Time-domain Green's functions for waves on simplicial complexes

Arnold, J.M. (2009) Time-domain Green's functions for waves on simplicial complexes. In: Proceedings of the 2009 International Conference on Electromagnetics in Advanced Applications, Torino, Italy, 14-18 Sept 2009. IEEE Computer Society: Piscataway, N.J., USA, pp. 720-722. ISBN 9781424433858 (doi: 10.1109/ICEAA.2009.5297291)

Abstract

Maxwell's laws of classical electrodynamics have exact counterparts on a purely discrete space, reformulated as discrete Stokes' Theorems on simplicial complexes. We here address the formulation of discrete Green's Theorems and discrete Green's functions in discrete-time on simplicial complexes in 3-space as the fully discretised versions of continuum wave equations that preserve Stokes' Theorems in all sub-dimensions of the simplicial complexes. These Green's functions have the same applications in discrete wave systems as their continuum counterparts, but are pre-conditioned to live wholly on the discrete space. 3-complexes in space with discrete time-stepping are the natural setting for generalisations of the FDTD algorithm from Yee-cells to general unstructured meshes.

• Item Type: Book Sections
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Arnold, Professor John
• Authors: Arnold, J.M.
• Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering
• College/School: College of Science and Engineering > School of Engineering > Electronics and Nanoscale Engineering
• Publisher: IEEE Computer Society
• ISBN: 9781424433858