Manicore

Classes
class	HArDCore3D::DDR_PEC
class	HArDCore3D::DDR_Spaces
struct	HArDCore3D::DDR_Spaces::DDR_function_type

Typedefs
typedef Eigen::KroneckerProduct< Eigen::MatrixXd, Eigen::MatrixXd >	HArDCore3D::DDR_PEC::Kronecker
typedef std::function< double(const Eigen::Vector3d &)>	HArDCore3D::DDR_Spaces::DDR_function_type::scalar
typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)>	HArDCore3D::DDR_Spaces::DDR_function_type::vector

Functions
	HArDCore3D::DDR_PEC::DDR_PEC (Mesh const &mesh, int r, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.
Kronecker	HArDCore3D::DDR_PEC::get_mass (size_t k, size_t d, size_t i) const
	Return the mass matrix for the k-forms on the i-th d-cell.
Kronecker	HArDCore3D::DDR_PEC::get_trace (size_t k, size_t d, size_t i, size_t j) const
	Return the trace for the k-forms on the i-th d-cell onto its j-th (d-1)-neighbour.
const Eigen::MatrixXd &	HArDCore3D::DDR_PEC::get_diff (size_t l, size_t d) const
	Getters for the generic operators matrices.
const Eigen::MatrixXd &	HArDCore3D::DDR_PEC::get_Koszul (size_t l, size_t d) const
const Eigen::MatrixXd &	HArDCore3D::DDR_PEC::get_diff_as_degr (size_t l, size_t d) const
const Eigen::MatrixXd &	HArDCore3D::DDR_PEC::get_trimmed (size_t l, size_t d) const
const Eigen::MatrixXd &	HArDCore3D::DDR_PEC::get_reduced_Koszul_m1 (size_t l, size_t d) const
Eigen::Matrix< double,-1,-1, 0, 3, 3 >	HArDCore3D::DDR_PEC::get_exterior_trace (size_t k, size_t d, size_t i_cell) const
	Trace of a k form from the global space to the mesh element of dimension d with index i_cell.
Eigen::Matrix< double,-1,-1, 0, 3, 3 >	HArDCore3D::DDR_PEC::get_hodge_star (size_t k, size_t d, size_t i_cell) const
	Gets the continuous Hodge star on k forms on the mesh element of dimension d with index i.
Eigen::MatrixXd	HArDCore3D::DDR_PEC::discrete_hodge_star (size_t k, size_t d, size_t i_cell) const
	Takes a k form on the polynomial k basis to a d-k form on the d-k basis (deals with scaling) on the mesh element of dimension d with index i_cell.
Eigen::MatrixXd	HArDCore3D::DDR_PEC::discrete_inv_hodge_star (size_t k, size_t d, size_t i_cell) const
	e.g. discrete_inv_hodge_star(d-k,d,i) * potential(k,d,i) is the potential P^k in PL(r,k,d)
double	HArDCore3D::DDR_PEC::evaluate_scalar_basis (Eigen::Vector3d const &x, size_t d, size_t i_cell, int i_basis) const
Eigen::Matrix< double,-1, 1, 0, 3, 1 >	HArDCore3D::DDR_PEC::evaluate_basis (Eigen::Vector3d const &x, size_t k, size_t d, size_t i_cell, int i_basis) const
	Evaluate at point x, the i th basis function of PL(r,k,d) in the cell with index i_cell.
Eigen::Matrix< double,-1, 1, 0, 3, 1 >	HArDCore3D::DDR_PEC::evaluate_basis (Eigen::Vector3d const &x, size_t k, size_t d, size_t i, Eigen::VectorXd const &b) const
	Evaluate at point x, the sum of the coefficients b times the basis of PL(r,k,d) in the cell with index i_cell.
double	HArDCore3D::DDR_PEC::get_scaling (size_t d, size_t i) const
	Gets scaling of the i-th d-cell.
	HArDCore3D::DDR_Spaces::DDR_Spaces (Mesh const &mesh, int r, bool use_threads=true, std::ostream &output=std::cout)
	Constructor.
const Mesh &	HArDCore3D::DDR_Spaces::mesh () const
	Return the mesh.
int	HArDCore3D::DDR_Spaces::degree () const
