TY - JOUR

T1 - A Note on the Choice Weighting Functions in the Method of Moments

AU - Sarkar, Tapan K.

PY - 1985

Y1 - 1985

N2 - The objective is to show from a mathematical standpoint that there are certain rules that must be followed in the choice of weighting functions used in the method of moments (MM). It is shown that for a particular problem it is the operator that dictates the method (Galerkin’s method or another method such as the method of least squares) to be applied, and it is not computational considerations only. For example, it is shown that in solving Hallen’s and Pocklington’s equation by the method of moments, it is unnatural to choose the weighting functions which are zero at the ends of the domain of the solution. The deficiency of certain weighting functions is presented based on mathematical reasoning, and a numerical example is given to illustrate the effect of the choice of the weighting functions on the rate of the convergence of the solution.

AB - The objective is to show from a mathematical standpoint that there are certain rules that must be followed in the choice of weighting functions used in the method of moments (MM). It is shown that for a particular problem it is the operator that dictates the method (Galerkin’s method or another method such as the method of least squares) to be applied, and it is not computational considerations only. For example, it is shown that in solving Hallen’s and Pocklington’s equation by the method of moments, it is unnatural to choose the weighting functions which are zero at the ends of the domain of the solution. The deficiency of certain weighting functions is presented based on mathematical reasoning, and a numerical example is given to illustrate the effect of the choice of the weighting functions on the rate of the convergence of the solution.

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U2 - 10.1109/TAP.1985.1143590

DO - 10.1109/TAP.1985.1143590

M3 - Article

AN - SCOPUS:0022045842

SN - 0018-926X

VL - 33

SP - 436

EP - 441

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

IS - 4

ER -