Commit 296de5db authored by Martin Bauer's avatar Martin Bauer
Browse files

Merge branch 'fvm' into 'master'

finite difference stencil derivation for staggered positions

See merge request !99
parents 47aee5fa d002888a
Pipeline #20266 failed with stage
in 2 minutes and 21 seconds
import warnings
from collections import defaultdict
import itertools
import numpy as np
import sympy as sp
from pystencils.field import Field
from pystencils.stencil import direction_string_to_offset
from pystencils.sympyextensions import multidimensional_sum, prod
from pystencils.utils import LinearEquationSystem, fully_contains
......@@ -228,3 +230,120 @@ class FiniteDifferenceStencilDerivation:
def __repr__(self):
return "Finite difference stencil of accuracy {}, isotropic error: {}".format(self.accuracy,
self.is_isotropic)
class FiniteDifferenceStaggeredStencilDerivation:
"""Derives a finite difference stencil for application at a staggered position
Args:
neighbor: the neighbor direction string or vector at whose staggered position to calculate the derivative
dim: how many dimensions (2 or 3)
derivative: a tuple of directions over which to perform derivatives
"""
def __init__(self, neighbor, dim, derivative=tuple()):
if type(neighbor) is str:
neighbor = direction_string_to_offset(neighbor)
if dim == 2:
assert neighbor[dim:] == 0
assert derivative is tuple() or max(derivative) < dim
neighbor = sp.Matrix(neighbor[:dim])
pos = neighbor / 2
def unitvec(i):
"""return the `i`-th unit vector in three dimensions"""
a = np.zeros(dim, dtype=int)
a[i] = 1
return a
def flipped(a, i):
"""return `a` with its `i`-th element's sign flipped"""
a = a.copy()
a[i] *= -1
return a
# determine the points to use, coordinates are relative to position
points = []
if np.linalg.norm(neighbor, 1) == 1:
main_points = [neighbor / 2, neighbor / -2]
elif np.linalg.norm(neighbor, 1) == 2:
nonzero_indices = [i for i, v in enumerate(neighbor) if v != 0 and i < dim]
main_points = [neighbor / 2, neighbor / -2, flipped(neighbor / 2, nonzero_indices[0]),
flipped(neighbor / -2, nonzero_indices[0])]
else:
main_points = [neighbor.multiply_elementwise(sp.Matrix(c) / 2)
for c in itertools.product([-1, 1], repeat=3)]
points += main_points
zero_indices = [i for i, v in enumerate(neighbor) if v == 0 and i < dim]
for i in zero_indices:
points += [point + sp.Matrix(unitvec(i)) for point in main_points]
points += [point - sp.Matrix(unitvec(i)) for point in main_points]
points_tuple = tuple([tuple(p) for p in points])
self._stencil = points_tuple
# determine the stencil weights
if len(derivative) == 0:
weights = None
else:
derivation = FiniteDifferenceStencilDerivation(derivative, points_tuple).get_stencil()
if not derivation.accuracy:
raise Exception('the requested derivative cannot be performed with the available neighbors')
weights = derivation.weights
# if the weights are underdefined, we can choose the free symbols to find the sparsest stencil
free_weights = set(itertools.chain(*[w.free_symbols for w in weights]))
if len(free_weights) > 0:
zero_counts = defaultdict(list)
for values in itertools.product([-1, -sp.Rational(1, 2), 0, 1, sp.Rational(1, 2)],
repeat=len(free_weights)):
subs = {free_weight: value for free_weight, value in zip(free_weights, values)}
weights = [w.subs(subs) for w in derivation.weights]
if not all(a == 0 for a in weights):
zero_count = sum([1 for w in weights if w == 0])
zero_counts[zero_count].append(weights)
best = zero_counts[max(zero_counts.keys())]
if len(best) > 1: # if there are multiple, pick the one that contains a nonzero center weight
center = [tuple(p + pos) for p in points].index((0, 0, 0))
best = [b for b in best if b[center] != 0]
if len(best) > 1:
raise NotImplementedError("more than one suitable set of weights found, don't know how to proceed")
weights = best[0]
assert weights
points_tuple = tuple([tuple(p + pos) for p in points])
self._points = points_tuple
self._weights = weights
@property
def points(self):
"""return the points of the stencil"""
return self._points
@property
def stencil(self):
"""return the points of the stencil relative to the staggered position specified by neighbor"""
return self._stencil
@property
def weights(self):
"""return the weights of the stencil"""
assert self._weights is not None
return self._weights
def visualize(self):
if self._weights is None:
ws = None
else:
ws = np.array([w for w in self.weights if w != 0], dtype=float)
pts = np.array([p for i, p in enumerate(self.points) if self.weights[i] != 0], dtype=int)
from pystencils.stencil import plot
plot(pts, data=ws)
def apply(self, field):
if field.index_dimensions == 0:
return sum([field.__getitem__(point) * weight for point, weight in zip(self.points, self.weights)])
else:
total = field.neighbor_vector(self.points[0]) * self.weights[0]
for point, weight in zip(self.points[1:], self.weights[1:]):
total += field.neighbor_vector(point) * weight
return total
......@@ -441,6 +441,22 @@ class Field(AbstractField):
center = tuple([0] * self.spatial_dimensions)
return Field.Access(self, center)
def neighbor_vector(self, offset):
"""Like neighbor, but returns the entire vector/tensor stored at offset."""
if self.spatial_dimensions == 2 and len(offset) == 3:
assert offset[2] == 0
offset = offset[:2]
if self.index_dimensions == 0:
return sp.Matrix([self.__getitem__(offset)])
elif self.index_dimensions == 1:
return sp.Matrix([self.__getitem__(offset)(i) for i in range(self.index_shape[0])])
elif self.index_dimensions == 2:
return sp.Matrix([[self.__getitem__(offset)(i, k) for k in range(self.index_shape[1])]
for i in range(self.index_shape[0])])
else:
raise NotImplementedError("neighbor_vector is not implemented for more than 2 index dimensions")
def __getitem__(self, offset):
if type(offset) is np.ndarray:
offset = tuple(offset)
......
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