helpers.problem_helper module

get_1d_grid(size, bc, left_boundary=0.0, right_boundary=1.0)[source]

Generate a grid in one dimension and obtain mesh spacing for finite difference discretization.

Parameters:

  • size (int) – Number of degrees of freedom per dimension

  • bc (str) – Boundary conditions for both sides

  • left_boundary (float) – x value at the left boundary

  • right_boundary (float) – x value at the right boundary

Returns:

mesh spacing numpy.ndarray: 1d mesh

Return type:

float

get_finite_difference_matrix(derivative, order, stencil_type=None, steps=None, dx=None, size=None, dim=None, bc=None, cupy=False, bc_params=None)[source]

Build FD matrix from stencils, with boundary conditions. Keep in mind that the boundary conditions may require further modification of the right hand side.

Parameters:

  • derivative (int) – Order of the spatial derivative

  • order (int) – Order of accuracy

  • stencil_type (str) – Type of stencil

  • steps (list) – Provide specific steps, overrides stencil_type

  • dx (float) – Mesh width

  • size (int) – Number of degrees of freedom per dimension

  • dim (int) – Number of dimensions

  • bc (str) – Boundary conditions for both sides

  • cupy (bool) – Construct a GPU ready matrix if yes

Returns:

Finite difference matrix numpy.ndarray: Vector containing information about the boundary conditions

Return type:

Sparse matrix

get_finite_difference_stencil(derivative, order=None, stencil_type=None, steps=None)[source]

Derive general finite difference stencils from Taylor expansions

Parameters:

  • derivative (int) – Order of the derivative

  • order (int) – Order of accuracy

  • stencil_type (str) – Type of the stencil

  • steps (list) – Provide specific steps, overrides stencil_type

Returns:

The weights of the stencil numpy.ndarray: The offsets for the stencil

Return type:

numpy.ndarray

get_steps(derivative, order, stencil_type)[source]

Get the offsets for the FD stencil.

Parameters:

  • derivative (int) – Order of the derivative

  • order (int) – Order of accuracy

  • stencil_type (str) – Type of the stencil

  • steps (list) – Provide specific steps, overrides stencil_type

Returns:

The number of elements in the stencil numpy.ndarray: The offsets for the stencil

Return type:

int