# 4.2.2.1. pde.grids.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_poisson_solver` make a operator that solves Poisson's equation
make_divergence(grid, backend='auto')[source]

make a divergence operator on a Cartesian grid

Parameters
• grid (`CartesianGrid`) – The grid for which the operator is created

• backend (str) – Backend used for calculating the divergence operator. If backend=’auto’, a suitable backend is chosen automatically.

Returns

A function that can be applied to an array of values

Return type

OperatorType

make a gradient operator on a Cartesian grid

Parameters
• grid (`CartesianGrid`) – The grid for which the operator is created

• backend (str) – Backend used for calculating the gradient operator. If backend=’auto’, a suitable backend is chosen automatically.

Returns

A function that can be applied to an array of values

Return type

OperatorType

make_laplace(grid, backend='auto')[source]

make a laplace operator on a Cartesian grid

Parameters
• grid (`CartesianGrid`) – The grid for which the operator is created

• backend (str) – Backend used for calculating the laplace operator. If backend=’auto’, a suitable backend is chosen automatically.

Returns

A function that can be applied to an array of values

Return type

OperatorType

make_poisson_solver(bcs, method='auto')[source]

make a operator that solves Poisson’s equation

Parameters
• bcs (`Boundaries`) – {ARG_BOUNDARIES_INSTANCE}

• method (str) – Method used for calculating the tensor divergence operator. If method=’auto’, a suitable method is chosen automatically.

Returns

A function that can be applied to an array of values

Return type

OperatorType

make_tensor_divergence(grid, backend='numba')[source]

make a tensor divergence operator on a Cartesian grid

Parameters
• grid (`CartesianGrid`) – The grid for which the operator is created

• backend (str) – Backend used for calculating the tensor divergence operator.

Returns

A function that can be applied to an array of values

Return type

OperatorType

make a vector gradient operator on a Cartesian grid

Parameters
• grid (`CartesianGrid`) – The grid for which the operator is created

• backend (str) – Backend used for calculating the vector gradient operator.

Returns

A function that can be applied to an array of values

Return type

OperatorType

make_vector_laplace(grid, backend='numba')[source]

make a vector Laplacian on a Cartesian grid

Parameters
• grid (`CartesianGrid`) – The grid for which the operator is created

• backend (str) – Backend used for calculating the vector laplace operator.

Returns

A function that can be applied to an array of values

Return type

OperatorType