FFT

class fridom.framework.grid.cartesian.fft.FFT(periodic: tuple[bool])

Bases: object

Class for performing fourier transforms on a cartesian grid.

Description

Model grids that have periodic boundary conditions in some directions, and non-periodic boundary conditions in other directions, require a combination of fast fourier transforms and discrete cosine transforms. This class provides a method to transform an array from physical space to spectral space and back. For the discrete cosine transform, the type 2 transform is used. This means that the variable must be located at the cell centers in that direction.

Parameters

periodictuple[bool]

A list of booleans that indicate whether the axis is periodic. If True, the axis is periodic, if False, the axis is non-periodic.

Examples

import numpy as np
from fridom.framework.grid.cartesian import FFT
fft = FFT(periodic=(True, True, False))
u = np.random.rand(*(32, 32, 8))
v = fft.forward(u)
w = fft.backward(v).real
assert np.allclose(u, w)

__init__(periodic: tuple[bool]) → None

Methods

__init__(periodic)
backward(u_hat[, axes, bc_types, positions])	Backward transform from spectral space to physical space.
forward(u[, axes, bc_types, positions])	Forward transform from physical space to spectral space.
get_freq(shape, dx)	Get the frequencies for the given shape and dx.

get_freq(shape: tuple[int], dx: tuple[float]) → tuple[ndarray]

Get the frequencies for the given shape and dx.

Description

This method calculates the frequencies for the given shape and dx. The returned frequencies could be used to construct wavenumber meshgrids.

Parameters

shapetuple[int]

The global shape (number of grid points in each direction).

dxtuple[float]

The grid spacing in each direction.

Returns

tuple[np.ndarray]

The frequencies in each direction.

Examples

import numpy as np
from fridom.framework.grid.cartesian import FFT
fft = FFT(periodic=(True, True, False))
shape = (32, 32, 8)  # Number of grid points in x,y,z
dx = (0.1, 0.1, 0.1)  # Grid spacing in x,y,z
kx, ky, kz = fft.get_freq(shape, dx)
KX, KY, KZ = np.meshgrid(kx, ky, kz, indexing='ij')

forward(u: ndarray, axes: list[int] | None = None, bc_types: tuple[BCType] | None = None, positions: tuple[AxisPosition] | None = None) → ndarray

Forward transform from physical space to spectral space.

Parameters

unp.ndarray

The array to transform from physical space to spectral space.

axeslist[int] | None

The axes to transform. If None, all axes are transformed.

bc_typestuple[fr.grid.BCType] | None

The type of boundary conditions for each axis.

positionstuple[fr.grid.AxisPosition] | None

The position of the variable in each direction.

Returns

np.ndarray

The transformed array in spectral space. If all dimensions are periodic, the obtained array is real, else it is complex.

backward(u_hat: ndarray, axes: list[int] | None = None, bc_types: tuple[BCType] | None = None, positions: tuple[AxisPosition] | None = None) → ndarray

Backward transform from spectral space to physical space.

Parameters

u_hatnp.ndarray

The array to transform from spectral space to physical space.

axeslist[int] | None

The axes to transform. If None, all axes are transformed.

bc_typestuple[fr.grid.BCType] | None

The type of boundary conditions for each axis.

positionstuple[fr.grid.AxisPosition] | None

The position of the variable in each direction.

Returns

np.ndarray

The transformed array in physical space.