Definition of the divergence-free polynomial basis. More...

Detailed Description

Definition of the divergence-free polynomial basis.

Let \(NB_d=\) the number of basis components in the scalar Taylor polynomial basis, for the same dimension \(d\) and up to the same degree of polynomial. Let \(NB_{(d-1)/v}=\) the number of basis components in the scalar Taylor polynomial basis, for one dimension lower \((d-1)\) that does not use same contain the direction v.

in 1D) No definition.
in 2D) The first \(NB_d\) elements are
\[\begin{bmatrix}b_i\\ -\int \frac{\partial}{\partial x}(b_i)\; dy\end{bmatrix},\]
where \(i\) is the basis element number for the divergence-free polynomial basis.\newline The next \(NB_{(d-1)/y}\) elements are
\[\begin{bmatrix}0\\b_j\end{bmatrix},\]
where \(j\) is the basis element number for the divergence-free polynomial basis of one dimension lower using only the variable \(x\).
in 3D) The first \(NB_d\) elements are
\[\begin{bmatrix}b_i\\ 0 \\-\int \frac{\partial}{\partial x}(b_i)\; dz\end{bmatrix},\]
where \(i\) is the basis element number for the divergence-free polynomial basis.\newline The next \(NB_d\) elements are
\[\begin{bmatrix}0\\ b_i \\-\int \frac{\partial}{\partial y}(b_i)\; dz\end{bmatrix},\]
where \(i\) is the basis element number for the divergence-free polynomial basis.\newline The next \(NB_{(d-1)/z}\) elements are
\[\begin{bmatrix}0\\0\\b_j\end{bmatrix},\]
where \(j\) is the basis element number for the divergence-free polynomial basis of one dimension lower using only the variables \(x\) and \(y\).

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 int component, 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 divergence-free 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 component, 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 the divergence-free 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 component, 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 the divergence-free polynomial basis delta[j] = weight_of_original_value * delta[j] + weight_of_new_value * (calculation of this function) More...

KOKKOS_INLINE_FUNCTION XYZ	evaluate (int np, const double sx, const double sy, const double sz)
	Evaluates the hard-coded divergence-free polynomial basis up to order 4 for 3D. More...

KOKKOS_INLINE_FUNCTION XYZ	evaluate (int np, const double sx, const double sy)
	Evaluates the hard-coded divergence-free polynomial basis up to order 4 for 2D. More...

KOKKOS_INLINE_FUNCTION XYZ	evaluatePartialDerivative (int np, const int partial_direction, const double h, const double sx, const double sy, const double sz)
	Evaluates the hard-coded first partial derivative of the divergence-free polynomial basis up to order 4 for 3D. More...

KOKKOS_INLINE_FUNCTION XYZ	evaluatePartialDerivative (int np, const int partial_direction, const double h, const double sx, const double sy)
	Evaluates the hard-coded first partial derivative of the divergence-free polynomial basis up to order 4 for 2D. More...

Function Documentation

◆ evaluate() [1/3]

KOKKOS_INLINE_FUNCTION void Compadre::DivergenceFreePolynomialBasis::evaluate	(	const member_type &	teamMember,
		double *	delta,
		double *	workspace,
		const int	dimension,
		const int	max_degree,
		const int	component,
		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 divergence-free 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 47 of file Compadre_DivergenceFreePolynomial.hpp.

◆ evaluate() [2/3]

KOKKOS_INLINE_FUNCTION XYZ Compadre::DivergenceFreePolynomialBasis::evaluate	(	int	np,
		const double	sx,
		const double	sy
	)

Evaluates the hard-coded divergence-free polynomial basis up to order 4 for 2D.

Polynomial degree is inferred from np

Warning: This function is deprecated.

Parameters

np	[in] - basis component number
sx	[in] - x coordinate (already shifted by target and scaled)
sy	[in] - y coordinate (already shifted by target and scaled)

Definition at line 776 of file Compadre_DivergenceFreePolynomial.hpp.

◆ evaluate() [3/3]

KOKKOS_INLINE_FUNCTION XYZ Compadre::DivergenceFreePolynomialBasis::evaluate	(	int	np,
		const double	sx,
		const double	sy,
		const double	sz
	)

Evaluates the hard-coded divergence-free polynomial basis up to order 4 for 3D.

Polynomial degree is inferred from np

Warning: This function is deprecated.

Parameters

np	[in] - basis component number
sx	[in] - x coordinate (already shifted by target and scaled)
sy	[in] - y coordinate (already shifted by target and scaled)
sz	[in] - z coordinate (already shifted by target and scaled)

Definition at line 656 of file Compadre_DivergenceFreePolynomial.hpp.

◆ evaluatePartialDerivative() [1/3]

KOKKOS_INLINE_FUNCTION void Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative	(	const member_type &	teamMember,
		double *	delta,
		double *	workspace,
		const int	dimension,
		const int	max_degree,
		const int	component,
		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 the divergence-free 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 219 of file Compadre_DivergenceFreePolynomial.hpp.

◆ evaluatePartialDerivative() [2/3]

KOKKOS_INLINE_FUNCTION XYZ Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative	(	int	np,
		const int	partial_direction,
		const double	h,
		const double	sx,
		const double	sy
	)

Evaluates the hard-coded first partial derivative of the divergence-free polynomial basis up to order 4 for 2D.

Polynomial degree is inferred from np

Warning: This function is deprecated.

Parameters

np	[in] - basis component number
partial_direction	[in] - partial derivative direction
sx	[in] - x coordinate (already shifted by target and scaled)
sy	[in] - y coordinate (already shifted by target and scaled)

Definition at line 1163 of file Compadre_DivergenceFreePolynomial.hpp.

◆ evaluatePartialDerivative() [3/3]

KOKKOS_INLINE_FUNCTION XYZ Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative	(	int	np,
		const int	partial_direction,
		const double	h,
		const double	sx,
		const double	sy,
		const double	sz
	)

Evaluates the hard-coded first partial derivative of the divergence-free polynomial basis up to order 4 for 3D.

Polynomial degree is inferred from np

Warning: This function is deprecated.

Parameters

np	[in] - basis component number
partial_direction	[in] - partial derivative direction
sx	[in] - x coordinate (already shifted by target and scaled)
sy	[in] - y coordinate (already shifted by target and scaled)
sz	[in] - z coordinate (already shifted by target and scaled)

Definition at line 831 of file Compadre_DivergenceFreePolynomial.hpp.

◆ evaluateSecondPartialDerivative()

KOKKOS_INLINE_FUNCTION void Compadre::DivergenceFreePolynomialBasis::evaluateSecondPartialDerivative	(	const member_type &	teamMember,
		double *	delta,
		double *	workspace,
		const int	dimension,
		const int	max_degree,
		const int	component,
		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 the divergence-free 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 438 of file Compadre_DivergenceFreePolynomial.hpp.

◆ getSize()

KOKKOS_INLINE_FUNCTION int Compadre::DivergenceFreePolynomialBasis::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 27 of file Compadre_DivergenceFreePolynomial.hpp.

Detailed Description

Functions

Function Documentation

◆ evaluate() [1/3]

◆ evaluate() [2/3]

◆ evaluate() [3/3]

◆ evaluatePartialDerivative() [1/3]

◆ evaluatePartialDerivative() [2/3]

◆ evaluatePartialDerivative() [3/3]

◆ evaluateSecondPartialDerivative()

◆ getSize()