4.1.2.1.1 pde.backends.numba.operators.cartesian module

This module implements differential operators on Cartesian grids.

`make_laplace`	Make a Laplace operator on a Cartesian grid.
`make_gradient`	Make a gradient operator on a Cartesian grid.
`make_divergence`	Make a divergence operator on a Cartesian grid.
`make_vector_gradient`	Make a vector gradient operator on a Cartesian grid.
`make_vector_laplace`	Make a vector Laplacian on a Cartesian grid.
`make_tensor_divergence`	Make a tensor divergence operator on a Cartesian grid.

make_divergence(grid, *, backend=None, method='central')[source]

Make a divergence operator on a Cartesian grid.

Parameters:

grid (CartesianGrid) – The grid for which the operator is created
backend (NumbaBackend) – References to the backend to read configuration details
method (str) – The method for calculating the derivative. Possible values are ‘central’, ‘forward’, and ‘backward’.

Returns:

A function that can be applied to an array of values

Return type:

OperatorImplType

make_gradient(grid, *, backend=None, method='central')[source]

Make a gradient operator on a Cartesian grid.

Parameters:

grid (CartesianGrid) – The grid for which the operator is created
backend (NumbaBackend) – References to the backend to read configuration details
method (str) – The method for calculating the derivative. Possible values are ‘central’, ‘forward’, and ‘backward’.

Returns:

A function that can be applied to an array of values

Return type:

OperatorImplType

make_laplace(grid, *, backend=None, spectral=None, **kwargs)[source]

Make a Laplace operator on a Cartesian grid.

Parameters:

grid (CartesianGrid) – The grid for which the operator is created
backend (NumbaBackend) – References to the backend to read configuration details
spectral (bool or None) – Flag deciding whether a spectral implementation is used. If None, the value is controlled by the configuration.
**kwargs – Specifies extra arguments influencing how the operator is created. Note that some laplace operators support the corner_weight argument, which allows setting weighting factors for corner points of the stencil.

Returns:

A function that can be applied to an array of values

Return type:

OperatorImplType

make_tensor_divergence(grid, *, backend=None, method='central')[source]

Make a tensor divergence operator on a Cartesian grid.

Parameters:

grid (CartesianGrid) – The grid for which the operator is created
backend (NumbaBackend) – References to the backend to read configuration details
method (str) – The method for calculating the derivative. Possible values are ‘central’, ‘forward’, and ‘backward’.

Returns:

A function that can be applied to an array of values

Return type:

OperatorImplType

make_vector_gradient(grid, *, backend=None, method='central')[source]

Make a vector gradient operator on a Cartesian grid.

Parameters:

grid (CartesianGrid) – The grid for which the operator is created
backend (NumbaBackend) – References to the backend to read configuration details
method (str) – The method for calculating the derivative. Possible values are ‘central’, ‘forward’, and ‘backward’.

Returns:

A function that can be applied to an array of values

Return type:

OperatorImplType

make_vector_laplace(grid, *, backend=None)[source]

Make a vector Laplacian on a Cartesian grid.

Parameters:

grid (CartesianGrid) – The grid for which the operator is created
backend (NumbaBackend) – References to the backend to read configuration details

Returns:

A function that can be applied to an array of values

Return type:

OperatorImplType