def describe_membrane_geometry(self, ig, field, sg, sd): # Coordinates of element vertices. coors = field.coors[sd.econn[:, :sg.n_fp]] # Coordinate transformation matrix (transposed!). self.mtx_t[ig] = membranes.create_transformation_matrix(coors) # Transform coordinates to the local coordinate system. coors_loc = dot_sequences((coors - coors[:, 0:1, :]), self.mtx_t[ig]) # Mapping from transformed element to reference element. gel = field.gel.surface_facet vm = membranes.create_mapping(coors_loc, gel, 1) qp = self.integral.get_qp(gel.name) ps = PolySpace.any_from_args(None, gel, field.approx_order) self.membrane_geo[ig] = vm.get_mapping(qp[0], qp[1], poly_space=ps) # Transformed base function gradient w.r.t. material coordinates # in quadrature points. self.bfg[ig] = self.membrane_geo[ig].bfg
def describe_geometry(self, field, gtype, region, integral, return_mapping=False): """ Compute jacobians, element volumes and base function derivatives for Volume-type geometries (volume mappings), and jacobians, normals and base function derivatives for Surface-type geometries (surface mappings). Notes ----- - volume mappings can be defined on a part of an element group, although the field has to be defined always on the whole group. - surface mappings are defined on the surface region - surface mappings require field order to be > 0 """ domain = field.domain group = domain.groups[self.ig] coors = domain.get_mesh_coors(actual=True) if gtype == 'volume': qp = self.get_qp('v', integral) iels = region.get_cells(self.ig) geo_ps = self.interp.get_geom_poly_space('v') ps = self.interp.poly_spaces['v'] bf = self.get_base('v', 0, integral, iels=iels) conn = nm.take(group.conn, iels.astype(nm.int32), axis=0) mapping = VolumeMapping(coors, conn, poly_space=geo_ps) vg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps, ori=self.ori) out = vg elif gtype == 'plate': import sfepy.mechanics.membranes as mm from sfepy.linalg import dot_sequences qp = self.get_qp('v', integral) iels = region.get_cells(self.ig) ps = self.interp.poly_spaces['v'] bf = self.get_base('v', 0, integral, iels=iels) conn = nm.take(group.conn, nm.int32(iels), axis=0) ccoors = coors[conn] # Coordinate transformation matrix (transposed!). mtx_t = mm.create_transformation_matrix(ccoors) # Transform coordinates to the local coordinate system. coors_loc = dot_sequences((ccoors - ccoors[:, 0:1, :]), mtx_t) # Mapping from transformed elements to reference elements. mapping = mm.create_mapping(coors_loc, field.gel, 1) vg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps, ori=self.ori) vg.mtx_t = mtx_t out = vg elif (gtype == 'surface') or (gtype == 'surface_extra'): assert_(field.approx_order > 0) if self.ori is not None: msg = 'surface integrals do not work yet with the' \ ' hierarchical basis!' raise ValueError(msg) sd = domain.surface_groups[self.ig][region.name] esd = self.surface_data[region.name] qp = self.get_qp(sd.face_type, integral) geo_ps = self.interp.get_geom_poly_space(sd.face_type) ps = self.interp.poly_spaces[esd.face_type] bf = self.get_base(esd.face_type, 0, integral) conn = sd.get_connectivity() mapping = SurfaceMapping(coors, conn, poly_space=geo_ps) sg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps, mode=gtype) if gtype == 'surface_extra': sg.alloc_extra_data(self.n_ep['v']) self.create_bqp(region.name, integral) qp = self.qp_coors[(integral.name, esd.bkey)] v_geo_ps = self.interp.get_geom_poly_space('v') bf_bg = v_geo_ps.eval_base(qp.vals, diff=True) ebf_bg = self.get_base(esd.bkey, 1, integral) sg.evaluate_bfbgm(bf_bg, ebf_bg, coors, sd.fis, group.conn) out = sg elif gtype == 'point': out = mapping = None else: raise ValueError('unknown geometry type: %s' % gtype) if out is not None: # Store the integral used. out.integral = integral out.qp = qp out.ps = ps # Update base. out.bf[:] = bf if return_mapping: out = (out, mapping) return out
def create_mapping(self, region, integral, integration, return_mapping=True): """ Create a new reference mapping. Compute jacobians, element volumes and base function derivatives for Volume-type geometries (volume mappings), and jacobians, normals and base function derivatives for Surface-type geometries (surface mappings). Notes ----- - surface mappings are defined on the surface region - surface mappings require field order to be > 0 """ domain = self.domain coors = domain.get_mesh_coors(actual=True) dconn = domain.get_conn() if integration == 'volume': qp = self.get_qp('v', integral) iels = region.get_cells() geo_ps = self.gel.poly_space ps = self.poly_space bf = self.get_base('v', 0, integral, iels=iels) conn = nm.take(dconn, iels.astype(nm.int32), axis=0) mapping = VolumeMapping(coors, conn, poly_space=geo_ps) vg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps, ori=self.ori) out = vg elif integration == 'plate': import sfepy.mechanics.membranes as mm from sfepy.linalg import dot_sequences qp = self.get_qp('v', integral) iels = region.get_cells() ps = self.interp.poly_spaces['v'] bf = self.get_base('v', 0, integral, iels=iels) conn = nm.take(dconn, nm.int32(iels), axis=0) ccoors = coors[conn] # Coordinate