuild the rhs with the projected primal solution
(dynamic_cast<ImplicitSystem&>(system)).assembly(true, false);
NumericVector<Number> & projected_residual = (dynamic_cast<ExplicitSystem&>(system)).get_vector("RHS Vector");
projected_residual.close();
// Solve the adjoint problem on the refined FE space
system.adjoint_solve();
// Now that we have the refined adjoint solution and the projected primal solution,
// we first compute the global QoI error estimate
// Resize the computed_global_QoI_errors vector to hold the error estimates for each QoI
computed_global_QoI_errors.resize(system.qoi.size());
// Loop over all the adjoint solutions and get the QoI error
// contributions from all of them
for (unsigned int j=0; j != system.qoi.size(); j++)
{
computed_global_QoI_errors[j] = projected_residual.dot(system.get_adjoint_solution(j));
}
// Done with the global error estimates, now construct the element wise error indicators
// We ought to account for 'spill-over' effects while computing the
// element error indicators This happens because the same dof is
// shared by multiple elements, one way of mitigating this is to
// scale the contribution from each dof by the number of elements it
// belongs to We first obtain the number of elements each node
// belongs to
// A map that relates a node id to an int that will tell us how many elements it is a node of
LIBMESH_BEST_UNORDERED_MAP<dof_id_type, unsigned int>shared_element_count;
// To fill this map, we will loop over elements, and then in each element, we will loop
// over the nodes each element contains, and then query it for the number of coarse
// grid elements it was a node of
// We will be iterating over all the active elements in the fine mesh that live on
// this processor
MeshBase::const_element_iterator elem_it = mesh.active_local_elements_begin();
const MeshBase::const_element_iterator elem_end = mesh.active_local_elements_end();
// Keep track of which nodes we have already dealt with
LIBMESH_BEST_UNORDERED_SET<dof_id_type> processed_node_ids;
// Start loop over elems
for(; elem_it != elem_end; ++elem_it)
{
// Pointer to this element
const Elem* elem = *elem_it;
// Loop over the nodes in the element
for(unsigned int n=0; n != elem->n_nodes(); ++n)
{
// Get a pointer to the current node
Node* node = elem->get_node(n);
// Get the id of this node
dof_id_type node_id = node->id();
// If we havent already processed this node, do so now
if(processed_node_ids.find(node_id) == processed_node_ids.end())
{
// Declare a neighbor_set to be filled by the find_point_neighbors
std::set<const Elem *> fine_grid_neighbor_set;
// Call find_point_neighbors to fill the neighbor_set
elem->find_point_neighbors(*node, fine_grid_neighbor_set);
// A vector to hold the coarse grid parents neighbors
std::vector<dof_id_type> coarse_grid_neighbors;
// Iterators over the fine grid neighbors set
std::set<const Elem*>::iterator fine_neighbor_it = fine_grid_neighbor_set.begin();
const std::set<const Elem*>::iterator fine_neighbor_end = fine_grid_neighbor_set.end();
// Loop over all the fine neighbors of this node
for(; fine_neighbor_it != fine_neighbor_end ; ++fine_neighbor_it)
{
// Pointer to the current fine neighbor element
const Elem* fine_elem = *fine_neighbor_it;
// Find the element id for the corresponding coarse grid element
const Elem* coarse_elem = fine_elem;
for (unsigned int j = 0; j != number_h_refinements; ++j)
{
libmesh_assert (coarse_elem->parent());
coarse_elem = coarse_elem->parent();
}
// Loop over the existing coarse neighbors and check if this one is
// already in there
const dof_id_type coarse_id = coarse_elem->id();
std::size_t j = 0;
for (; j != coarse_grid_neighbors.size(); j++)
{
// If the set already contains this element break out of the loop
if(coarse_grid_neighbors[j] == coarse_id)
{
break;
}
}
// If we didn't leave the loop even at the last element,
// this is a new neighbour, put in the coarse_grid_neighbor_set
if(j == coarse_grid_neighbors.size())
{
coarse_grid_neighbors.push_back(coarse_id);
}
} // End loop over fine neighbors
// Set the shared_neighbour index for this node to the
// size of the coarse grid neighbor set
shared_element_count[node_id] =
libmesh_cast_int<unsigned int>(coarse_grid_neighbors.size());
// Add this node to processed_node_ids vector
