import numpy as np
from pySDC.core.Errors import TransferError
from pySDC.core.SpaceTransfer import space_transfer
from pySDC.implementations.datatype_classes.mesh import mesh, imex_mesh
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class mesh_to_mesh_fft2d(space_transfer):
"""
Custon base_transfer class, implements Transfer.py
This implementation can restrict and prolong between 2d meshes with FFT for periodic boundaries
Attributes:
Rspace: spatial restriction matrix, dim. Nf x Nc
Pspace: spatial prolongation matrix, dim. Nc x Nf
"""
def __init__(self, fine_prob, coarse_prob, params):
"""
Initialization routine
Args:
fine_prob: fine problem
coarse_prob: coarse problem
params: parameters for the transfer operators
"""
# invoke super initialization
super(mesh_to_mesh_fft2d, self).__init__(fine_prob, coarse_prob, params)
# TODO: cleanup and move to real-valued FFT
assert len(self.fine_prob.nvars) == 2
assert len(self.coarse_prob.nvars) == 2
assert self.fine_prob.nvars[0] == self.fine_prob.nvars[1]
assert self.coarse_prob.nvars[0] == self.coarse_prob.nvars[1]
self.ratio = int(self.fine_prob.nvars[0] / self.coarse_prob.nvars[0])
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def restrict(self, F):
"""
Restriction implementation
Args:
F: the fine level data (easier to access than via the fine attribute)
"""
if isinstance(F, mesh):
G = mesh(self.coarse_prob.init, val=0.0)
G[:] = F[:: self.ratio, :: self.ratio]
elif isinstance(F, imex_mesh):
G = imex_mesh(self.coarse_prob.init, val=0.0)
G.impl[:] = F.impl[:: self.ratio, :: self.ratio]
G.expl[:] = F.expl[:: self.ratio, :: self.ratio]
else:
raise TransferError('Unknown data type, got %s' % type(F))
return G
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def prolong(self, G):
"""
Prolongation implementation
Args:
G: the coarse level data (easier to access than via the coarse attribute)
"""
if isinstance(G, mesh):
F = mesh(self.fine_prob.init)
tmpG = np.fft.fft2(G)
tmpF = np.zeros(self.fine_prob.init[0], dtype=np.complex128)
halfG = int(self.coarse_prob.init[0][0] / 2)
tmpF[0:halfG, 0:halfG] = tmpG[0:halfG, 0:halfG]
tmpF[self.fine_prob.init[0][0] - halfG :, 0:halfG] = tmpG[halfG:, 0:halfG]
tmpF[0:halfG, self.fine_prob.init[0][0] - halfG :] = tmpG[0:halfG, halfG:]
tmpF[self.fine_prob.init[0][0] - halfG :, self.fine_prob.init[0][0] - halfG :] = tmpG[halfG:, halfG:]
F[:] = np.real(np.fft.ifft2(tmpF)) * self.ratio * 2
elif isinstance(G, imex_mesh):
F = imex_mesh(G)
tmpG_impl = np.fft.fft2(G.impl)
tmpF_impl = np.zeros(self.fine_prob.init, dtype=np.complex128)
halfG = int(self.coarse_prob.init[0][0] / 2)
tmpF_impl[0:halfG, 0:halfG] = tmpG_impl[0:halfG, 0:halfG]
tmpF_impl[self.fine_prob.init[0][0] - halfG :, 0:halfG] = tmpG_impl[halfG:, 0:halfG]
tmpF_impl[0:halfG, self.fine_prob.init[0][0] - halfG :] = tmpG_impl[0:halfG, halfG:]
tmpF_impl[self.fine_prob.init[0][0] - halfG :, self.fine_prob.init[0][0] - halfG :] = tmpG_impl[
halfG:, halfG:
]
F.impl[:] = np.real(np.fft.ifft2(tmpF_impl)) * self.ratio * 2
tmpG_expl = np.fft.fft2(G.expl) / (self.coarse_prob.init[0] * self.coarse_prob.init[1])
tmpF_expl = np.zeros(self.fine_prob.init[0], dtype=np.complex128)
halfG = int(self.coarse_prob.init[0][0] / 2)
tmpF_expl[0:halfG, 0:halfG] = tmpG_expl[0:halfG, 0:halfG]
tmpF_expl[self.fine_prob.init[0][0] - halfG :, 0:halfG] = tmpG_expl[halfG:, 0:halfG]
tmpF_expl[0:halfG, self.fine_prob.init[0][0] - halfG :] = tmpG_expl[0:halfG, halfG:]
tmpF_expl[self.fine_prob.init[0][0] - halfG :, self.fine_prob.init[0][0] - halfG :] = tmpG_expl[
halfG:, halfG:
]
F.expl[:] = np.real(np.fft.ifft2(tmpF_expl)) * self.ratio * 2
else:
raise TransferError('Unknown data type, got %s' % type(G))
return F