Computation of Maxwell's equations on manifold using implicit DEC scheme

TL;DR

This paper introduces an implicit discrete exterior calculus scheme for numerically solving Maxwell's equations on manifolds, achieving unconditional stability and direct implementation in space manifolds.

Contribution

It develops an implicit Yee-like scheme combining discrete exterior calculus with an implicit time scheme for stable Maxwell's equations simulation on manifolds.

Findings

The scheme is unconditionally stable.

Error analysis confirms accuracy.

Direct implementation on space manifolds is feasible.

Abstract

Maxwell's equations can be solved numerically in space manifold and the time by discrete exterior calculus as a kind of lattice gauge theory.Since the stable conditions of this method is very severe restriction, we combine the implicit scheme of time variable and discrete exterior calculus to derive an unconditional stable scheme. It is an generation of implicit Yee-like scheme, since it can be implemented in space manifold directly. The analysis of its unconditional stability and error is also accomplished.