Efficient solution of the electric and magnetic current combined-field integral equation with the multilevel fast multipole algorithm and block-diagonal preconditioning

We consider the efficient solution of electromagnetics problems involving dielectric and composite dielectric-metallic structures, formulated with the electric and magnetic current combined-field integral equation (JMCFIE). Dense matrix equations obtained from the discretization of JMCFIE with Rao-Wilton-Glisson functions are solved iteratively, where the matrix-vector multiplications are performed efficiently with the multilevel fast multipole algorithm. JMCFIE usually provides well conditioned matrix equations that are easy to solve iteratively. However, iteration counts and the efficiency of solutions depend on the contrast, i.e., the relative variation of electromagnetic parameters across dielectric interfaces. Owing to the numerical imbalance of off-diagonal matrix partitions, solutions of JMCFIE become difficult with increasing contrast. We present a four-partition block-diagonal preconditioner (4PBDP), which provides efficient solutions of JMCFIE by reducing the number of iterations significantly. 4PBDP is useful, especially when the contrast increases, and the standard block-diagonal preconditioner fails to provide a rapid convergence.


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Computational solutions of plasmonic problems involving metals at optical frequencies formulated with surface integral equations are considered. Numerical inaccuracies arise when using the conventional formulations for penetrable bodies, especially as the negative real permittivity becomes very large at the lower frequencies of the optical spectrum. In order to close the gap between plasmonic and perfectly conducting simulations, it is required to extend the applicability of surface integral equations to in...
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Modified Superformula Contours Optimized via Genetic Algorithms for Exponentially Converging 2D Solutions of MFIE
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An infinitely smooth parametrical representation with derivatives of all orders is used, resulting into exponentially converging solutions of magnetic field integral equation (MFIE) in 2D either for TM or TE polarized excitations. A version of superformula modified for this purpose has been subject to optimization of its parameters via genetic algorithms to provide smooth parameterization for a desired boundary in two-dimensional problems. The organization of the MFIE kernel and convergence of the solution ...
Linear-linear basis functions for MLFMA solutions of magnetic-field and combined-field integral equations
Ergül, Özgür Salih (2007-04-01)
We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving closed conductors. We consider the solutions of relatively large scattering problems by employing the multilevel fast multipole algorithm. Accuracy problems of MFIE and CFIE arising from their implementations with the conventional Rao-Wilton-Glisson (RWG) basis functions can...
Citation Formats
Ö. S. Ergül, “Efficient solution of the electric and magnetic current combined-field integral equation with the multilevel fast multipole algorithm and block-diagonal preconditioning,” RADIO SCIENCE, pp. 0–0, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/45877.