Fast and Efficient Algorithms in Computational Electromagnetics
Fast and Efficient Algorithms in Computational Electromagnetics
A Preconditioner for the Electric Field Integral Equation Based on Calderon Formulas
SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Journal of Computational Physics
International Journal of Computer Mathematics - INNOVATIVE ALGORITHMS IN SCIENCE AND ENGINEERING
Journal of Computational Physics
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Preconditioning methods based on Calderón's formulae for the Poggio–Miller–Chang–Harrington–Wu–Tsai formulations for Maxwell's equations in 3D are discussed. Five different types of formulations are proposed. The first three use different basis functions for surface electric and magnetic currents. The first type is a preconditioning just by appropriately ordering the coefficient matrix using the Gramian matrix as the preconditioner. Other two types utilise preconditioners constructed using matrices needed in the main fast multipole method algorithms. The fourth and fifth types are similar to the second and third types, but they use the same basis functions for both surface electric and magnetic currents. We make several numerical experiments with proposed preconditioners to confirm the efficiency of these proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.