Topological and geometrical considerations for maxwell's equations on unstructured meshes

Cynthia Kaus, Richard W. Ziolkowski

Research output: Contribution to journalArticle

Abstract

A discrete differential form approach to solving Maxwell's equations on unstructured meshes is presented. Discrete representations of differential forms, the underlying manifolds, and associated operators are developed. The discrete boundary, coboundary, and hodge star operators are shown to maintain divergence-free regions. With the construction of a cell complex, its dual complex, and the associated discrete operators, we have determined the numerical update equations for the electromagnetic fields on unstructured meshes with second-order accuracy. The discrete differential form approach generalizes to the Yee algorithm on an orthogonal complex and to the discrete surface integral algorithm on a parallelepiped complex.

Original languageEnglish (US)
Pages (from-to)42-53
Number of pages12
JournalElectromagnetics
Volume28
Issue number1-2
DOIs
StatePublished - Jan 1 2008

Keywords

  • Differential forms
  • Electromagnetics
  • Maxwell's equations
  • Update equations

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Radiation
  • Electrical and Electronic Engineering

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