#include <RBFWithQuadraticLagrange.hpp>

Public Member Functions
	RBFWithQuadraticLagrange (const assembler::LinearAssembler &assembler, 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_2d_old (const int num_bases, const quadrature::Quadrature &quadr, Eigen::MatrixXd &C) const

void	compute_constraints_matrix_2d (const assembler::LinearAssembler &assembler, const int num_bases, const quadrature::Quadrature &quadr, Eigen::MatrixXd &C) const

void	compute_constraints_matrix_3d (const int num_bases, const quadrature::Quadrature &quadr, Eigen::MatrixXd &C) const

void	compute_weights (const assembler::LinearAssembler &assembler, 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 15 of file RBFWithQuadraticLagrange.hpp.

Constructor & Destructor Documentation

◆ RBFWithQuadraticLagrange()

RBFWithQuadraticLagrange::RBFWithQuadraticLagrange	(	const assembler::LinearAssembler &	assembler,
		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+dim*(dim+1)/2 of the constant right-hand side for the integral constraint for 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 79 of file RBFWithQuadraticLagrange.cpp.

References compute_weights().

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Member Function Documentation

◆ bases_grads()

void RBFWithQuadraticLagrange::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 130 of file RBFWithQuadraticLagrange.cpp.

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

Referenced by grad().

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◆ bases_values()

void RBFWithQuadraticLagrange::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 118 of file RBFWithQuadraticLagrange.cpp.

References compute_kernels_matrix(), val, and weights_.

Referenced by basis().

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◆ basis()

void RBFWithQuadraticLagrange::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 95 of file RBFWithQuadraticLagrange.cpp.

References bases_values(), and val.

Referenced by compute_weights().

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◆ compute_constraints_matrix_2d()

void RBFWithQuadraticLagrange::compute_constraints_matrix_2d	(	const assembler::LinearAssembler &	assembler,
		const int	num_bases,
		const quadrature::Quadrature &	quadr,
		Eigen::MatrixXd &	C
	)		const

private

Definition at line 264 of file RBFWithQuadraticLagrange.cpp.

References polyfem::assembler::LinearAssembler::assemble(), polyfem::assembler::ElementAssemblyValues::basis_values, centers_, polyfem::assembler::ElementAssemblyValues::has_parameterization, polyfem::basis::RBFWithQuadratic::index_mapping(), polyfem::assembler::Assembler::is_tensor(), is_volume(), polyfem::quadrature::Quadrature::points, polyfem::basis::RBFWithQuadratic::setup_monomials_strong_2d(), polyfem::basis::RBFWithQuadratic::setup_monomials_vals_2d(), and polyfem::quadrature::Quadrature::weights.

Referenced by compute_weights().

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◆ compute_constraints_matrix_2d_old()

void RBFWithQuadraticLagrange::compute_constraints_matrix_2d_old	(	const int	num_bases,
		const quadrature::Quadrature &	quadr,
		Eigen::MatrixXd &	C
	)		const

private

Definition at line 194 of file RBFWithQuadraticLagrange.cpp.

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

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◆ compute_constraints_matrix_3d()

void RBFWithQuadraticLagrange::compute_constraints_matrix_3d	(	const int	num_bases,
		const quadrature::Quadrature &	quadr,
		Eigen::MatrixXd &	C
	)		const

private

Definition at line 371 of file RBFWithQuadraticLagrange.cpp.

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

Referenced by compute_weights().

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◆ compute_kernels_matrix()

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

private

Definition at line 165 of file RBFWithQuadraticLagrange.cpp.

References centers_, is_volume(), and x.

Referenced by bases_values(), and compute_weights().

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◆ compute_weights()

void RBFWithQuadraticLagrange::compute_weights	(	const assembler::LinearAssembler &	assembler,
		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 458 of file RBFWithQuadraticLagrange.cpp.

References basis(), centers_, compute_constraints_matrix_2d(), compute_constraints_matrix_3d(), compute_kernels_matrix(), grad(), is_volume(), polyfem::logger(), polyfem::quadrature::Quadrature::points, val, polyfem::quadrature::Quadrature::weights, weights_, and x.

Referenced by RBFWithQuadraticLagrange().

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◆ grad()

void RBFWithQuadraticLagrange::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 104 of file RBFWithQuadraticLagrange.cpp.

References bases_grads(), centers_, and val.

Referenced by compute_weights().

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