KRYLOV’S SUBSPACES ITERATIVE METHODS TO EVALUATE ELECTROSTATIC PARAMETERS

Abstract

Most of the electromagnetic problems can be stated in terms of an inhomogeneous equation Af = g in which A is a differential, integral or integro-differential operator, g in the exitation source and f is the unknown function to be determined. Methods of Moments (MoM) is a procedure to solve the equation above and, by means of an appropriate choice of the Basis/Testing (B/T), the problem can be translated into an equivalent linear system even of bigger dimensions. In this work we investigate on how the performances of the major Krylov’s subspace iterative solvers are affected by different choice of these sets of functions. More specifically, as a test case, we consider the algebric linear system of equations obtained by an electrostatic problem of evaluation of the capacitance and electrostatic charge distribution in a cylindrical conductor of finite length. Results are compared in terms of analytical/computational complexity and speed of convergence by exploiting three leading iterative methods (GMRES, CGS, BibGStab) and B/T functions of Pulse/Pulse (P/P) and Pulse/Delta (P/D) type.