	Return the polynomial degree.
Eigen::VectorXd	HArDCore3D::DDR_Spaces::interpolate (const DDR_function_type &, size_t k) const
	Returns the interpolate of the given function as a k-form.
const Eigen::MatrixXd &	HArDCore3D::DDR_Spaces::full_diff (size_t k, size_t d, size_t i_cell) const
	Returns \star d in PL(r,d-k-1,d), the Hodge star of the full discrete exterior derivative of a discrete k-form on the mesh element of dimension d with index i_cell.
Eigen::MatrixXd	HArDCore3D::DDR_Spaces::compose_diff (size_t k, size_t d, size_t i_cell) const
	Returns \star \ul{d}^k in PLtrimmed(r,d-k-1,d) on the cell (including its boundary), the Hodge star of the discrete exterior derivative of a discrete k-form on the mesh element of dimension d with index i_cell (discrete subspace of X^{k+1})
const Eigen::MatrixXd &	HArDCore3D::DDR_Spaces::potential (size_t k, size_t d, size_t i_cell) const
	Returns \star P^k in PL(r,d-k,d), the Hodge star of the potential of a discrete k-form on the mesh element of dimension d with index i_cell.
GlobalDOFSpace const &	HArDCore3D::DDR_Spaces::dofspace (size_t k) const
	Returns the dofspace associated to discrete k-forms.
Eigen::Matrix< double,-1, 1, 0, 3, 1 >	HArDCore3D::DDR_Spaces::evaluate_basis (Eigen::Vector3d const &x, size_t k, size_t d, size_t i_cell, Eigen::VectorXd const &b) const
	Evaluate at point x, the sum of the coefficients b times the basis of PL(r,k,d) in the cell with index i_cell.
Eigen::Matrix< double,-1, 1, 0, 3, 1 >	HArDCore3D::DDR_Spaces::evaluate_basis (Eigen::Vector3d const &x, size_t k, size_t d, size_t i_cell, int i_basis) const
	Evaluate at point x, the i th basis function of PL(r,k,d) in the cell with index i_cell.
DDR_PEC::Kronecker	HArDCore3D::DDR_Spaces::get_mass (size_t k, size_t d, size_t i_cell) const
	Returns the mass matrix for the k-forms on the mesh element of dimension d with index i_cell.
Eigen::Matrix< double,-1,-1, 0, 3, 3 >	HArDCore3D::DDR_Spaces::get_hodge_star (size_t k, size_t d, size_t i_cell) const
	Gets the continuous Hodge star on k forms on the mesh element of dimension d with index i.
Eigen::MatrixXd	HArDCore3D::DDR_Spaces::discrete_hodge_star (size_t k, size_t d, size_t i_cell) const
	Takes a k form on the polynomial k basis to a d-k form on the d-k basis (deals with scaling) on the mesh element of dimension d with index i_cell.
Eigen::MatrixXd	HArDCore3D::DDR_Spaces::discrete_inv_hodge_star (size_t k, size_t d, size_t i_cell) const
	e.g. discrete_inv_hodge_star(d-k, d, i_cell) * potential(k, d, i_cell) is the potential P^k in PL(r,k,d)
Eigen::Matrix< double,-1,-1, 0, 3, 3 >	HArDCore3D::DDR_Spaces::get_exterior_trace (size_t k, size_t d, size_t i_cell) const
	Trace of a k form from the global space to the mesh element of dimension d with index i_cell.
Eigen::MatrixXd	HArDCore3D::DDR_Spaces::computeL2Product (size_t k, size_t i_cell, const double penalty_factor=0.1) const
	Computes the L2 product for discrete k-forms on the highest dimensional cell with index i_cell.
std::vector< VectorRd >	HArDCore3D::DDR_Spaces::computeVertexValues (size_t k, const Eigen::VectorXd &u) const
	Computes the averaged vertex values of a discrete k-form u using the potential.