transformation matrix (transposed!). mtx_t = mm.create_transformation_matrix(ccoors) # Transform coordinates to the local coordinate system. coors_loc = dot_sequences((ccoors - ccoors[:, 0:1, :]), mtx_t) # Mapping from transformed elements to reference elements. mapping = mm.create_mapping(coors_loc, self.gel, 1) vg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps, ori=self.ori) vg.mtx_t = mtx_t out = vg elif (integration == 'surface') or (integration == 'surface_extra'): assert_(self.approx_order > 0) if self.ori is not None: msg = 'surface integrals do not work yet with the' \ ' hierarchical basis!' raise ValueError(msg) sd = domain.surface_groups[region.name] esd = self.surface_data[region.name] geo_ps = self.gel.poly_space ps = self.poly_space conn = sd.get_connectivity() mapping = SurfaceMapping(coors, conn, poly_space=geo_ps) if not self.is_surface: self.create_bqp(region.name, integral) qp = self.qp_coors[(integral.order, esd.bkey)] abf = ps.eval_base(qp.vals[0]) bf = abf[..., self.efaces[0]] indx = self.gel.get_surface_entities()[0] # Fix geometry element's 1st facet orientation for gradients. indx = nm.roll(indx, -1)[::-1] mapping.set_basis_indices(indx) sg = mapping.get_mapping(qp.vals[0], qp.weights, poly_space=Struct(n_nod=bf.shape[-1]), mode=integration) if integration == 'surface_extra': sg.alloc_extra_data(self.econn.shape[1]) bf_bg = geo_ps.eval_base(qp.vals, diff=True) ebf_bg = self.get_base(esd.bkey, 1, integral) sg.evaluate_bfbgm(bf_bg, ebf_bg, coors, sd.fis, dconn) else: # Do not use BQP for surface fields. qp = self.get_qp(sd.face_type, integral) bf = ps.eval_base(qp.vals) sg = mapping.get_mapping(qp.vals, qp.weights, poly_space=Struct(n_nod=bf.shape[-1]), mode=integration) out = sg elif integration == 'point': out = mapping = None else: raise ValueError('unknown inegration geometry type: %s' % integration) if out is not None: # Store the integral used. out.integral = integral out.qp = qp out.ps = ps # Update base. out.bf[:] = bf if return_mapping: out = (out, mapping) return out
def describe_geometry(self, field, gtype, region, integral, return_mapping=False): """ Compute jacobians, element volumes and base function derivatives for Volume-type geometries (volume mappings), and jacobians, normals and base function derivatives for Surface-type geometries (surface mappings). Notes ----- - volume mappings can be defined on a part of an element group, although the field has to be defined always on the whole group. - surface mappings are defined on the surface region - surface mappings require field order to be > 0 """ domain = field.domain group = domain.groups[self.ig] coors = domain.get_mesh_coors(actual=True) if gtype == 'volume': qp = self.get_qp('v', integral) iels = region.get_cells(self.ig) geo_ps = self.interp.get_geom_poly_space('v') ps = self.interp.poly_spaces['v'] bf = self.get_base('v', 0, integral, iels=iels) conn = nm.take(group.conn, iels.astype(nm.int32), axis=0) mapping = VolumeMapping(coors, conn, poly_space=geo_ps) vg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps, ori=self.ori) out = vg elif gtype == 'plate': import sfepy.mechanics.membranes as mm from sfepy.linalg import dot_sequences qp = self.get_qp('v', integral) iels = region.get_cells(self.ig) ps = self.interp.poly_spaces['v'] bf = self.get_base('v', 0, integral, iels=iels) conn = nm.take(group.conn, nm.int32(iels), axis=0) ccoors = coors[conn] # Coordinate transformation matrix (transposed!). mtx_t = mm.create_transformation_matrix(ccoors) # Transform coordinates to the local coordinate system. coors_loc = dot_sequences((ccoors - ccoors[:, 0:1, :]), mtx_t) # Mapping from transformed elements to reference elements. mapping = mm.create_mapping(coors_loc, field.gel, 1) vg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps, ori=self.ori) vg.mtx_t = mtx_t out = vg elif (gtype == 'surface') or (gtype == 'surface_extra'): assert_(field.approx_order > 0) if self.ori is not None: msg = 'surface integrals do not work yet with the' \ ' hierarchical basis!' raise ValueError(msg) sd = domain.surface_groups[self.ig][region.name] esd = self.surface_data[region.name] qp = self.get_qp(sd.face_type, integral) geo_ps = self.interp.get_geom_poly_space(sd.face_type) ps = self.interp.poly_spaces[esd.face_type] bf = self.get_base(esd.face_type, 0, integral) conn = sd.get_connectivity() mapping = SurfaceMapping(coors, conn, poly_space=geo_ps) sg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps, mode=gtype) if gtype == 'surface_extra': sg.alloc_extra_data(self.n_ep['v']) self.create_bqp(region.name, integral) qp = self.qp_coors[(integral.order, esd.bkey)] v_geo_ps = self.interp.get_geom_poly_space('v') bf_bg = v_geo_ps.eval_base(qp.vals, diff=True) ebf_bg = self.get_base(esd.bkey, 1, integral) sg.evaluate_bfbgm(bf_bg, ebf_bg, coors, sd.fis, group.conn) out = sg elif gtype == 'point': out = mapping = None else: raise ValueError('unknown geometry type: %s' % gtype) if out is not None: # Store the integral used. out.integral = integral out.qp = qp out.ps = ps # Update base. out.bf[:] = bf if return_mapping: out = (out, mapping) return out