FVTD—integral equation hybrid for Maxwell's equations

✍ Scribed by Dmitry K. Firsov; Joe LoVetri

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 280 KB
• Volume: 21
• Category: Article
• ISSN: 0894-3370
• DOI: 10.1002/jnm.662

✦ Synopsis

Abstract

A new hybrid finite‐volume time‐domain integral equation (FVTD/IE) algorithm for the solution of Maxwell's Equations on unstructured meshes of arbitrary flat‐faceted volume elements is presented. A time‐domain IE‐based numerical algorithm is applied on the boundary of the computational domain to determine the incoming fluxes for the boundary facets of the mesh. This method is a global grid‐truncation technique similar to the method previously introduced for the finite‐difference time‐domain scheme by Ziolkowski et al. The three main advantages of this IE truncation method are that (1) it allows geometrical objects to be located (almost) arbitrarily close to the mesh boundaries without compromising the physics of the problem, (2) it couples the physics of unconnected meshes so that distant scatterers can be surrounded by their own local mesh, thus reducing total mesh size, and (3) the same IE formulation can be used to compute electromagnetic field values at points outside the mesh. Currently, the main disadvantage is that an acceleration scheme for performing the IE update, which requires integrating field components on an interior surface at a retarded time, is not available. Computational results are presented for the scattering from a perfectly electrical conducting sphere and compared numerically with the analytic time‐domain solution as well as the solution obtained using a large spherical outer mesh boundary with local absorbing boundary conditions. Results are excellent and show almost no reflections from the mesh boundary even when the observation point is located close to the corner of the cubically shaped outside mesh boundary. Results are also presented and validated for the scattering from two objects that are contained inside their own unconnected meshes. Copyright © 2007 John Wiley & Sons, Ltd.