#include <RBFWithLinear.hpp>

Public Member Functions
	RBFWithLinear (const Eigen::MatrixXd &centers, const Eigen::MatrixXd &collocation_points, const Eigen::MatrixXd &local_basis_integral, const quadrature::Quadrature &quadr, Eigen::MatrixXd &rhs, bool with_constraints=true)
	Initialize RBF functions over a polytope element.

void	basis (const int local_index, const Eigen::MatrixXd &uv, Eigen::MatrixXd &val) const
	Evaluates one RBF function over a list of coordinates.

void	grad (const int local_index, const Eigen::MatrixXd &uv, Eigen::MatrixXd &val) const
	Evaluates the gradient of one RBF function over a list of coordinates.

void	bases_values (const Eigen::MatrixXd &samples, Eigen::MatrixXd &val) const
	Batch evaluates the RBF + polynomials on a set of sample points.

void	bases_grads (const int axis, const Eigen::MatrixXd &samples, Eigen::MatrixXd &val) const
	Batch evaluates the gradient of the RBF + polynomials on a set of sample points.

Private Member Functions
bool	is_volume () const

void	compute_kernels_matrix (const Eigen::MatrixXd &samples, Eigen::MatrixXd &A) const

void	compute_constraints_matrix (const int num_bases, const quadrature::Quadrature &quadr, const Eigen::MatrixXd &local_basis_integral, Eigen::MatrixXd &L, Eigen::MatrixXd &t) const

void	compute_weights (const Eigen::MatrixXd &collocation_points, const Eigen::MatrixXd &local_basis_integral, const quadrature::Quadrature &quadr, Eigen::MatrixXd &rhs, bool with_constraints)

Private Attributes
Eigen::MatrixXd	centers_

Eigen::MatrixXd	weights_

Detailed Description

Definition at line 10 of file RBFWithLinear.hpp.

Constructor & Destructor Documentation

◆ RBFWithLinear()

RBFWithLinear::RBFWithLinear	(	const Eigen::MatrixXd &	centers,
		const Eigen::MatrixXd &	collocation_points,
		const Eigen::MatrixXd &	local_basis_integral,
		const quadrature::Quadrature &	quadr,
		Eigen::MatrixXd &	rhs,
		bool	with_constraints = `true`
	)

Initialize RBF functions over a polytope element.

Parameters

[in]	centers	#C x dim positions of the kernels used to define functions over the polytope. The centers are placed at a small offset distance from the boundary of the element, due to the singularity at the centers
[in]	collocation_points	#S x dim positions of the collocation points, used to approximate the RBF functions over the boundary of the element
[in]	local_basis_integral	#B x dim containing the expected value of the integral of each basis over the polytope
[in]	quadr	Quadrature points and weights inside the polytope
[in]	rhs	#S x #B of boundary conditions. Each column defines how the i-th basis of the mesh should evaluate on the collocation points sampled on the boundary of the polytope
[in]	with_constraints	Impose integral constraints to guarantee linear reproduction for the Poisson equation

Definition at line 62 of file RBFWithLinear.cpp.

References compute_weights().

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Member Function Documentation

◆ bases_grads()

void RBFWithLinear::bases_grads	(	const int	axis,
		const Eigen::MatrixXd &	samples,
		Eigen::MatrixXd &	val
	)		const

Batch evaluates the gradient of the RBF + polynomials on a set of sample points.

Parameters

[in]	axis	The axis (0, 1, 2) with respect to which to compute the gradient
[in]	uv	#uv x dim matrix of points to evaluate
[out]	val	#uv x n_loc_bases of bases gradient wrt axis over the sample points

Definition at line 111 of file RBFWithLinear.cpp.

References centers_, is_volume(), val, weights_, and x.

Referenced by grad().

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◆ bases_values()

void RBFWithLinear::bases_values	(	const Eigen::MatrixXd &	samples,
		Eigen::MatrixXd &	val
	)		const

Batch evaluates the RBF + polynomials on a set of sample points.

