Investigation of Different Basis and Testing Functions in Method of Moments for Electrostatic Problems

Abstract

Abstract-This paper presents comparative studies on different types of basis and testing functions used in Method of Moments (MoM) in terms of analytical complexity, convergence and condition number of the co-efficient matrix when applied to electrostatic problem of evaluating capacitance and charge distribution of conducting bodies. A thin conducting cylinder of finite length has been taken as a representative case study to evaluate the capacitance and charge distribution. The basis and testing functions which have been studied for this problem are pulse-delta, pulse-pulse, triangulardelta, triangular-pulse and triangular-triangular functions respectively. Numerical data on capacitance and charge distribution has been presented for each set of basis and testing functions in terms of condition number and convergence.

KRYLOV’S SUBSPACES ITERATIVE METHODS TO EVALUATE ELECTROSTATIC PARAMETERS

“…Similarly, as for the P/D case, the evaluation of the coefficients of the matrix A and relative integration lead to the expression (Alad and Chakrabarty, 2012) Equation 16:…”

“…In such a context, the Method of Moment (MoM) can be considered an excellent candidate for the problem resolution because, by means of a suitable couple of Basis and Testing functions (B/T), it translates the integral equation into a correspondent matrix equation whose solvability requires an iterative numerical procedure above all in those cases in which the matrix dimension is too high to exploit direct procedures. The exploitation of MoM has become popular since in 1967 published a pioneering work about the MoM application in electrostatic problems and the scientific community has produced meaningful works of electrostatic modelling on different geometries exploiting MoM (Chakrabarty et al, 2002;Alad and Chakrabarty, 2012;Prarthan and Chakrabarty, 2001) in which the choice of the B/T couple was asked to the accuracy of the solution, the dimension of the matrix and the evaluation of the elements of the matrix and to problems linked to the conditioning of the same matrix and more, MoM has been applied to many problems in Science Publications AJAS several scientific domains. In Electromagnetics MoM has been applied to radiation problems, scattering problems, analysis and design of microstrips; analysis abd design of antennas; lossy structures, propagation problems (Sadiku, 2000;Angiulli and Versaci, 2002;2003;Misran et al, 2008;Elangovan and Perinbam, 2012;Sultan et al, 2012;Wu et al, 2012;Zhang et al, 2013;Mouheddin and Jamel, 2009;Apaydin and Sevgi, 2012;Kumar and Parvathi, 2012).…”

Electrostatic Capacity of a Metallic Cylinder: Effect of the Moment Method Discretization Process on the Performances of the Krylov Subspace Techniques

“…The scientific literature is rich concerning the study of q e distributions and C computations through the MoM in which different basis and testing functions are exploited [10,[13][14][15][16][17][18][19]. For example, in [14], related to a single cylindrical conductor, the q e distribution was studied, and the C were studied when different basis and testing functions were exploited (pulse, delta, triangular functions). However, in these works, the solutions were obtained by exploiting only direct techniques for solving the (2) [17,19].…”

“…In this paper, starting from [14], the problem of the distribution of q e on a cylindrical metallic conductor of finite length as well as the calculation of the related C was addressed when an external electric voltage V was applied. In particular, once the geometry of the problem was defined and the source and observation points fixed, the problem was formulated in terms of electrostatic potential φ by means of an integral formulation.…”