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Article: A novel fast solver for poisson's equation with neumann boundary condition

TitleA novel fast solver for poisson's equation with neumann boundary condition
Authors
Issue Date2013
PublisherElectromagnetics Academy. The Journal's web site is located at http://www.jpier.org/PIER/
Citation
Progress In Electromagnetics Research, 2013, v. 136, p. 195-209 How to Cite?
AbstractIn this paper, we present a novel fast method to solve Poisson's equation in an arbitrary two dimensional region with Neumann boundary condition, which are frequently encountered in solving electrostatic boundary problems. The basic idea is to solve the original Poisson's equation by a two-step procedure. In the first stage, we expand the electric field of interest by a set of tree basis functions and solve it with a fast tree solver in O(N) operations. The field such obtained, however, fails to expand the exact field because the tree basis is not curl-free. Despite of this, we can retrieve the correct electric field by purging the divergence-free field. Next, for the second stage, we find the potential distribution rapidly with a same fast solution of O(N) complexity. As a result, the proposed method dramatically reduces solution time compared with traditional FEM methods. In addition, it is the first time that the loop-tree decomposition technique has been introduced to develop fast Poisson solvers. Numerical examples including electrostatic simulations are presented to demonstrate the e±ciency of the proposed method.
Persistent Identifierhttp://hdl.handle.net/10722/182793
ISSN
2015 SCImago Journal Rankings: 0.682
References

 

DC FieldValueLanguage
dc.contributor.authorMa, Zen_US
dc.contributor.authorChew, WCen_US
dc.contributor.authorJiang, Len_US
dc.date.accessioned2013-05-02T05:16:52Z-
dc.date.available2013-05-02T05:16:52Z-
dc.date.issued2013en_US
dc.identifier.citationProgress In Electromagnetics Research, 2013, v. 136, p. 195-209en_US
dc.identifier.issn1070-4698en_US
dc.identifier.urihttp://hdl.handle.net/10722/182793-
dc.description.abstractIn this paper, we present a novel fast method to solve Poisson's equation in an arbitrary two dimensional region with Neumann boundary condition, which are frequently encountered in solving electrostatic boundary problems. The basic idea is to solve the original Poisson's equation by a two-step procedure. In the first stage, we expand the electric field of interest by a set of tree basis functions and solve it with a fast tree solver in O(N) operations. The field such obtained, however, fails to expand the exact field because the tree basis is not curl-free. Despite of this, we can retrieve the correct electric field by purging the divergence-free field. Next, for the second stage, we find the potential distribution rapidly with a same fast solution of O(N) complexity. As a result, the proposed method dramatically reduces solution time compared with traditional FEM methods. In addition, it is the first time that the loop-tree decomposition technique has been introduced to develop fast Poisson solvers. Numerical examples including electrostatic simulations are presented to demonstrate the e±ciency of the proposed method.en_US
dc.languageengen_US
dc.publisherElectromagnetics Academy. The Journal's web site is located at http://www.jpier.org/PIER/en_US
dc.relation.ispartofProgress in Electromagnetics Researchen_US
dc.titleA novel fast solver for poisson's equation with neumann boundary conditionen_US
dc.typeArticleen_US
dc.identifier.emailChew, WC: wcchew@hku.hken_US
dc.identifier.emailJiang, L: jianglj@hku.hken_US
dc.identifier.authorityChew, WC=rp00656en_US
dc.identifier.authorityJiang, L=rp01338en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.2528/PIER12112010-
dc.identifier.scopuseid_2-s2.0-84872831086en_US
dc.identifier.hkuros218835-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84872831086&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume136en_US
dc.identifier.spage195en_US
dc.identifier.epage209en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridMa, Z=24483672700en_US
dc.identifier.scopusauthoridChew, WC=36014436300en_US
dc.identifier.scopusauthoridJiang, L=36077777200en_US

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