#include <high_order_grid.h>

Collaboration diagram for PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >:

Public Member Functions
	HighOrderGrid (const unsigned int max_degree, const std::shared_ptr< MeshType > triangulation_input, const bool check_valid_metric_Jacobian_input=true, const bool renumber_dof_handler_Cuthill_Mckee_input=true, const bool output_high_order_grid=true)
	Principal constructor that will call delegated constructor.

void	reinit ()
	Reinitialize high_order_grid after a change in triangulation.

void	update_mapping_fe_field ()
	Update the MappingFEField. More...

void	ensure_conforming_mesh ()
	Ensures that hanging nodes are updated for a conforming mesh.

void	initialize_with_triangulation_manifold (const bool output_mesh=true)
	Sets the volume_nodes to the interpolated position of the Manifold associated to the triangulation.

void	allocate ()
	Needed to allocate the correct number of volume_nodes when initializing and after the mesh is refined.

dealii::MappingFEField< dim, dim, VectorType, DoFHandlerType >	get_MappingFEField ()
	Return a MappingFEField that corresponds to the current node locations.

void	reset_initial_nodes ()
	Sets the initial_volume_nodes and initial_surface_nodes to the current volume_nodes and surface_nodes.

void	update_map_nodes_surf_to_vol ()
	Sets the initial_volume_nodes and initial_surface_nodes to the current volume_nodes and surface_nodes.

void	update_surface_nodes ()
	Update list of surface nodes (all_locally_relevant_surface_nodes). More...

VectorType	transform_surface_nodes (std::function< dealii::Point< dim >(dealii::Point< dim >)> transformation) const

void	deform_mesh (std::vector< real > local_surface_displacements)
	RBF mesh deformation - To be done.

void	test_jacobian ()
	Test metric Jacobian.

std::vector< real >	evaluate_jacobian_at_points (const VectorType &solution, const typename DoFHandlerType::cell_iterator &cell, const std::vector< dealii::Point< dim >> &points) const
	Evaluates Jacobian of a cell given some points using a global solution vector.

template<typename real2 >
void	evaluate_jacobian_at_points (const std::vector< real2 > &dofs, const dealii::FESystem< dim > &fe, const std::vector< dealii::Point< dim >> &points, std::vector< real2 > &jacobian_determinants) const
	Evaluates Jacobian given some DoF, associated FE, and some points. More...

template<typename real2 >
real2	evaluate_jacobian_at_point (const std::vector< real2 > &dofs, const dealii::FESystem< dim > &fe, const dealii::Point< dim > &point) const
	Evaluates Jacobian given some DoF, associated FE, and some point. More...

bool	check_valid_cell (const typename DoFHandlerType::cell_iterator &cell) const
	Evaluate exact Jacobian determinant polynomial and uses Bernstein polynomials to determine positivity.

bool	fix_invalid_cell (const typename DoFHandlerType::cell_iterator &cell)
	Evaluate exact Jacobian determinant polynomial and uses Bernstein polynomials to determine positivity.

void	evaluate_lagrange_to_bernstein_operator (const unsigned int order)
	Evaluates the operator to obtain Bernstein coefficients from a set of Lagrange coefficients. More...

void	output_results_vtk (const unsigned int cycle) const
	Output mesh with metric informations.

void	refine_global ()
	Globally refines the high-order mesh. More...

void	prepare_for_coarsening_and_refinement ()
	Prepares the solution transfer such that the curved refined grid is on top of the curved coarse grid. More...

void	execute_coarsening_and_refinement (const bool output_mesh=false)
	Executes the solution transfer such that the curved refined grid is on top of the curved coarse grid. More...

Public Attributes
const unsigned int	max_degree
	Maximum degree of the geometry polynomial representing the grid.

const std::shared_ptr< MeshType >	triangulation
	Mesh.

const bool	check_valid_metric_Jacobian
	Flag to check validity of Jacobian.

const bool	renumber_dof_handler_Cuthill_Mckee
	Flag to renumber dof_handler_grid with Cuthill Mckee.

dealii::DoFHandler< dim >	dof_handler_grid
	Degrees of freedom handler for the high-order grid.

VectorType	volume_nodes
	Current nodal coefficients of the high-order grid. More...

VectorType	surface_nodes

VectorType	initial_volume_nodes
	Initial nodal coefficients of the high-order grid. More...

VectorType	initial_surface_nodes
	Distributed ghosted vector of initial surface nodes. More...

dealii::LinearAlgebra::distributed::Vector< int >	surface_to_volume_indices

dealii::TrilinosWrappers::SparseMatrix	map_nodes_surf_to_vol

dealii::IndexSet	locally_owned_surface_nodes_indexset

dealii::IndexSet	ghost_surface_nodes_indexset

std::vector< unsigned int >	n_locally_owned_surface_nodes_per_mpi

std::vector< real >	locally_relevant_surface_nodes
	List of surface nodes. More...

std::vector< dealii::types::global_dof_index >	locally_relevant_surface_nodes_indices
	List of surface node indices.

