Partial Differential Equations - Modelling and ... - ResearchGate

Comparison of Two Explicit Time Domain
Unstructured Mesh Algorithms
for Computational Electromagnetics
Igor Sazonov, Oubay Hassan, Ken Morgan, and Nigel P. Weatherill
Civil and Computational Engineering Centre, School of Engineering, University of
Wales, Swansea SA2 8PP, Wales, UK
{i.sazonov,O.Hassan,K.Morgan,N.P.Weatherill}@swansea.ac.uk
Summary. An explicit finite element time domain method and a co-volume approach,
based upon a generalization of the well-known finite difference time domain
scheme of Yee to unstructured meshes, are employed for the solution of Maxwell’s
curl equations in the time domain. A stitching method is employed to produce
meshes that are suitable for use with a co-volume algorithm. Examples, involving
EM wave propagation and scattering, are included and the numerical performance
of the two techniques is compared.
Key words: computationalelectromagnetics,Delaunaytriangulation,Voronoï
tessellation,co-volumemeshgeneration,explicitschemes,finiteelementmethod,
co-volume method, EM wave propagation and scattering
1 Introduction
Computational methods are widely employed for the solution of Maxwell’s
equations in a variety of different application areas that fall within the general
field of electromagnetics. For practical applications, the requirement of modelling
complex geometries means that unstructured mesh methods are particularly
attractive, as fully automatic unstructured mesh generation procedures
are now widely available [Geo91, WH94, PPM99]. Following this philosophy
requires the identification of a suitable unstructured mesh-based solution algorithm
and several low-order time domain procedures have been proposed
[MSH91, PLD92, CFS93, DL97, MWH + 99]. These methods are readily implemented,
but may require a significant computational resource to undertake
accurate simulations involving wave propagation over a large number of
wavelengths [DBB99]. On the other hand, the Yee scheme [Yee66] is a covolume
solution technique, on a structured Cartesian mesh, that exhibits a
high degree of computationally efficiency, in terms of both CPU and memory
requirements.