TY - JOUR
T1 - On the Choice of Expansion and Weighting Functions in the Numerical Solution of Operator Equations
AU - Sarkar, Tapan K.
AU - Djordjević, Antonije R.
AU - Arvas, Ercument
PY - 1985/9
Y1 - 1985/9
N2 - 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.
AB - 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.
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U2 - 10.1109/TAP.1985.1143707
DO - 10.1109/TAP.1985.1143707
M3 - Article
AN - SCOPUS:0022117238
SN - 0018-926X
VL - 33
SP - 988
EP - 996
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
IS - 9
ER -