# Computation of Maxwell's equations on Manifold using DEC

## TL;DR

This paper presents a numerical method using discrete exterior calculus to solve Maxwell's equations on manifolds, analyzing stability and errors, with implementation for simulating electromagnetic waves in vacuum.

## Contribution

Introduces a discrete exterior calculus approach for Maxwell's equations on manifolds, including stability analysis and implementation details.

## Key findings

- Stable numerical scheme for Maxwell's equations on manifolds
- Error analysis of the discretization method
- Simulation of TE/M waves in vacuum

## Abstract

In this paper, the method of discrete exterior calculus for numerically solving Maxwell's equations in space manifold and the time is discussed, which is a kind of lattice gauge theory. The analysis of its stable condition and error is also accomplished. This algorithm has been implemented on C++ plateform for simulating TE/M waves in vacuum.