processed_node_ids.insert(node_id);
} // End if not processed node
} // End loop over nodes
} // End loop over elems
// Get a DoF map, will be used to get the nodal dof_indices for each element
DofMap &dof_map = system.get_dof_map();
// The global DOF indices, we will use these later on when we compute the element wise indicators
std::vector<dof_id_type> dof_indices;
// Localize the global rhs and adjoint solution vectors (which might be shared on multiple processsors) onto a
// local ghosted vector, this ensures each processor has all the dof_indices to compute an error indicator for
// an element it owns
AutoPtr<NumericVector<Number> > localized_projected_residual = NumericVector<Number>::build(system.comm());
localized_projected_residual->init(system.n_dofs(), system.n_local_dofs(), system.get_dof_map().get_send_list(), false, GHOSTED);
projected_residual.localize(*localized_projected_residual, system.get_dof_map().get_send_list());
// Each adjoint solution will also require ghosting; for efficiency we'll reuse the same memory
AutoPtr<NumericVector<Number> > localized_adjoint_solution = NumericVector<Number>::build(system.comm());
localized_adjoint_solution->init(system.n_dofs(), system.n_local_dofs(), system.get_dof_map().get_send_list(), false, GHOSTED);
// We will loop over each adjoint solution, localize that adjoint
// solution and then loop over local elements
for (unsigned int i=0; i != system.qoi.size(); i++)
{
// Skip this QoI if not in the QoI Set
if (_qoi_set.has_index(i))
{
// Get the weight for the current QoI
Real error_weight = _qoi_set.weight(i);
(system.get_adjoint_solution(i)).localize(*localized_adjoint_solution, system.get_dof_map().get_send_list());
// Loop over elements
MeshBase::const_element_iterator elem_it = mesh.active_local_elements_begin();
const MeshBase::const_element_iterator elem_end = mesh.active_local_elements_end();
for(; elem_it != elem_end; ++elem_it)
{
// Pointer to the element
const Elem* elem = *elem_it;
// Go up number_h_refinements levels up to find the coarse parent
const Elem* coarse = elem;
for (unsigned int j = 0; j != number_h_refinements; ++j)
{
libmesh_assert (coarse->parent());
coarse = coarse->parent();
}
const dof_id_type e_id = coarse->id();
// Get the local to global degree of freedom maps for this element
dof_map.dof_indices (elem, dof_indices);
// We will have to manually do the dot products.
Number local_contribution = 0.;
for (unsigned int j=0; j != dof_indices.size(); j++)
{
// The contribution to the error indicator for this element from the current QoI
local_contribution += (*localized_projected_residual)(dof_indices[j]) * (*localized_adjoint_solution)(dof_indices[j]);
}
// Multiply by the error weight for this QoI
local_contribution *= error_weight;
// FIXME: we're throwing away information in the
// --enable-complex case
error_per_cell[e_id] += static_cast<ErrorVectorReal>
(libmesh_real(local_contribution));
} // End loop over elements
} // End if belong to QoI set
} // End loop over QoIs
// Don't bother projecting the solution; we'll restore from backup
// after coarsening
system.project_solution_on_reinit() = false;
// Uniformly coarsen the mesh, without projecting the solution
libmesh_assert (number_h_refinements > 0 || number_p_refinements > 0);
for (unsigned int i = 0; i != number_h_refinements; ++i)
{
mesh_refinement.uniformly_coarsen(1);
// FIXME - should the reinits here be necessary? - RHS
es.reinit();
}
for (unsigned int i = 0; i != number_p_refinements; ++i)
{
mesh_refinement.uniformly_p_coarsen(1);
es.reinit();
}
// We should be back where we started
libmesh_assert_equal_to (n_coarse_elem, mesh.n_elem());
// Restore old solutions and clean up the heap
system.project_solution_on_reinit() = old_projection_setting;
// Restore the coarse solution vectors and delete their copies
*system.solution = *coarse_solution;
delete coarse_solution;
*system.current_local_solution = *coarse_local_solution;
delete coarse_local_solution;
delete projected_solution;
for (System::vectors_iterator vec = system.vectors_begin(); vec !=
system.vectors_end(); ++vec)
{
// The (string) name of this vector
const std::string& var_name = vec->first;
// If it's a vector we already had (and not a newly created
// vector like an adjoint rhs), we need to restore it.
