template<class Derived>
Rodin::Variational::FiniteElementSpaceInverseMappingBase class

Base class for inverse mappings taking functions defined on to reference elements.

For all $ \tau \in \mathcal{T}_h $ the inverse mapping

\[ \psi^{-1} : V(K) \rightarrow V(\tau) \]

takes functions defined on the reference Banach space $ V(K) $ to the physical Banach space $ V(K) $ . Here $ \tau = x(K) $ is the physical element, $ K $ is the reference element, and $ x : K \rightarrow \tau $ is the polytope transformation.

Public functions

auto operator()(const Geometry::Point& pc) const -> auto
Evaluates the mapped function on the physical coordinates.

Function documentation

template<class Derived>
auto Rodin::Variational::FiniteElementSpaceInverseMappingBase<Derived>::operator()(const Geometry::Point& pc) const

Evaluates the mapped function on the physical coordinates.

For the given function $ v \in V(K) $ , performs the following evaluation:

\[ \psi^{-1}(v)(p) \]

on the physical coordinates $ p \in \tau $ .