Source code for felupe.tools._project

# -*- coding: utf-8 -*-
"""
This file is part of FElupe.

FElupe is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

FElupe is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with FElupe.  If not, see <http://www.gnu.org/licenses/>.
"""

import numpy as np
from scipy.sparse import csr_matrix as sparsematrix

from .._field import Field
from ..region import Region


[docs]def topoints(values, region, sym=True, mode="tensor"): rows = region.mesh.cells.T.ravel() cols = np.zeros_like(rows) if mode == "tensor": dim = values.shape[0] if sym: if dim == 3: ij = [(0, 0), (1, 1), (2, 2), (0, 1), (1, 2), (0, 2)] elif dim == 2: ij = [(0, 0), (1, 1), (0, 1)] else: if dim == 3: ij = [ (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), ] elif dim == 2: ij = [(0, 0), (0, 1), (1, 0), (1, 1)] out = Field(region, dim=len(ij)).values for a, (i, j) in enumerate(ij): out[:, a] = ( sparsematrix( (values.reshape(dim, dim, -1)[i, j], (rows, cols)), shape=(region.mesh.npoints, 1), ).toarray()[:, 0] / region.mesh.cells_per_point ) elif mode == "scalar": out = sparsematrix( (values.ravel(), (rows, cols)), shape=(region.mesh.npoints, 1) ).toarray()[:, 0] out = out / region.mesh.cells_per_point return out
[docs]def project(values, region, average=True, mean=False): """Projection (and optionally averaging) of scalar or vectorial values at quadrature points to mesh-points. """ dim = values.shape[:-2] size = int(np.product(dim)) weights = region.quadrature.weights # transpose values idx = np.arange(len(values.shape)) idx[: len(dim)] = idx[: len(dim)][::-1] values = values.transpose(idx) if mean: # evaluate how often the values must be repeated to match the number # of element-points reps = np.ones(len(values.shape), dtype=int) reps[-2] = len(region.element.points) # np.average(keepdims=True) requires numpy >= 1.23.0 values = np.average(values, axis=-2, weights=weights) # workaround for np.average(keepdims=True) shape = values.shape shape = np.insert(shape, -1, 1) values = values.reshape(*shape) # broadcast averaged values to match the number of element-points values = np.broadcast_to(values, shape=np.broadcast_shapes(shape, reps)) # reshape from (shape, nint.points, nelements) to 1d-values u = values.T.reshape(-1, size) # disconnect the mesh m = region.mesh.disconnect() if mean: # region on disconnected mesh with original quadrature scheme # a single-point quadrature would be sufficient # but would require additional (not available) informations r = Region(m, region.element, region.quadrature, grad=False) else: # region on disconnected mesh with inverse quadrature scheme r = Region(m, region.element, region.quadrature.inv(), grad=False) # field for values on disconnected mesh; project values to mesh-points f = Field(r, dim=size, values=u) v = f.interpolate() if mean: # due to the usage of the original quadrature scheme the averaging must be # applied again # np.average(keepdims=True) requires numpy >= 1.23.0 v = np.average(v, axis=-2, weights=weights).reshape(size, 1, -1) # broadcast averaged values to match the number of element-points shape = np.array([*v.shape[:-2], len(region.element.points), v.shape[-1]]) v = np.broadcast_to(v, shape=shape) if average: # create dummy field for values on original mesh # (used for calculation of sparse-matrix indices) g = Field(region, dim=size) # average values w = sparsematrix( (v.T.ravel(), g.indices.ai), shape=(size * region.mesh.npoints, 1) ).toarray().reshape(-1, size) / region.mesh.cells_per_point.reshape(-1, 1) else: w = v.T.reshape(-1, size) return w