Compadre 1.5.5
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Compadre::DivergenceFreePolynomialBasis Namespace Reference

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.
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).
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).
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).
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.
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.
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.
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.

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.

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