Schur complement preconditioners for surface integral-equation formulations of dielectric problems solved with the multilevel fast multipole algorithm

Simple item page
buir.contributor.authorGürel, Levent
dc.citation.epage2467en_US
dc.citation.issueNumber5en_US
dc.citation.spage2440en_US
dc.citation.volumeNumber33en_US
dc.contributor.authorMalas, Tahiren_US
dc.contributor.authorGürel, Leventen_US
dc.date.accessioned2016-02-08T12:17:18Z
dc.date.available2016-02-08T12:17:18Z
dc.date.issued2011-10-04en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.departmentComputational Electromagnetics Research Center (BiLCEM)en_US
dc.description.abstractSurface integral-equation methods accelerated with the multilevel fast multipole algorithm (MLFMA) provide a suitable mechanism for electromagnetic analysis of real-life dielectric problems. Unlike the perfect-electric-conductor case, discretizations of surface formulations of dielectric problems yield 2 × 2 partitioned linear systems. Among various surface formulations, the combined tangential formulation (CTF) is the closest to the category of first-kind integral equations, and hence it yields the most accurate results, particularly when the dielectric constant is high and/or the dielectric problem involves sharp edges and corners. However, matrix equations of CTF are highly ill-conditioned, and their iterative solutions require powerful preconditioners for convergence. Second-kind surface integral-equation formulations yield better conditioned systems, but their conditionings significantly degrade when real-life problems include high dielectric constants. In this paper, for the first time in the context of surface integral-equation methods of dielectric objects, we propose Schur complement preconditioners to increase their robustness and efficiency. First, we approximate the dense system matrix by a sparse near-field matrix, which is formed naturally by MLFMA. The Schur complement preconditioning requires approximate solutions of systems involving the (1,1) partition and the Schur complement. We approximate the inverse of the (1,1) partition with a sparse approximate inverse (SAI) based on the Frobenius norm minimization. For the Schur complement, we first approximate it via incomplete sparse matrix-matrix multiplications, and then we generate its approximate inverse with the same SAI technique. Numerical experiments on sphere, lens, and photonic crystal problems demonstrate the effectiveness of the proposed preconditioners. In particular, the results for the photonic crystal problem, which has both surface singularity and a high dielectric constant, shows that accurate CTF solutions for such problems can be obtained even faster than with second-kind integral equation formulations, with the acceleration provided by the proposed Schur complement preconditioners.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T12:17:18Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2011en
dc.description.sponsorshipScientific and Technical Research Council of Turkey (TÜBİTAKen_US
dc.identifier.doi10.1137/090780808en_US
dc.identifier.issn1064-8275
dc.identifier.urihttp://hdl.handle.net/11693/28317
dc.language.isoEnglishen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1137/090780808en_US
dc.source.titleSIAM Journal on Scientific Computingen_US
dc.subjectComputational electromagneticsen_US
dc.subjectDielectric problemsen_US
dc.subjectIntegral-equation methodsen_US
dc.subjectPartitioned matricesen_US
dc.subjectPreconditioningen_US
dc.subjectSchur complement reduction methoden_US
dc.subjectSparse-approximate-inverse preconditionersen_US
dc.titleSchur complement preconditioners for surface integral-equation formulations of dielectric problems solved with the multilevel fast multipole algorithmen_US
dc.typeArticleen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Schur complement preconditioners for surface integral-equation formulations of dielectric problems solved with the multilevel fast multipole algorithm.pdf
Size:
1.28 MB
Format:
Adobe Portable Document Format
Description:
Full printable version
Download

Collections

Scholarly Publications - Electrical and Electronics Engineering
Scholarly Publications - BİLCEM