Computation of Maxwell's equations on Manifold using DEC
Zheng Xie, Yujie Ma
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.
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.
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Taxonomy
TopicsElectromagnetic Simulation and Numerical Methods · Advanced Numerical Methods in Computational Mathematics · Numerical methods for differential equations