A mass-lumped mixed finite element method for Maxwell's equations

TL;DR

This paper introduces a new mass-lumped mixed finite element method for Maxwell's equations that extends the Yee scheme to unstructured grids and anisotropic materials, providing a flexible and variational approach.

Contribution

A novel mass-lumping strategy for mixed finite element approximation of Maxwell's equations that generalizes the Yee scheme to unstructured grids and anisotropic materials.

Findings

Method coincides with Yee scheme on structured grids

Generalizes to unstructured grids and anisotropic materials

Provides a variational extension of the Yee scheme

Abstract

A novel mass-lumping strategy for a mixed finite element approximation of Maxwell's equations is proposed. On structured orthogonal grids the resulting method coincides with the spatial discretization of the Yee scheme. The proposed method, however, generalizes naturally to unstructured grids and anisotropic materials and thus yields a variational extension of the Yee scheme for these situations.