A Yee-like finite element scheme for Maxwell's equations on hybrid grids

TL;DR

This paper introduces a Yee-like finite element scheme for Maxwell's equations on hybrid grids, enabling efficient explicit time integration with mass-lumping and providing a comprehensive error analysis and numerical validation.

Contribution

It presents a novel finite element method with diagonal mass matrices for Maxwell's equations on hybrid grids, combining features of FIT and FDTD methods and allowing flexible element shapes.

Findings

Diagonal mass matrices enable efficient explicit time integration.

Method coincides with FIT and FDTD on rectangular grids.

Numerical tests validate the accuracy and efficiency.

Abstract

A novel finite element method for the approximation of Maxwell's equations over hybrid two-dimensional grids is studied. The choice of appropriate basis functions and numerical quadrature leads to diagonal mass matrices which allow for efficient time integration by explicit methods. On purely rectangular grids, the proposed schemes coincide with well-established FIT and FDTD methods. Additional internal degrees of freedom introduced on triangles allow for mass-lumping without the usual constraints on the shape of these elements. A full error analysis of the method is developed and numerical tests are presented for illustration.