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Calderón preconditioning approaches for PMCHWT formulations for Maxwell's equations
Author(s) -
Niino K.,
Nishimura N.
Publication year - 2012
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.1834
Subject(s) - preconditioner , coefficient matrix , maxwell's equations , gramian matrix , matrix (chemical analysis) , basis (linear algebra) , multipole expansion , mathematics , mathematical analysis , physics , linear system , chemistry , eigenvalues and eigenvectors , geometry , quantum mechanics , chromatography
SUMMARY 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.