Analysis of photonic-crystal problems with MLFMA and approximate Schur preconditioners
Date
2009-07
Advisor
Instructor
Source Title
Computational Electromagnetics International Workshop, CEM 2009
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Publisher
IEEE
Volume
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Pages
82 - 86
Language
English
Type
Conference Paper
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Abstract
We consider fast and accurate solutions of electromagnetics problems involving three-dimensional photonic crystals (PhCs). Problems are formulated with the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE) discretized with the Rao-Wilton-Glisson functions. Matrix equations are solved iteratively by the multilevel fast multipole algorithm. Since PhC problems are difficult to solve iteratively, robust preconditioning techniques are required to accelerate iterative solutions. We show that novel approximate Schur preconditioners enable efficient solutions of PhC problems by reducing the number of iterations significantly for both CTF and JMCFIE. ©2009 IEEE.
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Keywords
Combined field integral equations, Electromagnetics, Iterative solutions, Magnetic currents, Matrix equations, Multi-level fast multi-pole algorithm, Number of iterations, Preconditioners, Preconditioning techniques, Rao-wilton-glisson functions, Three dimensional photonic crystals, Computational efficiency, Electromagnetism, Photonic crystals