implementations.problem_classes.generic_MPIFFT_Laplacian module

class IMEX_Laplacian_MPIFFT(nvars=None, spectral=False, L=6.283185307179586, alpha=1.0, comm=mpi4py.MPI.COMM_WORLD, dtype='d', useGPU=False, x0=0.0)[source]

Bases: Problem

Generic base class for IMEX problems using a spectral method to solve the Laplacian implicitly and a possible rest explicitly. The FFTs are done with``mpi4py-fft`` [1]. Works in two and three dimensions.

Parameters:

  • nvars (tuple, optional) – Spatial resolution

  • spectral (bool, optional) – If True, the solution is computed in spectral space.

  • L (float, optional) – Denotes the period of the function to be approximated for the Fourier transform.

  • alpha (float, optional) – Multiplicative factor before the Laplacian

  • comm (MPI.COMM_World) – Communicator for parallelisation.

fft

Object for parallel FFT transforms.

Type:

PFFT

X

Grid coordinates in real space.

Type:

mesh-grid

K2

Laplace operator in spectral space.

Type:

matrix

References

dtype_f

alias of imex_mesh

dtype_u

alias of mesh

eval_f(u, t)[source]

Routine to evaluate the right-hand side of the problem.

Parameters:

  • u (dtype_u) – Current values of the numerical solution.

  • t (float) – Current time at which the numerical solution is computed.

Returns:

f – The right-hand side of the problem.

Return type:

dtype_f

fft_backend = 'fftw'
fft_comm_backend = 'MPI'
getLaplacian()[source]
getLocalGrid()[source]
classmethod setup_GPU()[source]

switch to GPU modules

solve_system(rhs, factor, u0, t)[source]

Simple FFT solver for the diffusion part.

Parameters:

  • rhs (dtype_f) – Right-hand side for the linear system.

  • factor (float) – Abbrev. for the node-to-node stepsize (or any other factor required).

  • u0 (dtype_u) – Initial guess for the iterative solver (not used here so far).

  • t (float) – Current time (e.g. for time-dependent BCs).

Returns:

me – The solution as mesh.

Return type:

dtype_u

xp = <module 'numpy' from '/home/runner/micromamba/envs/pySDC/lib/python3.14/site-packages/numpy/__init__.py'>