Coverage for pySDC/implementations/problem_classes/generic_MPIFFT_Laplacian.py: 99%
86 statements
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1import numpy as np
2from mpi4py import MPI
3from mpi4py_fft import PFFT
5from pySDC.core.errors import ProblemError
6from pySDC.core.problem import Problem, WorkCounter
7from pySDC.implementations.datatype_classes.mesh import mesh, imex_mesh
9from mpi4py_fft import newDistArray
12class IMEX_Laplacian_MPIFFT(Problem):
13 r"""
14 Generic base class for IMEX problems using a spectral method to solve the Laplacian implicitly and a possible rest
15 explicitly. The FFTs are done with``mpi4py-fft`` [1]_.
17 Parameters
18 ----------
19 nvars : tuple, optional
20 Spatial resolution
21 spectral : bool, optional
22 If True, the solution is computed in spectral space.
23 L : float, optional
24 Denotes the period of the function to be approximated for the Fourier transform.
25 alpha : float, optional
26 Multiplicative factor before the Laplacian
27 comm : MPI.COMM_World
28 Communicator for parallelisation.
30 Attributes
31 ----------
32 fft : PFFT
33 Object for parallel FFT transforms.
34 X : mesh-grid
35 Grid coordinates in real space.
36 K2 : matrix
37 Laplace operator in spectral space.
39 References
40 ----------
41 .. [1] Lisandro Dalcin, Mikael Mortensen, David E. Keyes. Fast parallel multidimensional FFT using advanced MPI.
42 Journal of Parallel and Distributed Computing (2019).
43 """
45 dtype_u = mesh
46 dtype_f = imex_mesh
48 xp = np
49 fft_backend = 'fftw'
50 fft_comm_backend = 'MPI'
52 @classmethod
53 def setup_GPU(cls):
54 """switch to GPU modules"""
55 import cupy as cp
56 from pySDC.implementations.datatype_classes.cupy_mesh import cupy_mesh, imex_cupy_mesh
58 cls.xp = cp
60 cls.dtype_u = cupy_mesh
61 cls.dtype_f = imex_cupy_mesh
63 cls.fft_backend = 'cupy'
64 cls.fft_comm_backend = 'NCCL'
66 def __init__(
67 self, nvars=None, spectral=False, L=2 * np.pi, alpha=1.0, comm=MPI.COMM_WORLD, dtype='d', useGPU=False, x0=0.0
68 ):
69 """Initialization routine"""
71 if useGPU:
72 self.setup_GPU()
74 if nvars is None:
75 nvars = (128, 128)
77 if not (isinstance(nvars, tuple) and len(nvars) > 1):
78 raise ProblemError('Need at least two dimensions for distributed FFTs')
80 # Creating FFT structure
81 self.ndim = len(nvars)
82 axes = tuple(range(self.ndim))
83 self.fft = PFFT(
84 comm,
85 list(nvars),
86 axes=axes,
87 dtype=dtype,
88 collapse=True,
89 backend=self.fft_backend,
90 comm_backend=self.fft_comm_backend,
91 )
93 # get test data to figure out type and dimensions
94 tmp_u = newDistArray(self.fft, spectral)
96 L = np.array([L] * self.ndim, dtype=float)
98 # invoke super init, passing the communicator and the local dimensions as init
99 super().__init__(init=(tmp_u.shape, comm, tmp_u.dtype))
100 self._makeAttributeAndRegister(
101 'nvars', 'spectral', 'L', 'alpha', 'comm', 'x0', localVars=locals(), readOnly=True
102 )
104 # get local mesh
105 X = list(self.xp.ogrid[self.fft.local_slice(False)])
106 N = self.fft.global_shape()
107 for i in range(len(N)):
108 X[i] = x0 + (X[i] * L[i] / N[i])
109 self.X = [self.xp.broadcast_to(x, self.fft.shape(False)) for x in X]
111 # get local wavenumbers and Laplace operator
112 s = self.fft.local_slice()
113 N = self.fft.global_shape()
114 k = [self.xp.fft.fftfreq(n, 1.0 / n).astype(int) for n in N]
115 K = [ki[si] for ki, si in zip(k, s)]
116 Ks = list(self.xp.meshgrid(*K, indexing='ij', sparse=True))
117 Lp = 2 * np.pi / self.L
118 for i in range(self.ndim):
119 Ks[i] = (Ks[i] * Lp[i]).astype(float)
120 K = [self.xp.broadcast_to(k, self.fft.shape(True)) for k in Ks]
121 K = self.xp.array(K).astype(float)
122 self.K2 = self.xp.sum(K * K, 0, dtype=float) # Laplacian in spectral space
124 # Need this for diagnostics
125 self.dx = self.L[0] / nvars[0]
126 self.dy = self.L[1] / nvars[1]
128 # work counters
129 self.work_counters['rhs'] = WorkCounter()
131 def eval_f(self, u, t):
132 """
133 Routine to evaluate the right-hand side of the problem.
135 Parameters
136 ----------
137 u : dtype_u
138 Current values of the numerical solution.
139 t : float
140 Current time at which the numerical solution is computed.
142 Returns
143 -------
144 f : dtype_f
145 The right-hand side of the problem.
146 """
148 f = self.dtype_f(self.init)
150 f.impl[:] = self._eval_Laplacian(u, f.impl)
152 if self.spectral:
153 tmp = self.fft.backward(u)
154 tmp[:] = self._eval_explicit_part(tmp, t, tmp)
155 f.expl[:] = self.fft.forward(tmp)
157 else:
158 f.expl[:] = self._eval_explicit_part(u, t, f.expl)
160 self.work_counters['rhs']()
161 return f
163 def _eval_Laplacian(self, u, f_impl, alpha=None):
164 alpha = alpha if alpha else self.alpha
165 if self.spectral:
166 f_impl[:] = -alpha * self.K2 * u
167 else:
168 u_hat = self.fft.forward(u)
169 lap_u_hat = -alpha * self.K2 * u_hat
170 f_impl[:] = self.fft.backward(lap_u_hat, f_impl)
171 return f_impl
173 def _eval_explicit_part(self, u, t, f_expl):
174 return f_expl
176 def solve_system(self, rhs, factor, u0, t):
177 """
178 Simple FFT solver for the diffusion part.
180 Parameters
181 ----------
182 rhs : dtype_f
183 Right-hand side for the linear system.
184 factor : float
185 Abbrev. for the node-to-node stepsize (or any other factor required).
186 u0 : dtype_u
187 Initial guess for the iterative solver (not used here so far).
188 t : float
189 Current time (e.g. for time-dependent BCs).
191 Returns
192 -------
193 me : dtype_u
194 The solution as mesh.
195 """
196 me = self.dtype_u(self.init)
197 me[:] = self._invert_Laplacian(me, factor, rhs)
199 return me
201 def _invert_Laplacian(self, me, factor, rhs, alpha=None):
202 alpha = alpha if alpha else self.alpha
203 if self.spectral:
204 me[:] = rhs / (1.0 + factor * alpha * self.K2)
206 else:
207 rhs_hat = self.fft.forward(rhs)
208 rhs_hat /= 1.0 + factor * alpha * self.K2
209 me[:] = self.fft.backward(rhs_hat)
210 return me