std::map<std::string, NumericVector<Number> *>::iterator it =
coarse_vectors.find(var_name);
if (it != coarse_vectors.end())
{
NumericVector<Number> *coarsevec = it->second;
system.get_vector(var_name) = *coarsevec;
coarsevec->clear();
delete coarsevec;
}
}
// Restore old partitioner and renumbering settings
mesh.partitioner() = old_partitioner;
mesh.allow_renumbering(old_renumbering_setting);
// Fiinally sum the vector of estimated error values.
this->reduce_error(error_per_cell, system.comm());
// We don't take a square root here; this is a goal-oriented
// estimate not a Hilbert norm estimate.
} // end estimate_error function
void EnsightIO::write_vector_ascii(const std::string &sys, const std::vector<std::string> &vec, const std::string &var_name)
{
std::ostringstream vec_file;
vec_file<<_ensight_file_name<<"_"<<var_name<<".vec";
vec_file << std::setw(3)
<< std::setprecision(0)
<< std::setfill('0')
<< std::right
<< _time_steps.size()-1;
FILE * fout = fopen(vec_file.str().c_str(),"w");
fprintf(fout,"Per vector per value\n");
fprintf(fout,"part\n");
fprintf(fout,"%10d\n",1);
fprintf(fout,"coordinates\n");
// Get a constant reference to the mesh object.
const MeshBase& the_mesh = MeshOutput<MeshBase>::mesh();
// The dimension that we are running
const unsigned int dim = the_mesh.mesh_dimension();
const System &system = _equation_systems.get_system(sys);
const DofMap& dof_map = system.get_dof_map();
const unsigned int u_var = system.variable_number(vec[0]);
const unsigned int v_var = system.variable_number(vec[1]);
const unsigned int w_var = (dim==3) ? system.variable_number(vec[2]) : 0;
std::vector<dof_id_type> dof_indices;
std::vector<dof_id_type> dof_indices_u;
std::vector<dof_id_type> dof_indices_v;
std::vector<dof_id_type> dof_indices_w;
// Now we will loop over all the elements in the mesh.
MeshBase::const_element_iterator el = the_mesh.active_local_elements_begin();
const MeshBase::const_element_iterator end_el = the_mesh.active_local_elements_end();
typedef std::map<int,std::vector<Real> > map_local_soln;
typedef map_local_soln::iterator local_soln_iterator;
map_local_soln local_soln;
for ( ; el != end_el ; ++el){
const Elem* elem = *el;
const FEType& fe_type = system.variable_type(u_var);
dof_map.dof_indices (elem, dof_indices);
dof_map.dof_indices (elem, dof_indices_u,u_var);
dof_map.dof_indices (elem, dof_indices_v,v_var);
if(dim==3) dof_map.dof_indices (elem, dof_indices,w_var);
std::vector<Number> elem_soln_u;
std::vector<Number> elem_soln_v;
std::vector<Number> elem_soln_w;
std::vector<Number> nodal_soln_u;
std::vector<Number> nodal_soln_v;
std::vector<Number> nodal_soln_w;
elem_soln_u.resize(dof_indices_u.size());
elem_soln_v.resize(dof_indices_v.size());
if(dim == 3) elem_soln_w.resize(dof_indices_w.size());
for (unsigned int i = 0; i < dof_indices_u.size(); i++)
{
elem_soln_u[i] = system.current_solution(dof_indices_u[i]);
elem_soln_v[i] = system.current_solution(dof_indices_v[i]);
if(dim==3) elem_soln_w[i] = system.current_solution(dof_indices_w[i]);
}
FEInterface::nodal_soln (dim,fe_type,elem,elem_soln_u,nodal_soln_u);
FEInterface::nodal_soln (dim,fe_type,elem,elem_soln_v,nodal_soln_v);
