On the Choice of Expansion and Weighting Functions in the Numerical Solution of Operator Equations

Tapan K. Sarkar, Antonije R. Djordjević, Ercument Arvas

Research output: Contribution to journalArticle

48 Scopus citations

Abstract

One of the objectives of this paper is to discuss the mathematical requirements that the expansion functions must satisfy in the method of moments (MM) solution of an operator equation. A simple differential equation is solved to demonstrate these requirements. The second objective is to study the numerical stability of point matching method, Galerkin's method, and the method of least squares. Pock-lington's integral equation is considered and numerical results are presented to illustrate the effect of various choices of weighting functions on the rate of convergence. Finally, it is shown that certain choices of expansion and weighting functions yield numerically acceptable results even though they are not admissible from a strictly mathematical point of view. The reason for this paradox is outlined.

Original languageEnglish (US)
Pages (from-to)988-996
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Volume33
Issue number9
DOIs
StatePublished - Sep 1985

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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