std::vector< dealii::types::global_dof_index >	locally_relevant_surface_nodes_boundary_id
	List of surface node boundary IDs, corresponding to locally_relevant_surface_nodes_indices.

std::vector< real >	locally_owned_surface_nodes
	List of surface nodes. More...

std::vector< real >	all_surface_nodes
	List of all surface nodes. More...

std::vector< dealii::types::global_dof_index >	all_surface_indices

std::vector< dealii::types::global_dof_index >	locally_owned_surface_nodes_indices
	List of surface node indices.

std::vector< dealii::Point< dim > >	locally_relevant_surface_points
	Locally relevant surface points. More...

std::vector< dealii::Point< dim > >	initial_locally_relevant_surface_points
	Initial locally relevant surface points. More...

std::map< dealii::types::global_dof_index, std::pair< unsigned int, unsigned int > >	global_index_to_point_and_axis

std::map< std::pair< unsigned int, unsigned int >, dealii::types::global_dof_index >	point_and_axis_to_global_index

dealii::FullMatrix< double >	lagrange_to_bernstein_operator
	Used to transform coefficients from a Lagrange basis to a Bernstein basis.

const dealii::FE_Q< dim >	fe_q
	Use Lagrange polynomial to represent the spatial location.

const dealii::FESystem< dim >	fe_system
	Using system of polynomials to represent the x, y, and z directions.

const dealii::FE_DGQ< 1 >	oneD_fe_q
	Use oneD Lagrange polynomial to represent the spatial location. More...

const dealii::FESystem< 1 >	oneD_fe_system
	One-dimensional fe system for each direction.

const dealii::QGaussLobatto< 1 >	oneD_grid_nodes
	One Dimensional grid nodes in reference space.

const dealii::QGaussLobatto< dim >	dim_grid_nodes
	Dim-Dimensional grid nodes in reference space.

std::shared_ptr< dealii::MappingFEField< dim, dim, VectorType, DoFHandlerType > >	mapping_fe_field
	MappingFEField that will provide the polynomial-based grid. More...

std::shared_ptr< dealii::MappingFEField< dim, dim, VectorType, DoFHandlerType > >	initial_mapping_fe_field
	MappingFEField that will provide the polynomial-based grid for the initial volume_nodes. More...

dealii::IndexSet	locally_owned_dofs_grid
	Locally own degrees of freedom for the grid.

dealii::IndexSet	ghost_dofs_grid
	Locally relevant ghost degrees of freedom for the grid.

dealii::IndexSet	locally_relevant_dofs_grid
	Union of locally owned degrees of freedom and relevant ghost degrees of freedom for the grid.

Static Public Attributes
static unsigned int	nth_refinement =0
	Used to name the various files outputted.

Protected Member Functions
void	update_surface_indices ()
	Update list of surface indices (locally_relevant_surface_nodes_indices and locally_relevant_surface_nodes_boundary_id)

template<typename real2 >
real2	determinant (const std::array< dealii::Tensor< 1, dim, real2 >, dim > jacobian) const
	Evaluate the determinant of a matrix given in the format of a std::array<dealii::Tensor<1,dim,real2>,dim>. More...

void	get_position_vector (const DoFHandlerType &dh, VectorType &vector, const dealii::ComponentMask &mask)
	A stripped down copy of dealii::VectorTools::get_position_vector()

void	get_projected_position_vector (const DoFHandlerType &dh, VectorType &vector, const dealii::ComponentMask &mask)

Protected Attributes
int	n_mpi
	Number of MPI processes.

int	mpi_rank

VectorType	old_volume_nodes
	Used for the SolutionTransfer when performing grid adaptation.

SolutionTransfer	solution_transfer

MPI_Comm	mpi_communicator
	MPI communicator.

dealii::ConditionalOStream	pcout
	Parallel std::cout that only outputs on mpi_rank==0.

Private Types
using	SolutionTransfer = typename MeshTypeHelper< MeshType >::template SolutionTransfer< dim, VectorType, DoFHandlerType >

Detailed Description

template<int dim = PHILIP_DIM, typename real = double, typename MeshType = dealii::parallel::distributed::Triangulation<dim>, typename VectorType = typename MeshTypeHelper<MeshType>::VectorType, typename DoFHandlerType = typename MeshTypeHelper<MeshType>::DoFHandlerType>
class PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >

This HighOrderGrid class basically contains all the different part necessary to generate a dealii::MappingFEField that corresponds to the current Triangulation and attached Manifold. Once the high order grid is generated, the mesh can be deformed by assigning different values to the volume_nodes vector. The dof_handler_grid is used to access and loop through those volume_nodes. This will especially be useful when performing shape optimization, where the surface and volume volume_nodes will need to be displaced. Note that there are a lot of pre-processor statements, and that is because the SolutionTransfer class and the Vector class act quite differently between serial and parallel implementation. Hopefully, deal.II will change this one day such that we have one interface for both.

Definition at line 130 of file high_order_grid.h.

Member Function Documentation

◆ determinant()

template<int dim, typename real , typename MeshType , typename VectorType , typename DoFHandlerType >

template<typename real2 >

real2 PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >::determinant ( const std::array< dealii::Tensor< 1, dim, real2 >, dim > jacobian ) const

inlineprotected

Evaluate the determinant of a matrix given in the format of a std::array<dealii::Tensor<1,dim,real2>,dim>.

