Manicore::DDR_Spaces< dimension > Class Template Reference

Implement the discrete operators of DDR-PEC. More...

#include <ddr_spaces.hpp>

Inheritance diagram for Manicore::DDR_Spaces< dimension >:

Public Types
template<size_t k>
using	FunctionType = std::function< Eigen::Vector< double, Dimension::ExtDim(k, dimension)>(size_t map_id, const Eigen::Vector< double, dimension > &)>
	Signature of the function to use in interpolate. More...

Public Member Functions
	DDR_Spaces (Mesh< dimension > const &mesh, int r, bool use_threads=true, std::array< int, dimension > const *dqr_p=nullptr, std::ostream &output=std::cout)
template<size_t k>
Eigen::VectorXd	interpolate (FunctionType< k > const &func, std::array< int, dimension > const *dqr_p=nullptr) const
	Interpolate the given function on the discrete spaces. More...
const Eigen::MatrixXd &	full_diff (size_t k, size_t d, size_t i_cell) const
	Compute the full differential operator. More...
Eigen::MatrixXd	compose_diff (size_t k, size_t d, size_t i_cell) const
	Compute the projected differential operator. More...
const Eigen::MatrixXd &	potential (size_t k, size_t d, size_t i_cell) const
	Compute the potential operator. More...
DOFSpace< dimension > const &	dofspace (size_t k) const
	Return DOFSpace associated to k forms. More...
const Mesh< dimension > *	mesh () const
	Return the Mesh associated with the class. More...
int	degree () const
	Return the polynomial degree associated with the class. More...
Eigen::MatrixXd	computeL2Product (size_t k, size_t i_cell) const
	Compute the local \(L^2\) product (including the cell boundary) More...
double	hmax () const
	Return the mesh size. More...

Detailed Description

template<size_t dimension>
class Manicore::DDR_Spaces< dimension >

Implement the discrete operators of DDR-PEC.

Interpolator, discrete differential and potential reconstruction.

This class compute store a matrix for each operator on each cell. It also create and store the corresponding PEC object (holding the masses and traces of the cells)

Template Parameters

dimension

Dimension of the manifold

Warning

This does not take ownership of the mesh but keep a pointer of it. Ensure that the mesh survives this class.

Member Typedef Documentation

FunctionType

template<size_t dimension>

template<size_t k>

using Manicore::DDR_Spaces< dimension >::FunctionType = std::function<Eigen::Vector<double,Dimension::ExtDim(k,dimension)>(size_t map_id, const Eigen::Vector<double,dimension> &)>

Signature of the function to use in interpolate.

Template Parameters

k	Form degree

Constructor & Destructor Documentation

DDR_Spaces()

template<size_t dimension>

DDR_Spaces::DDR_Spaces	(	Mesh< dimension > const &	mesh,
		int	r,
		bool	use_threads = true,
		std::array< int, dimension > const *	dqr_p = nullptr,
		std::ostream &	output = std::cout
	)

Warning

Ensure that the mesh survives this class

Parameters

mesh	Mesh to use
r	Polynomial degree
use_threads	Enable pthreads parallelism
dqr_p	Degree of quadrature used to generate the mass matrices. It cannot be exact for generic metric and default to a pretty high degree. Use a lower degree if the metric and cells are almost flat.
output	Output stream for status messages.

Member Function Documentation

compose_diff()

template<size_t dimension>

Eigen::MatrixXd DDR_Spaces::compose_diff	(	size_t	k,
		size_t	d,
		size_t	i_cell
	)		const

Compute the projected differential operator.

Returns

\(\star \underline{d}_r^k\) on a cell including its boundary in \(\cup_{d' = k}^{d} \mathcal{P}_r\Lambda^{d-k-1}(\mathbb{R}^{d'})\)

Parameters

k	Form degree
d	Cell dimension
i_cell	Cell index

computeL2Product()

template<size_t dimension>

Eigen::MatrixXd DDR_Spaces::computeL2Product	(	size_t	k,
		size_t	i_cell
	)		const

Compute the local \(L^2\) product (including the cell boundary)

The contribution on the cell is \(\int_f \langle P^k , P^k \rangle \text{vol}_f \). The contribution from a cell \(f' \in \partial f \) of the boundary is \(\int_f \langle \text{tr}_{f'} P^k_f - P^k_{f'} , \text{tr}_{f'} P^k_f - P^k_{f'} \rangle \text{vol}_{f'} \) multiplied by a scaling factor.

Parameters

k	Form degree
i_cell	Cell index

degree()

template<size_t dimension>

int Manicore::DDR_Spaces< dimension >::degree ( ) const

inline

Return the polynomial degree associated with the class.

dofspace()

template<size_t dimension>

DOFSpace<dimension> const& Manicore::DDR_Spaces< dimension >::dofspace ( size_t  k ) const

inline

Return DOFSpace associated to k forms.

Parameters

k	Form degree

full_diff()

template<size_t dimension>

const Eigen::MatrixXd& Manicore::DDR_Spaces< dimension >::full_diff ( size_t  k, size_t  d, size_t  i_cell  ) const

inline

Compute the full differential operator.

Returns

\(\star d_r^k \) in \(\mathcal{P}_r\Lambda^{d-k-1}(\mathbb{R}^d)\)

Parameters

k	Form degree
d	Cell dimension
i_cell	Cell index

hmax()

template<size_t dimension>

double DDR_Spaces::hmax

Return the mesh size.

Returns

\(\max_{f\in \delta_{\text{dimension}}} h_f\)

interpolate()

template<size_t dimension>

template<size_t k>

Eigen::VectorXd DDR_Spaces::interpolate	(	FunctionType< k > const &	func,
		std::array< int, dimension > const *	dqr_p = nullptr
	)		const

Interpolate the given function on the discrete spaces.

Template Parameters

k	Form degree

Parameters

func	Function to interpolate
dqr_p	Quadrature degree to use

mesh()

template<size_t dimension>

const Mesh<dimension>* Manicore::DDR_Spaces< dimension >::mesh ( ) const

inline

Return the Mesh associated with the class.

potential()

template<size_t dimension>

const Eigen::MatrixXd& Manicore::DDR_Spaces< dimension >::potential ( size_t  k, size_t  d, size_t  i_cell  ) const

inline

Compute the potential operator.

Returns

\(\star P_r^k\) in \(\mathcal{P}_r\Lambda^{d-k}(\mathbb{R}^d)\)

Parameters

k	Form degree
d	Cell dimension
i_cell	Cell index

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

• src/DDR/ddr_spaces.hpp
• src/DDR/ddr_spaces.cpp