if(dim == 3) FEInterface::nodal_soln (dim,fe_type,elem,elem_soln_w,nodal_soln_w);
libmesh_assert_equal_to (nodal_soln_u.size(), elem->n_nodes());
libmesh_assert_equal_to (nodal_soln_v.size(), elem->n_nodes());
#ifdef LIBMESH_ENABLE_COMPLEX
libMesh::err << "Complex-valued Ensight output not yet supported" << std::endl;
libmesh_not_implemented()
#endif
for (unsigned int n=0; n<elem->n_nodes(); n++)
{
std::vector<Real> node_vec(3);
node_vec[0]= libmesh_real(nodal_soln_u[n]);
node_vec[1]= libmesh_real(nodal_soln_v[n]);
node_vec[2]=0.0;
if(dim==3) node_vec[2]= libmesh_real(nodal_soln_w[n]);
local_soln[elem->node(n)] = node_vec;
}
}
local_soln_iterator sol = local_soln.begin();
const local_soln_iterator sol_end = local_soln.end();
for(; sol != sol_end; ++sol)
fprintf(fout,"%12.5e\n",static_cast<double>((*sol).second[0]));
sol = local_soln.begin();
for(; sol != sol_end; ++sol)
fprintf(fout,"%12.5e\n",static_cast<double>((*sol).second[1]));
sol = local_soln.begin();
for(; sol != sol_end; ++sol)
fprintf(fout,"%12.5e\n",static_cast<double>((*sol).second[2]));
fclose(fout);
}
void EnsightIO::write_scalar_ascii(const std::string &sys, const std::string &var_name)
{
std::ostringstream scl_file;
scl_file << _ensight_file_name << "_" << var_name << ".scl";
scl_file << std::setw(3)
<< std::setprecision(0)
<< std::setfill('0')
<< std::right
<< _time_steps.size()-1;
FILE * fout = fopen(scl_file.str().c_str(),"w");
fprintf(fout,"Per node scalar value\n");
fprintf(fout,"part\n");
fprintf(fout,"%10d\n",1);
fprintf(fout,"coordinates\n");
const MeshBase& the_mesh = MeshOutput<MeshBase>::mesh();
const unsigned int dim = the_mesh.mesh_dimension();
const System &system = _equation_systems.get_system(sys);
const DofMap& dof_map = system.get_dof_map();
int var = system.variable_number(var_name);
std::vector<dof_id_type> dof_indices;
std::vector<dof_id_type> dof_indices_scl;
// Now we will loop over all the elements in the mesh.
MeshBase::const_element_iterator el = the_mesh.active_local_elements_begin();
const MeshBase::const_element_iterator end_el = the_mesh.active_local_elements_end();
typedef std::map<int,Real> map_local_soln;
typedef map_local_soln::iterator local_soln_iterator;
map_local_soln local_soln;
std::vector<Number> elem_soln;
std::vector<Number> nodal_soln;
for ( ; el != end_el ; ++el){
const Elem* elem = *el;
const FEType& fe_type = system.variable_type(var);
dof_map.dof_indices (elem, dof_indices);
dof_map.dof_indices (elem, dof_indices_scl, var);
elem_soln.resize(dof_indices_scl.size());
for (unsigned int i = 0; i < dof_indices_scl.size(); i++)
elem_soln[i] = system.current_solution(dof_indices_scl[i]);
FEInterface::nodal_soln (dim,fe_type, elem, elem_soln, nodal_soln);
libmesh_assert_equal_to (nodal_soln.size(), elem->n_nodes());
#ifdef LIBMESH_USE_COMPLEX_NUMBERS
libMesh::err << "Complex-valued Ensight output not yet supported" << std::endl;
libmesh_not_implemented();
#endif
for (unsigned int n=0; n<elem->n_nodes(); n++)
local_soln[elem->node(n)] = libmesh_real(nodal_soln[n]);
}
local_soln_iterator sol = local_soln.begin();
const local_soln_iterator sol_end = local_soln.end();
for(; sol != sol_end; ++sol)
fprintf(fout,"%12.5e\n",static_cast<double>((*sol).second));
fclose(fout);
}