Source code for sfepy.discrete.fem.mappings

"""
Finite element reference mappings.
"""
import numpy as nm

from sfepy.base.base import get_default, output
from sfepy.discrete.common.mappings import Mapping
from sfepy.discrete.common.extmods.mappings import CMapping
from sfepy.discrete.fem.poly_spaces import PolySpace

[docs]class FEMapping(Mapping): """ Base class for finite element mappings. """ def __init__(self, coors, conn, poly_space=None, gel=None, order=1): self.coors = coors self.conn = conn try: nm.take(self.coors, self.conn) except IndexError: output('coordinates shape: %s' % list(coors.shape)) output('connectivity: min: %d, max: %d' % (conn.min(), conn.max())) msg = 'incompatible connectivity and coordinates (see above)' raise IndexError(msg) self.n_el, self.n_ep = conn.shape self.dim = self.coors.shape[1] if poly_space is None: poly_space = PolySpace.any_from_args(None, gel, order, base='lagrange', force_bubble=False) self.poly_space = poly_space self.indices = slice(None)
[docs] def get_geometry(self): """ Return reference element geometry as a GeometryElement instance. """ return self.poly_space.geometry
[docs] def get_base(self, coors, diff=False): """ Get base functions or their gradient evaluated in given coordinates. """ bf = self.poly_space.eval_base(coors, diff=diff) return bf
[docs] def get_physical_qps(self, qp_coors): """ Get physical quadrature points corresponding to given reference element quadrature points. Returns ------- qps : array The physical quadrature points ordered element by element, i.e. with shape (n_el, n_qp, dim). """ bf = self.get_base(qp_coors) qps = nm.dot(nm.atleast_2d(bf.squeeze()), self.coors[self.conn]) # Reorder so that qps are really element by element. qps = nm.ascontiguousarray(nm.swapaxes(qps, 0, 1)) return qps
[docs]class VolumeMapping(FEMapping): """ Mapping from reference domain to physical domain of the same space dimension. """
[docs] def get_mapping(self, qp_coors, weights, poly_space=None, ori=None, transform=None): """ Get the mapping for given quadrature points, weights, and polynomial space. Returns ------- cmap : CMapping instance The volume mapping. """ poly_space = get_default(poly_space, self.poly_space) bf_g = self.get_base(qp_coors, diff=True) ebf_g = poly_space.eval_base(qp_coors, diff=True, ori=ori, force_axis=True, transform=transform) flag = (ori is not None) or (ebf_g.shape[0] > 1) cmap = CMapping(self.n_el, qp_coors.shape[0], self.dim, poly_space.n_nod, mode='volume', flag=flag) cmap.describe(self.coors, self.conn, bf_g, ebf_g, weights) return cmap
[docs]class SurfaceMapping(FEMapping): """ Mapping from reference domain to physical domain of the space dimension higher by one. """
[docs] def set_basis_indices(self, indices): """ Set indices to cell-based basis that give the facet-based basis. """ self.indices = indices
[docs] def get_base(self, coors, diff=False): """ Get base functions or their gradient evaluated in given coordinates. """ bf = self.poly_space.eval_base(coors, diff=diff) return nm.ascontiguousarray(bf[..., :self.dim-1:, self.indices])
[docs] def get_mapping(self, qp_coors, weights, poly_space=None, mode='surface'): """ Get the mapping for given quadrature points, weights, and polynomial space. Returns ------- cmap : CMapping instance The surface mapping. """ poly_space = get_default(poly_space, self.poly_space) bf_g = self.get_base(qp_coors, diff=True) if nm.allclose(bf_g, 0.0): raise ValueError('zero base function gradient!') cmap = CMapping(self.n_el, qp_coors.shape[0], self.dim, poly_space.n_nod, mode=mode) cmap.describe(self.coors, self.conn, bf_g, None, weights) return cmap