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Article: Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies

TitleIntegral equation solution of Maxwell's equations from zero frequency to microwave frequencies
Authors
Issue Date2000
Citation
Ieee Transactions On Antennas And Propagation, 2000, v. 48 n. 10, p. 1635-1645 How to Cite?
AbstractWe develop a new method to precondition the matrix equation resulting from applying the method of moments (MoM) to the electric field integral equation (EFIE). This preconditioning method is based on first applying the loop-tree or loop-star decomposition of the currents to arrive at a Helmholtz decomposition of the unknown currents. However, the MoM matrix thus obtained still cannot be solved efficiently by iterative solvers due to the large number of iterations required. We propose a permutation of the loop-tree or loop-star currents by a connection matrix, to arrive at a current basis that yields a MoM matrix that can be solved efficiently by iterative solvers. Consequently, dramatic reduction in iteration count has been observed. The various steps can be regarded as a rearrangement of the basis functions to arrive at the MoM matrix. Therefore, they are related to the original MoM matrix by matrix transformation, where the transformation requires the inverse of the connection matrix. We have also developed a fast method to invert the connection matrix so that the complexity of the preconditioning procedure is of O(N) and, hence, can be used in fast solvers such as the low-frequency multilevel fast multipole algorithm (LF-MLFMA). This procedure also makes viable the use of fast solvers such as MLFMA to seek the iterative solutions of Maxwell's equations from zero frequency to microwave frequencies.
Persistent Identifierhttp://hdl.handle.net/10722/182637
ISSN
2015 Impact Factor: 2.053
2015 SCImago Journal Rankings: 2.130
References

 

DC FieldValueLanguage
dc.contributor.authorZhao, JSen_US
dc.contributor.authorChew, WCen_US
dc.date.accessioned2013-05-02T05:16:13Z-
dc.date.available2013-05-02T05:16:13Z-
dc.date.issued2000en_US
dc.identifier.citationIeee Transactions On Antennas And Propagation, 2000, v. 48 n. 10, p. 1635-1645en_US
dc.identifier.issn0018-926Xen_US
dc.identifier.urihttp://hdl.handle.net/10722/182637-
dc.description.abstractWe develop a new method to precondition the matrix equation resulting from applying the method of moments (MoM) to the electric field integral equation (EFIE). This preconditioning method is based on first applying the loop-tree or loop-star decomposition of the currents to arrive at a Helmholtz decomposition of the unknown currents. However, the MoM matrix thus obtained still cannot be solved efficiently by iterative solvers due to the large number of iterations required. We propose a permutation of the loop-tree or loop-star currents by a connection matrix, to arrive at a current basis that yields a MoM matrix that can be solved efficiently by iterative solvers. Consequently, dramatic reduction in iteration count has been observed. The various steps can be regarded as a rearrangement of the basis functions to arrive at the MoM matrix. Therefore, they are related to the original MoM matrix by matrix transformation, where the transformation requires the inverse of the connection matrix. We have also developed a fast method to invert the connection matrix so that the complexity of the preconditioning procedure is of O(N) and, hence, can be used in fast solvers such as the low-frequency multilevel fast multipole algorithm (LF-MLFMA). This procedure also makes viable the use of fast solvers such as MLFMA to seek the iterative solutions of Maxwell's equations from zero frequency to microwave frequencies.en_US
dc.languageengen_US
dc.relation.ispartofIEEE Transactions on Antennas and Propagationen_US
dc.titleIntegral equation solution of Maxwell's equations from zero frequency to microwave frequenciesen_US
dc.typeArticleen_US
dc.identifier.emailChew, WC: wcchew@hku.hken_US
dc.identifier.authorityChew, WC=rp00656en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1109/8.899680en_US
dc.identifier.scopuseid_2-s2.0-0034290010en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0034290010&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume48en_US
dc.identifier.issue10en_US
dc.identifier.spage1635en_US
dc.identifier.epage1645en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridZhao, JS=7410309451en_US
dc.identifier.scopusauthoridChew, WC=36014436300en_US

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