Definition of scalar Taylor polynomial basis. More...

Detailed Description

Definition of scalar Taylor polynomial basis.

For order P, the sum of the basis is defined by:

in 1D)
$\sum_{n=0}^{n=P} \frac{(x/h)^n}{n!}$
in 2D)
$\sum_{n=0}^{n=P} \sum_{k=0}^{k=n} \frac{(x/h)^{n-k}*(y/h)^k}{(n-k)!k!}$
in 3D)
$\sum_{p=0}^{p=P} \sum_{k_1+k_2+k_3=n} \frac{(x/h)^{k_1}*(y/h)^{k_2}*(z/h)^{k_3}}{k_1!k_2!k_3!}$

Functions
KOKKOS_INLINE_FUNCTION int	getSize (const int degree, const int dimension)
	Returns size of basis. More...

KOKKOS_INLINE_FUNCTION void	evaluate (const member_type &teamMember, double delta, double workspace, const int dimension, const int max_degree, const double h, const double x, const double y, const double z, const int starting_order=0, const double weight_of_original_value=0.0, const double weight_of_new_value=1.0)
	Evaluates the scalar Taylor polynomial basis delta[j] = weight_of_original_value * delta[j] + weight_of_new_value * (calculation of this function) More...

KOKKOS_INLINE_FUNCTION void	evaluatePartialDerivative (const member_type &teamMember, double delta, double workspace, const int dimension, const int max_degree, const int partial_direction, const double h, const double x, const double y, const double z, const int starting_order=0, const double weight_of_original_value=0.0, const double weight_of_new_value=1.0)
	Evaluates the first partial derivatives of scalar Taylor polynomial basis delta[j] = weight_of_original_value * delta[j] + weight_of_new_value * (calculation of this function) More...

KOKKOS_INLINE_FUNCTION void	evaluateSecondPartialDerivative (const member_type &teamMember, double delta, double workspace, const int dimension, const int max_degree, const int partial_direction_1, const int partial_direction_2, const double h, const double x, const double y, const double z, const int starting_order=0, const double weight_of_original_value=0.0, const double weight_of_new_value=1.0)
	Evaluates the second partial derivatives of scalar Taylor polynomial basis delta[j] = weight_of_original_value * delta[j] + weight_of_new_value * (calculation of this function) More...

Function Documentation

◆ evaluate()

KOKKOS_INLINE_FUNCTION void Compadre::ScalarTaylorPolynomialBasis::evaluate	(	const member_type &	teamMember,
		double *	delta,
		double *	workspace,
		const int	dimension,
		const int	max_degree,
		const double	h,
		const double	x,
		const double	y,
		const double	z,
		const int	starting_order = `0`,
		const double	weight_of_original_value = `0.0`,
		const double	weight_of_new_value = `1.0`
	)

Evaluates the scalar Taylor polynomial basis delta[j] = weight_of_original_value * delta[j] + weight_of_new_value * (calculation of this function)

Parameters

delta	[in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _basis_multipler*the dimension of the polynomial basis.
workspace	[in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _poly_order*the spatial dimension of the polynomial basis.
dimension	[in] - spatial dimension to evaluate
max_degree	[in] - highest degree of polynomial
h	[in] - epsilon/window size
x	[in] - x coordinate (already shifted by target)
y	[in] - y coordinate (already shifted by target)
z	[in] - z coordinate (already shifted by target)
starting_order	[in] - polynomial order to start with (default=0)
weight_of_original_value	[in] - weighting to assign to original value in delta (default=0, replace, 1-increment current value)
weight_of_new_value	[in] - weighting to assign to new contribution (default=1, add to/replace)

Definition at line 42 of file Compadre_ScalarTaylorPolynomial.hpp.

◆ evaluatePartialDerivative()

KOKKOS_INLINE_FUNCTION void Compadre::ScalarTaylorPolynomialBasis::evaluatePartialDerivative	(	const member_type &	teamMember,
		double *	delta,
		double *	workspace,
		const int	dimension,
		const int	max_degree,
		const int	partial_direction,
		const double	h,
		const double	x,
		const double	y,
		const double	z,
		const int	starting_order = `0`,
		const double	weight_of_original_value = `0.0`,
		const double	weight_of_new_value = `1.0`
	)

Evaluates the first partial derivatives of scalar Taylor polynomial basis delta[j] = weight_of_original_value * delta[j] + weight_of_new_value * (calculation of this function)

Parameters

delta	[in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _basis_multipler*the dimension of the polynomial basis.
workspace	[in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _poly_order*the spatial dimension of the polynomial basis.
dimension	[in] - spatial dimension to evaluate
max_degree	[in] - highest degree of polynomial
partial_direction	[in] - direction in which to take partial derivative
h	[in] - epsilon/window size
x	[in] - x coordinate (already shifted by target)
y	[in] - y coordinate (already shifted by target)
z	[in] - z coordinate (already shifted by target)
starting_order	[in] - polynomial order to start with (default=0)
weight_of_original_value	[in] - weighting to assign to original value in delta (default=0, replace, 1-increment current value)
weight_of_new_value	[in] - weighting to assign to new contribution (default=1, add to/replace)

Definition at line 123 of file Compadre_ScalarTaylorPolynomial.hpp.

◆ evaluateSecondPartialDerivative()

KOKKOS_INLINE_FUNCTION void Compadre::ScalarTaylorPolynomialBasis::evaluateSecondPartialDerivative	(	const member_type &	teamMember,
		double *	delta,
		double *	workspace,
		const int	dimension,
		const int	max_degree,
		const int	partial_direction_1,
		const int	partial_direction_2,
		const double	h,
		const double	x,
		const double	y,
		const double	z,
		const int	starting_order = `0`,
		const double	weight_of_original_value = `0.0`,
		const double	weight_of_new_value = `1.0`
	)

Evaluates the second partial derivatives of scalar Taylor polynomial basis delta[j] = weight_of_original_value * delta[j] + weight_of_new_value * (calculation of this function)

Parameters

delta	[in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _basis_multipler*the dimension of the polynomial basis.
workspace	[in/out] - scratch space that is allocated so that each thread has its own copy. Must be at least as large as the _poly_order*the spatial dimension of the polynomial basis.
dimension	[in] - spatial dimension to evaluate
max_degree	[in] - highest degree of polynomial
partial_direction_1	[in] - direction in which to take first partial derivative
partial_direction_2	[in] - direction in which to take second partial derivative
h	[in] - epsilon/window size
x	[in] - x coordinate (already shifted by target)
y	[in] - y coordinate (already shifted by target)
z	[in] - z coordinate (already shifted by target)
starting_order	[in] - polynomial order to start with (default=0)
weight_of_original_value	[in] - weighting to assign to original value in delta (default=0, replace, 1-increment current value)
weight_of_new_value	[in] - weighting to assign to new contribution (default=1, add to/replace)

Definition at line 234 of file Compadre_ScalarTaylorPolynomial.hpp.

◆ getSize()

KOKKOS_INLINE_FUNCTION int Compadre::ScalarTaylorPolynomialBasis::getSize	(	const int	degree,
		const int	dimension
	)

Returns size of basis.

Parameters

degree	[in] - highest degree of polynomial
dimension	[in] - spatial dimension to evaluate

Definition at line 21 of file Compadre_ScalarTaylorPolynomial.hpp.

Detailed Description

Functions

Function Documentation

◆ evaluate()

◆ evaluatePartialDerivative()

◆ evaluateSecondPartialDerivative()

◆ getSize()