Elements¶
Element formulations in torch-fem define interpolation on a reference domain and quadrature rules for numerical integration.
For an element with nodal coordinates \(\mathbf{x}_i\) and shape functions \(N_i(\pmb{\xi})\), the isoparametric mapping is
\[
\mathbf{x}(\pmb{\xi}) = \sum_{i=1}^{n} N_i(\pmb{\xi})\,\mathbf{x}_i.
\]
All concrete elements derive from the abstract Element base class and provide
- shape functions via
N() - derivatives in reference coordinates via
B() - reference nodal coordinates via
iso_coords - integration points and weights via
ipointsandiweights