Parameters

[in]	uv	#uv x dim matrix of points to evaluate
[out]	val	#uv x n_loc_bases of bases values over the sample points

Definition at line 99 of file RBFWithLinear.cpp.

References compute_kernels_matrix(), val, and weights_.

Referenced by basis().

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◆ basis()

void RBFWithLinear::basis	(	const int	local_index,
		const Eigen::MatrixXd &	uv,
		Eigen::MatrixXd &	val
	)		const

Evaluates one RBF function over a list of coordinates.

Parameters

[in]	local_index	i-th RBF function to evaluate
[in]	uv	#uv x dim matrix of coordinates to evaluate (in object domain)
[out]	val	#uv x 1 matrix of computed values

Definition at line 76 of file RBFWithLinear.cpp.

References bases_values(), and val.

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◆ compute_constraints_matrix()

void RBFWithLinear::compute_constraints_matrix	(	const int	num_bases,
		const quadrature::Quadrature &	quadr,
		const Eigen::MatrixXd &	local_basis_integral,
		Eigen::MatrixXd &	L,
		Eigen::MatrixXd &	t
	)		const

private

Definition at line 151 of file RBFWithLinear.cpp.

References centers_, is_volume(), polyfem::quadrature::Quadrature::points, polyfem::quadrature::Quadrature::weights, and x.

Referenced by compute_weights().

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◆ compute_kernels_matrix()

void RBFWithLinear::compute_kernels_matrix	(	const Eigen::MatrixXd &	samples,
		Eigen::MatrixXd &	A
	)		const

private

Definition at line 134 of file RBFWithLinear.cpp.

References centers_, is_volume(), and x.

Referenced by bases_values(), and compute_weights().

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◆ compute_weights()

void RBFWithLinear::compute_weights	(	const Eigen::MatrixXd &	collocation_points,
		const Eigen::MatrixXd &	local_basis_integral,
		const quadrature::Quadrature &	quadr,
		Eigen::MatrixXd &	rhs,
		bool	with_constraints
	)

private

Definition at line 191 of file RBFWithLinear.cpp.

References centers_, compute_constraints_matrix(), compute_kernels_matrix(), polyfem::logger(), polyfem::quadrature::Quadrature::weights, and weights_.

Referenced by RBFWithLinear().

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◆ grad()

void RBFWithLinear::grad	(	const int	local_index,
		const Eigen::MatrixXd &	uv,
		Eigen::MatrixXd &	val
	)		const

Evaluates the gradient of one RBF function over a list of coordinates.

Parameters

[in]	local_index	i-th RBF function to evaluate
[in]	uv	#uv x dim matrix of coordinates to evaluate (in object domain)
[out]	val	#uv x dim matrix of computed gradients

Definition at line 85 of file RBFWithLinear.cpp.

References bases_grads(), centers_, and val.

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◆ is_volume()

bool polyfem::basis::RBFWithLinear::is_volume ( ) const

inlineprivate

Definition at line 63 of file RBFWithLinear.hpp.

References centers_.

Referenced by bases_grads(), compute_constraints_matrix(), and compute_kernels_matrix().

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Member Data Documentation

◆ centers_

Eigen::MatrixXd polyfem::basis::RBFWithLinear::centers_

private

Definition at line 79 of file RBFWithLinear.hpp.

Referenced by bases_grads(), compute_constraints_matrix(), compute_kernels_matrix(), compute_weights(), grad(), and is_volume().

◆ weights_

Eigen::MatrixXd polyfem::basis::RBFWithLinear::weights_

private

Definition at line 82 of file RBFWithLinear.hpp.

Referenced by bases_grads(), bases_values(), and compute_weights().

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

src/polyfem/basis/function/RBFWithLinear.hpp
src/polyfem/basis/function/RBFWithLinear.cpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ RBFWithLinear()

Member Function Documentation

◆ bases_grads()

◆ bases_values()

◆ basis()

◆ compute_constraints_matrix()

◆ compute_kernels_matrix()

◆ compute_weights()

◆ grad()

◆ is_volume()

Member Data Documentation

◆ centers_

◆ weights_