Variables
std::variant< scalar, vector >	HArDCore3D::DDR_Spaces::DDR_function_type::func
int	HArDCore3D::DDR_Spaces::DDR_function_type::dqr [4] = {-1,-1,-1,-1}
std::array< Eigen::MatrixXd, 4 >	HArDCore3D::DDR_Spaces::DDR_Operators::full_diff
std::array< Eigen::MatrixXd, 4 >	HArDCore3D::DDR_Spaces::DDR_Operators::diff
std::array< Eigen::MatrixXd, 4 >	HArDCore3D::DDR_Spaces::DDR_Operators::P

Detailed Description

Typedef Documentation

Kronecker

typedef Eigen::KroneckerProduct<Eigen::MatrixXd,Eigen::MatrixXd> HArDCore3D::DDR_PEC::Kronecker

scalar

typedef std::function<double(const Eigen::Vector3d &)> HArDCore3D::DDR_Spaces::DDR_function_type::scalar

vector

typedef std::function<Eigen::Vector3d(const Eigen::Vector3d &)> HArDCore3D::DDR_Spaces::DDR_function_type::vector

Function Documentation

compose_diff()

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

Returns \star \ul{d}^k in PLtrimmed(r,d-k-1,d) on the cell (including its boundary), the Hodge star of the discrete exterior derivative of a discrete k-form on the mesh element of dimension d with index i_cell (discrete subspace of X^{k+1})

computeL2Product()

Eigen::MatrixXd DDR_Spaces::computeL2Product	(	size_t	k,
		size_t	i_cell,
		const double	penalty_factor = 0.1
	)		const

Computes the L2 product for discrete k-forms on the highest dimensional cell with index i_cell.

Non recursive calculation of the inner products

computeVertexValues()

std::vector< VectorRd > DDR_Spaces::computeVertexValues	(	size_t	k,
		const Eigen::VectorXd &	u
	)		const

Computes the averaged vertex values of a discrete k-form u using the potential.

DDR_PEC()

DDR_PEC::DDR_PEC	(	Mesh const &	mesh,
		int	r,
		bool	use_threads = true,
		std::ostream &	output = std::cout
	)

Constructor.

---

---

DDR_Spaces()

DDR_Spaces::DDR_Spaces	(	Mesh const &	mesh,
		int	r,
		bool	use_threads = true,
		std::ostream &	output = std::cout
	)

Constructor.

degree()

int HArDCore3D::DDR_Spaces::degree ( ) const

inline

Return the polynomial degree.

discrete_hodge_star() [1/2]

Eigen::MatrixXd DDR_PEC::discrete_hodge_star	(	size_t	k,
		size_t	d,
		size_t	i_cell
	)		const

Takes a k form on the polynomial k basis to a d-k form on the d-k basis (deals with scaling) on the mesh element of dimension d with index i_cell.

discrete_hodge_star() [2/2]

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

Takes a k form on the polynomial k basis to a d-k form on the d-k basis (deals with scaling) on the mesh element of dimension d with index i_cell.

discrete_inv_hodge_star() [1/2]

Eigen::MatrixXd DDR_PEC::discrete_inv_hodge_star	(	size_t	k,
		size_t	d,
		size_t	i_cell
	)		const

e.g. discrete_inv_hodge_star(d-k,d,i) * potential(k,d,i) is the potential P^k in PL(r,k,d)

discrete_inv_hodge_star() [2/2]

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

e.g. discrete_inv_hodge_star(d-k, d, i_cell) * potential(k, d, i_cell) is the potential P^k in PL(r,k,d)

dofspace()

GlobalDOFSpace const & HArDCore3D::DDR_Spaces::dofspace ( size_t  k ) const

inline

Returns the dofspace associated to discrete k-forms.

evaluate_basis() [1/4]

Eigen::Matrix< double,-1, 1, 0, 3, 1 > DDR_PEC::evaluate_basis	(	Eigen::Vector3d const &	x,
		size_t	k,
		size_t	d,
		size_t	i,
		Eigen::VectorXd const &	b
	)		const

Evaluate at point x, the sum of the coefficients b times the basis of PL(r,k,d) in the cell with index i_cell.

evaluate_basis() [2/4]

Eigen::Matrix< double,-1, 1, 0, 3, 1 > DDR_Spaces::evaluate_basis	(	Eigen::Vector3d const &	x,
		size_t	k,
		size_t	d,
		size_t	i_cell,
		Eigen::VectorXd const &	b
	)		const

Evaluate at point x, the sum of the coefficients b times the basis of PL(r,k,d) in the cell with index i_cell.

evaluate_basis() [3/4]

Eigen::Matrix< double,-1, 1, 0, 3, 1 > DDR_PEC::evaluate_basis	(	Eigen::Vector3d const &	x,
		size_t	k,
		size_t	d,
		size_t	i_cell,
		int	i_basis
	)		const

Evaluate at point x, the i th basis function of PL(r,k,d) in the cell with index i_cell.

evaluate_basis() [4/4]

Eigen::Matrix< double,-1, 1, 0, 3, 1 > DDR_Spaces::evaluate_basis	(	Eigen::Vector3d const &	x,
		size_t	k,
		size_t	d,
		size_t	i_cell,
		int	i_basis
	)		const

Evaluate at point x, the i th basis function of PL(r,k,d) in the cell with index i_cell.

