aurel.finitedifference

finitedifference.py

This module provides finite difference schemes for computing spatial derivatives of scalar or tensor fields on 3D grids.

It contains the following classes and functions:

• 4th, 6th, and 8th order finite difference schemes for backward, centered, and forward differences.

• FiniteDifference: A class that applies finite difference schemes to 3D data grids.

  • Provides Cartesian and Spherical coordinates.

  • Functions for computing the spatial derivatives of rank 0, 1, and 2 tensors along the x, y, and z axes.

  • Function for removing points affected by the boundary condition.

class aurel.finitedifference.FiniteDifference(param, boundary='no boundary', fd_order=4, verbose=True, veryverbose=False)

Bases: object

This class applies the FD schemes to the entire data grid.

Parameters:

• param (dict) –

  Dictionary containing the data grid parameters:

  ’xmin’, ‘ymin’, ‘zmin’: float, minimum x, y, and z coordinates

  ’dx’, ‘dy’, ‘dz’ : float, elementary grid size in x, y, and z direction

  ’Nx’, ‘Ny’, ‘Nz’ : int, number of data points in x, y, and z direction

• boundary (string, default 'no boundary') – Options are: ‘periodic’, ‘symmetric’, or ‘no boundary’. If ‘periodic’ or ‘symmetric’ a centered FD scheme is used, otherwise a combination of forward + centered + backward FD schemes are used.

• fd_order (int, default 4) – 4, 6 or 8 order of FD schemes used.

xarray, yarray, zarray

(jax.numpy.ndarray) - 1D arrays of x, y, and z coordinates.

Type:

jax.numpy.ndarray

ixcenter, iycenter, izcenter

(int) - Indexes of the x, y, and z coordinates closest to zero.

Type:

int

x, y, z

(jax.numpy.ndarray) - 3D arrays of x, y, and z coordinates.

Type:

jax.numpy.ndarray

cartesian_coords

(jax.numpy.ndarray) - 3D array of x, y, and z coordinates.

Type:

jax.numpy.ndarray

r, phi, theta

(jax.numpy.ndarray) - 3D arrays of radius, azimuth, and inclination coordinates.

Type:

jax.numpy.ndarray

spherical_coords

(jax.numpy.ndarray) - 3D array of radius, azimuth, and inclination coordinates.

Type:

jax.numpy.ndarray

mask_len

(int) - Length of the finite difference mask.

Type:

int

cutoffmask(f)

Remove boundary points, for when FDs were applied once.

cutoffmask2(f)

Remove boundary points, for when FDs were applied twice.

d3(f, idx, N)

Apply the finite difference scheme to the data grid.

d3_rank1tensor(f)

Spatial derivatives of a spatial rank 1 tensor: \(\partial_i (f_{j})\) or \(\partial_i (f^{j})\).

d3_rank2tensor(f)

Spatial derivatives of a spatial rank 2 tensor: \(\partial_i (f_{kj})\) or \(\partial_i (f^{kj})\) or \(\partial_i (f^{k}_{j})\).

d3_scalar(f)

Spatial derivatives of a scalar: \(\partial_i (f)\).

d3x(f)

Derivative along x of a scalar: \(\partial_x (f)\).

d3x_rank2tensor(f)

Spatial derivatives along x of a spatial rank 2 tensor: \(\partial_x (f_{kj})\) or \(\partial_x (f^{kj})\) or \(\partial_x (f^{k}_{j})\).

d3y(f)

Derivative along y of a scalar: \(\partial_y (f)\).

d3y_rank2tensor(f)

Spatial derivatives along y of a spatial rank 2 tensor: \(\partial_y (f_{kj})\) or \(\partial_y (f^{kj})\) or \(\partial_y (f^{k}_{j})\).

d3z(f)

Derivative along z of a scalar: \(\partial_z (f)\).

d3z_rank2tensor(f)

Spatial derivatives along z of a spatial rank 2 tensor: \(\partial_z (f_{kj})\) or \(\partial_z (f^{kj})\) or \(\partial_z (f^{k}_{j})\).

excision(finput, isingularity='find')

Excision of the singularity, for when FDs were applied once.

excision2(finput, isingularity='find')

Double singularity excision, for when FDs were applied twice.

reconstruct(data)

If partial simulation box with symmetries, reconstruct full box

aurel.finitedifference.fd4_backward(f, i, inverse_dx)

4th order backward finite difference scheme.

aurel.finitedifference.fd4_centered(f, i, inverse_dx)

4th order centered finite difference scheme.

aurel.finitedifference.fd4_forward(f, i, inverse_dx)

4th order forward finite difference scheme.

aurel.finitedifference.fd6_backward(f, i, inverse_dx)

6th order backward finite difference scheme.

aurel.finitedifference.fd6_centered(f, i, inverse_dx)

6th order centered finite difference scheme.

aurel.finitedifference.fd6_forward(f, i, inverse_dx)

6th order forward finite difference scheme.

aurel.finitedifference.fd8_backward(f, i, inverse_dx)

8th order backward finite difference scheme.

aurel.finitedifference.fd8_centered(f, i, inverse_dx)

8th order centered finite difference scheme.

aurel.finitedifference.fd8_forward(f, i, inverse_dx)

8th order forward finite difference scheme.

aurel.finitedifference.fd_map(func, farray, idx, imin, imax)

Map the finite difference function over the grid.