The indices of the array represent the matrix rows, and the indices of the Tensor represents its columns.

Definition at line 439 of file high_order_grid.cpp.

◆ evaluate_jacobian_at_point()

template<int dim, typename real , typename MeshType , typename VectorType , typename DoFHandlerType >

template<typename real2 >

real2 PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >::evaluate_jacobian_at_point	(	const std::vector< real2 > &	dofs,
		const dealii::FESystem< dim > &	fe,
		const dealii::Point< dim > &	point
	)		const

Evaluates Jacobian given some DoF, associated FE, and some point.

Can be used in conjunction with AD since the type is templated.

Definition at line 504 of file high_order_grid.cpp.

◆ evaluate_jacobian_at_points()

template<int dim, typename real , typename MeshType , typename VectorType , typename DoFHandlerType >

template<typename real2 >

void PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >::evaluate_jacobian_at_points	(	const std::vector< real2 > &	dofs,
		const dealii::FESystem< dim > &	fe,
		const std::vector< dealii::Point< dim >> &	points,
		std::vector< real2 > &	jacobian_determinants
	)		const

Evaluates Jacobian given some DoF, associated FE, and some points.

Calls evaluate_jacobian_at_point() on the vector of points. Can be used in conjunction with AD since the type is templated.

Definition at line 524 of file high_order_grid.cpp.

◆ evaluate_lagrange_to_bernstein_operator()

template<int dim, typename real , typename MeshType , typename VectorType , typename DoFHandlerType >

void PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >::evaluate_lagrange_to_bernstein_operator ( const unsigned int order )

Evaluates the operator to obtain Bernstein coefficients from a set of Lagrange coefficients.

This is used in the evaluation of the Jacobian positivity by checking the convex hull of the resulting Bezier curve.

Definition at line 555 of file high_order_grid.cpp.

◆ execute_coarsening_and_refinement()

template<int dim, typename real , typename MeshType , typename VectorType , typename DoFHandlerType >

void PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >::execute_coarsening_and_refinement ( const bool output_mesh = false )

Executes the solution transfer such that the curved refined grid is on top of the curved coarse grid.

This function needs to be after this->prepare_for_coarsening_and_refinement() and dealii::Triangulation::execute_coarsening_and_refinement() or dealii::Triangulation::refine_global().

Definition at line 1034 of file high_order_grid.cpp.

◆ get_projected_position_vector()

template<int dim, typename real , typename MeshType , typename VectorType , typename DoFHandlerType >

void PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >::get_projected_position_vector	(	const DoFHandlerType &	dh,
		VectorType &	vector,
		const dealii::ComponentMask &	mask
	)

protected

Another version of dealii::VectorTools::get_position_vector() that projects the points instead of interpolating them.

Definition at line 274 of file high_order_grid.cpp.

◆ prepare_for_coarsening_and_refinement()

template<int dim, typename real , typename MeshType , typename VectorType , typename DoFHandlerType >

void PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >::prepare_for_coarsening_and_refinement ( )

Prepares the solution transfer such that the curved refined grid is on top of the curved coarse grid.

This function needs to be called before dealii::Triangulation::execute_coarsening_and_refinement() or dealii::Triangulation::refine_global() and this->execute_coarsening_and_refinement().

Definition at line 1025 of file high_order_grid.cpp.

◆ refine_global()

template<int dim, typename real , typename MeshType , typename VectorType , typename DoFHandlerType >

void PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >::refine_global ( )

Globally refines the high-order mesh.

The metric Jacobian is given by the gradient of the physical location with respect to the reference locations

Definition at line 1016 of file high_order_grid.cpp.

◆ transform_surface_nodes()

template<int dim, typename real , typename MeshType , typename VectorType , typename DoFHandlerType >

VectorType PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >::transform_surface_nodes ( std::function< dealii::Point< dim >(dealii::Point< dim >)> transformation ) const

Transforms the surface_nodes vector using a std::function tranformation.

Definition at line 1358 of file high_order_grid.cpp.

◆ update_mapping_fe_field()

template<int dim, typename real , typename MeshType , typename VectorType , typename DoFHandlerType >

void PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >::update_mapping_fe_field ( )

Update the MappingFEField.

Note that this rarely needs to be called since MappingFEField stores a pointer to the DoFHandler and to the node Vector.

Definition at line 186 of file high_order_grid.cpp.

◆ update_surface_nodes()

template<int dim, typename real , typename MeshType , typename VectorType , typename DoFHandlerType >

void PHiLiP::HighOrderGrid< dim, real, MeshType, VectorType, DoFHandlerType >::update_surface_nodes ( )

Update list of surface nodes (all_locally_relevant_surface_nodes).

Given the Point index within the locally_relevant_surface_points and its component, this will return the index of the surface_nodes' index. This allows us to obtain a deformation vector matching the locally_relevant_surface_points, and then copy its results to the surface_nodes.

Definition at line 1088 of file high_order_grid.cpp.