Convergence Properties of a Diakoptics Method for Electromagnetic Scattering From 3-D Complex Structures

Abstract

Abstract-Linear embedding via Green's operators (LEGO) is a diakoptics method that employs electromagnetic "bricks" to formulate problems of wave scattering from complex structures (e.g., penetrable bodies with inclusions). In its latest version the LEGO integral equations are solved through the Method of Moments combined with adaptive generation of Arnoldi basis functions (ABF) to compress the resulting algebraic system. In this paper we review and discuss the convergence properties of the numerical solution in relation to the number of ABFs. Besides, we address the issue of setting the threshold for stopping the generation of ABFs in conjunction with the adaptive Arnoldi algorithm.

Solving Wave Propagation Within Finite-Sized Composite Media With Linear Embedding via Green's Operators

“…The convergence properties of the ABFs are investigated to a great extent in [9] and literature cited therein.…”

“…In view of said feature, LEGO has also been employed for solving scattering problems that involve composite and diverse media [8][9][10].…”

“…In light of LEGO modularity, not only is the addition of generator/probe bricks straightforward but it also marginally affects the IE which describes a problem. Hence, we can adopt the numerical strategy based on Arnoldi basis functions (ABFs) [8,9] without substantial changes.…”