Source code for felupe._basis._basis

# -*- coding: utf-8 -*-
"""
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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 einsumt import einsumt


[docs]class Basis: r"""A basis and its gradient built on top of a scalar- or vector-valued field. *Basis* refers to the trial and test field, either values or gradients evaluated at quadrature points. The first two indices of a basis are used for looping over the element shape functions ``a`` and its components ``i``. The third index represents the vector component ``j`` of the field. The two trailing axes ``(p, c)`` contain the evaluated element shape functions at quadrature points ``p`` per cell ``c``. .. math:: \varphi_{aijpc} = \delta_{ij} \left( h_a \right)_{pc} For gradients, the fourth index is used for the vector component of the partial derivative ``k``. .. math:: \text{grad}(\varphi)_{aijkpc} = \delta_{ij} \left( \frac{\partial h_a}{\partial X_K} \right)_{pc} Parameters ---------- field : Field A field on which the basis should be created. parallel : bool, optional (default is False) Flag to activate parallel (threaded) basis evaluation. Attributes ---------- basis : ndarray The evaluated basis functions at quadrature points. grad : ndarray The evaluated gradient of the basis (if provided by the region). """ def __init__(self, field, parallel=False): self.field = field einsum = einsumt if parallel else np.einsum self.basis = einsum( "ij,apc->aijpc", np.eye(self.field.dim), self.field.region.h, ) if hasattr(self.field.region, "dhdX"): self.grad = einsum( "ij,akpc->aijkpc", np.eye(self.field.dim), self.field.region.dhdX ) else: self.grad = None
class BasisMixed: r"""A basis and its gradient built on top of a scalar- or vector-valued field container. *Basis* refers to the trial and test field, either values or gradients evaluated at quadrature points. The first two indices of a basis are used for looping over the element shape functions ``a`` and its components ``i``. The third index represents the vector component ``j`` of the field. The two trailing axes ``(p, c)`` contain the evaluated element shape functions at quadrature points ``p`` per cell ``c``. .. math:: \varphi_{aijpc} = \delta_{ij} \left( h_a \right)_{pc} For gradients, the fourth index is used for the vector component of the partial derivative ``k``. .. math:: \text{grad}(\varphi)_{aijkpc} = \delta_{ij} \left( \frac{\partial h_a}{\partial X_K} \right)_{pc} Parameters ---------- field : FieldContainer A field container on which the basis should be created. Attributes ---------- basis : ndarray The evaluated basis functions at quadrature points. grad : ndarray The evaluated gradient of the basis (if provided by the region). """ def __init__(self, field, parallel=False): self.field = field self.basis = [Basis(f, parallel=parallel) for f in self.field] def __getitem__(self, idx): "Slice-based access to underlying bases." return self.basis[idx]