Numerical Analysis of Combined Field Integral Equation Formulations for Electromagnetic Scattering by Dielectric and Composite Objects

Abstract

Abstract-Numerical analysis of a generalized form of the recently developed electric and magnetic current combined field integral equation (JM-CFIE) for electromagnetic scattering by homogeneous dielectric and composite objects is presented. This new formulation contains a similar coupling parameter α as CFIE contains in the case of perfectly conducting objects. Two alternative JM-CFIE(α) formulations are introduced and their numerical properties (solution accuracy and convergence of iterative Krylov subspace methods) are investigated. The properties of these formulations are found to be very sensitive to the choice of α and to the permittivity of the object. By using normalized fields and currents the optimal value of α minimizing the number of iterations becomes only weakly dependent on the permittivity object. Using linear-linear basis functions instead of the more conventional constant-linear (RWG) basis functions the solution accuracy can be made less dependent on the choice of α.

Solutions of large-scale electromagnetics problems involving dielectric objects with the parallel multilevel fast multipole algorithm

“…where α ∈ ½0; 1 is a combination parameter [18],n is the unit normal vector at the observation point r, and…”

“…This paper present an efficient parallelization of MLFMA for the solution of large-scale problems involving threedimensional homogeneous dielectric objects. The problems are formulated with the electric and magnetic current combined-field integral equation (JMCFIE) [17][18][19][20] and discretized with the Rao-Wilton-Glisson (RWG) [21] functions on planar triangles. The resulting dense matrix equations are solved iteratively by using a parallel implementation of MLFMA on distributed-memory architectures.…”

Fast and accurate solutions of extremely large integral-equation problems discretised with tens of millions of unknowns

“…Similar to CFIE for conducting objects, a Galerkin discretization of JMCFIE results in well-tested identity operators, which lead to very efficient iterative solutions [33], but may reduce the accuracy of the results. Therefore, the combination parameter in JMCFIE is extremely important for the tradeoff between the accuracy and the efficiency [32], [36].…”

An EM scattering algorithm for all materials

“…In spite of its apparent generality, it requires a variety of special cases to produce accurate results in all situations. Different formulations are used for different types of materials; conductors [4] and dielectrics [5,6] singly or together [2,3,7,8]; and even for a single type of material accuracy can be quite variable [8][9][10][11] over a range of values of material properties.…”