Temporal discretization choices for stable boundary element methods in electromagnetic scattering problems

Authors:
Amir Geranmayeh;Wolfgang Ackermann;Thomas Weiland
Affiliations:
Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstrasse 8, 64289 Darmstadt, Germany;Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstrasse 8, 64289 Darmstadt, Germany;Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstrasse 8, 64289 Darmstadt, Germany
Venue:
Applied Numerical Mathematics
Year:
2009

Citing 5
Cited 0

Averaging techniques for time-marching schemes for retarded potential integral equations

Applied Numerical Mathematics
A stability analysis of a time marching scheme for the general surface electric field integral equation

Applied Numerical Mathematics
Time-domain combined field integral equation using Laguerre polynomials as temporal basis functions: Research Articles

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields - Special Issue on the 5th CEM-TD
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Numerical Recipes 3rd Edition: The Art of Scientific Computing

Numerical Recipes 3rd Edition: The Art of Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Diverse alternative temporal discretization schemes are analyzed for stable numerical solution of the surface integral equations in obtaining the transient scattering response of arbitrarily shaped conducting bodies. Streamlined formulations for three main categories including using either the conventional time integrators or the subdomain temporal basis functions, or the entire-domain time bases are presented in conceptually similar frameworks for solving types of the electric, magnetic, and combined field integral equations. To this end, first compatible temporal interpolations with conveniently usable time integrators are introduced based on stability analysis of the delay differential equations (DDE). Detailed guidelines for effective implementation of appropriate subdomain time basis functions are then studied. It is demonstrated that since in the latter approach the time derivatives are handled analytically, the extension of the stable region tremendously enhances while approaching small time step sizes. Eventually, the orthogonal weighted Laguerre polynomials are set forth to provide unconditionally stable schemes. Besides, adaptive partitioning of triangular patches is proposed to efficiently control the precision of numerical quadratures over the surface of source distribution. Numerical results are verified through comparison with the results obtained using the finite integration technique (FIT). Convergence behaviour of the widely used schemes is also investigated.