PHiLiP::AnisotropicMeshAdaptation< dim, nstate, real, MeshType > Class Template Reference

#include <anisotropic_mesh_adaptation.h>

Collaboration diagram for PHiLiP::AnisotropicMeshAdaptation< dim, nstate, real, MeshType >:

Public Member Functions
	AnisotropicMeshAdaptation (std::shared_ptr< DGBase< dim, real, MeshType > > dg_input, const real _norm_Lp, const real _complexity, const bool _use_goal_oriented_approach=false)
	Constructor.
void	adapt_mesh ()
	Function which adapts mesh and loads in new mesh.

Private Types
using	VectorType = dealii::LinearAlgebra::distributed::Vector< double >
	Alias for dealii's parallel distributed vector.

Private Member Functions
dealii::Tensor< 2, dim, real >	get_positive_definite_tensor (const dealii::Tensor< 2, dim, real > &input_tensor) const
	Returns positive tensor from an input tensor by taking absolute of eigenvalues.
void	compute_cellwise_optimal_metric ()
	Computes optimal metric depending on goal oriented or feature based approach.
void	compute_abs_hessian ()
	Computes hessian using the input coefficients, which can be a solution sensor or (for goal oriented approach) convective flux. More...
void	initialize_cellwise_metric_and_hessians ()
	Initializes cellwise metric and hessian to zero tensors.
void	compute_feature_based_hessian ()
	Computes feature based hessian (i.e. hessian of the solution).
void	compute_goal_oriented_hessian ()
	Computes pseudo Hessian for the goal oriented approach.
void	change_p_degree_and_interpolate_solution (const unsigned int poly_degree)
	Change the polynomial order and interpolate solution.
void	reconstruct_p2_solution ()
	Reconstructs p2 solution after interpolation. More...
unsigned int	get_iquad_near_cellcenter (const dealii::Quadrature< dim > &volume_quadrature) const
	Returns quadrature number of a point which is closest to the reference cell's center.
void	get_flux_at_support_pts (std::vector< std::array< dealii::Tensor< 1, dim, real >, nstate >> &flux_at_support_pts, const dealii::FEValues< dim, dim > &fe_values_input, const std::vector< dealii::types::global_dof_index > &dof_indices, typename dealii::DoFHandler< dim >::active_cell_iterator cell) const
	Returns flux coeffs by evaluating flux at support points of fe. More...

Private Attributes
std::shared_ptr< DGBase< dim, real, MeshType > >	dg
	Shared pointer to DGBase.
const bool	use_goal_oriented_approach
	Flag to use goal oriented approach. It is set to false by default.
std::vector< dealii::Tensor< 2, dim, real > >	cellwise_hessian
	Stores hessian in each cell.
const real	normLp
	Lp Norm w.r.t. which the anlytical optimization is done.
const real	complexity
	Analogue of number of vertices/elements in continuous mesh framework.
MPI_Comm	mpi_communicator
	Alias for MPI_COMM_WORLD.
dealii::ConditionalOStream	pcout
	std::cout only on processor #0.
int	mpi_rank
	Processor# of current processor.
int	n_mpi
	Total no. of processors.
const unsigned int	initial_poly_degree
	Stores initial polynomial degree.
std::shared_ptr< Physics::PhysicsBase< dim, nstate, real > >	pde_physics_double
	Contains the physics of the PDE with real type.
std::shared_ptr< Functional< dim, nstate, real, MeshType > >	functional
	Functional to evaluate the adjoint for goal oriented anisotropic meshing.
std::vector< dealii::Tensor< 2, dim, real > >	cellwise_optimal_metric
	Stores optimal metric in each cell.
const unsigned int	max_dofs_per_cell
	Stores max dofs per cell to initialize dof_indices.

Detailed Description

template<int dim, int nstate, typename real, typename MeshType = dealii::parallel::distributed::Triangulation<dim>>
class PHiLiP::AnisotropicMeshAdaptation< dim, nstate, real, MeshType >

Performs anisotropic mesh adaptation with an optimal metric for P1 solution. Implements the optimal metric field derived from continuous optimization framework. See papers from INRIA for further details: Feature based : Loseille, A. and Alauzet, F. "Continuous mesh framework part I: well-posed continuous interpolation error.", 2011. Goal oriented: Loseille, A., Dervieux, A., and Alauzet, F. "Fully anisotropic goal-oriented mesh adaptation for 3d steady Euler equations.", 2010.

Note

The goal oriented approach is currently implemented for convection dominated flows.

Definition at line 22 of file anisotropic_mesh_adaptation.h.

Member Function Documentation

compute_abs_hessian()

template<int dim, int nstate, typename real , typename MeshType >

void PHiLiP::AnisotropicMeshAdaptation< dim, nstate, real, MeshType >::compute_abs_hessian ( )

private

Computes hessian using the input coefficients, which can be a solution sensor or (for goal oriented approach) convective flux.

This function is called by compute_optimal_metric().

Definition at line 198 of file anisotropic_mesh_adaptation.cpp.

get_flux_at_support_pts()

template<int dim, int nstate, typename real , typename MeshType >

void PHiLiP::AnisotropicMeshAdaptation< dim, nstate, real, MeshType >::get_flux_at_support_pts ( std::vector< std::array< dealii::Tensor< 1, dim, real >, nstate >> &  flux_at_support_pts, const dealii::FEValues< dim, dim > &  fe_values_input, const std::vector< dealii::types::global_dof_index > &  dof_indices, typename dealii::DoFHandler< dim >::active_cell_iterator  cell  ) const

private

Returns flux coeffs by evaluating flux at support points of fe.

Referenced by flux[idof][istate][idim]

Definition at line 422 of file anisotropic_mesh_adaptation.cpp.

reconstruct_p2_solution()

template<int dim, int nstate, typename real , typename MeshType >

void PHiLiP::AnisotropicMeshAdaptation< dim, nstate, real, MeshType >::reconstruct_p2_solution ( )

private

Reconstructs p2 solution after interpolation.

Currenlty done using 1 linear solve of the implicit system.

Definition at line 251 of file anisotropic_mesh_adaptation.cpp.

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

• src/mesh/mesh_adaptation/anisotropic_mesh_adaptation.h
• src/mesh/mesh_adaptation/anisotropic_mesh_adaptation.cpp