Hierarchical FIT/FE Discretization for Dielectric Subcell Interfaces

The discretization of an electrostatic problem by the finite integration technique (FIT) is augmented with specialized finite-element shape functions for resolving dielectric interfaces that are not resolved by the Cartesian grid. The numerical validation shows that the achieved accuracy matches the one of a conformal discretization. The additional approximation space is implemented as a perturbation of the original Cartesian FIT formulation.