evaluate_scalar_basis()

double DDR_PEC::evaluate_scalar_basis	(	Eigen::Vector3d const &	x,
		size_t	d,
		size_t	i_cell,
		int	i_basis
	)		const

full_diff()

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

Returns \star d in PL(r,d-k-1,d), the Hodge star of the full discrete exterior derivative of a discrete k-form on the mesh element of dimension d with index i_cell.

get_diff()

const Eigen::MatrixXd & HArDCore3D::DDR_PEC::get_diff ( size_t  l, size_t  d  ) const

inline

Getters for the generic operators matrices.

get_diff_as_degr()

const Eigen::MatrixXd & HArDCore3D::DDR_PEC::get_diff_as_degr ( size_t  l, size_t  d  ) const

inline

get_exterior_trace() [1/2]

Eigen::Matrix< double,-1,-1, 0, 3, 3 > DDR_PEC::get_exterior_trace	(	size_t	k,
		size_t	d,
		size_t	i_cell
	)		const

Trace of a k form from the global space to the mesh element of dimension d with index i_cell.

get_exterior_trace() [2/2]

Eigen::Matrix< double,-1,-1, 0, 3, 3 > DDR_Spaces::get_exterior_trace	(	size_t	k,
		size_t	d,
		size_t	i_cell
	)		const

Trace of a k form from the global space to the mesh element of dimension d with index i_cell.

get_hodge_star() [1/2]

Eigen::Matrix< double,-1,-1, 0, 3, 3 > DDR_PEC::get_hodge_star	(	size_t	k,
		size_t	d,
		size_t	i_cell
	)		const

Gets the continuous Hodge star on k forms on the mesh element of dimension d with index i.

get_hodge_star() [2/2]

Eigen::Matrix< double,-1,-1, 0, 3, 3 > DDR_Spaces::get_hodge_star	(	size_t	k,
		size_t	d,
		size_t	i_cell
	)		const

Gets the continuous Hodge star on k forms on the mesh element of dimension d with index i.

get_Koszul()

const Eigen::MatrixXd & HArDCore3D::DDR_PEC::get_Koszul ( size_t  l, size_t  d  ) const

inline

get_mass() [1/2]

DDR_PEC::Kronecker DDR_PEC::get_mass	(	size_t	k,
		size_t	d,
		size_t	i
	)		const

Return the mass matrix for the k-forms on the i-th d-cell.

get_mass() [2/2]

DDR_PEC::Kronecker DDR_Spaces::get_mass	(	size_t	k,
		size_t	d,
		size_t	i_cell
	)		const

Returns the mass matrix for the k-forms on the mesh element of dimension d with index i_cell.

get_reduced_Koszul_m1()

const Eigen::MatrixXd & HArDCore3D::DDR_PEC::get_reduced_Koszul_m1 ( size_t  l, size_t  d  ) const

inline

get_scaling()

double DDR_PEC::get_scaling	(	size_t	d,
		size_t	i
	)		const

Gets scaling of the i-th d-cell.

get_trace()

DDR_PEC::Kronecker DDR_PEC::get_trace	(	size_t	k,
		size_t	d,
		size_t	i,
		size_t	j
	)		const

Return the trace for the k-forms on the i-th d-cell onto its j-th (d-1)-neighbour.

get_trimmed()

const Eigen::MatrixXd & HArDCore3D::DDR_PEC::get_trimmed ( size_t  l, size_t  d  ) const

inline

interpolate()

Eigen::VectorXd DDR_Spaces::interpolate	(	const DDR_function_type &	func,
		size_t	k
	)		const

Returns the interpolate of the given function as a k-form.

mesh()

const Mesh & HArDCore3D::DDR_Spaces::mesh ( ) const

inline

Return the mesh.

potential()

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

Returns \star P^k in PL(r,d-k,d), the Hodge star of the potential of a discrete k-form on the mesh element of dimension d with index i_cell.

Variable Documentation

diff

std::array<Eigen::MatrixXd,4> HArDCore3D::DDR_Spaces::DDR_Operators::diff

dqr

int HArDCore3D::DDR_Spaces::DDR_function_type::dqr[4] = {-1,-1,-1,-1}

full_diff

std::array<Eigen::MatrixXd,4> HArDCore3D::DDR_Spaces::DDR_Operators::full_diff

func

std::variant<scalar,vector> HArDCore3D::DDR_Spaces::DDR_function_type::func

P

std::array<Eigen::MatrixXd,4> HArDCore3D::DDR_Spaces::DDR_Operators::P