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Article: Finite difference schemes for heat conduction analysis in integrated circuit design and manufacturing

TitleFinite difference schemes for heat conduction analysis in integrated circuit design and manufacturing
Authors
KeywordsBoundary Condition
Crank-Nicolson (CN)
Finite Difference Scheme
Heat Conduction
Partial Differential Equation (PDE)
Truncation Error (TR)
Issue Date2011
PublisherJohn Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/1976
Citation
International Journal of Circuit Theory And Applications, 2011, v. 39 n. 9, p. 905-921 How to Cite?
AbstractThe importance of thermal effects on the reliability and performance of VLSI circuits has grown in recent years. The heat conduction problem is commonly described as a second-order partial differential equation (PDE), and several numerical methods, including simple explicit, simple implicit and Crank-Nicolson methods, all having at most second-order spatial accuracy, have been applied to solve the problem. This paper reviews these methods and further proposes a fourth-order spatial-accurate finite difference scheme to better approximate the PDE solution. Moreover, we devise a fourth-order accurate approximation of the convection boundary condition, and apply it to the proposed finite difference scheme. We use a block cyclic reduction and a recently developed numerically stable algorithm for inversion of block-tridiagonal and banded matrices to solve the PDE-based system efficiently. Despite their higher computation complexity than direct computation in a sequential processor, we make it possible for the very first time to employ a divide-and-conquer algorithm, viable for parallel computation, in heat conduction analysis. Experimental results prove such possibility, suggesting that applying divide-and-conquer algorithms, higher-order finite difference schemes can achieve better simulation accuracy with even faster speed and less memory requirement than conventional methods. Copyright © 2010 John Wiley & Sons, Ltd.
Persistent Identifierhttp://hdl.handle.net/10722/155665
ISSN
2015 Impact Factor: 1.179
2015 SCImago Journal Rankings: 0.384
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorShen, Yen_US
dc.contributor.authorWong, Nen_US
dc.contributor.authorLam, EYen_US
dc.contributor.authorKoh, CKen_US
dc.date.accessioned2012-08-08T08:34:44Z-
dc.date.available2012-08-08T08:34:44Z-
dc.date.issued2011en_US
dc.identifier.citationInternational Journal of Circuit Theory And Applications, 2011, v. 39 n. 9, p. 905-921en_US
dc.identifier.issn0098-9886en_US
dc.identifier.urihttp://hdl.handle.net/10722/155665-
dc.description.abstractThe importance of thermal effects on the reliability and performance of VLSI circuits has grown in recent years. The heat conduction problem is commonly described as a second-order partial differential equation (PDE), and several numerical methods, including simple explicit, simple implicit and Crank-Nicolson methods, all having at most second-order spatial accuracy, have been applied to solve the problem. This paper reviews these methods and further proposes a fourth-order spatial-accurate finite difference scheme to better approximate the PDE solution. Moreover, we devise a fourth-order accurate approximation of the convection boundary condition, and apply it to the proposed finite difference scheme. We use a block cyclic reduction and a recently developed numerically stable algorithm for inversion of block-tridiagonal and banded matrices to solve the PDE-based system efficiently. Despite their higher computation complexity than direct computation in a sequential processor, we make it possible for the very first time to employ a divide-and-conquer algorithm, viable for parallel computation, in heat conduction analysis. Experimental results prove such possibility, suggesting that applying divide-and-conquer algorithms, higher-order finite difference schemes can achieve better simulation accuracy with even faster speed and less memory requirement than conventional methods. Copyright © 2010 John Wiley & Sons, Ltd.en_US
dc.languageengen_US
dc.publisherJohn Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/1976en_US
dc.relation.ispartofInternational Journal of Circuit Theory and Applicationsen_US
dc.subjectBoundary Conditionen_US
dc.subjectCrank-Nicolson (CN)en_US
dc.subjectFinite Difference Schemeen_US
dc.subjectHeat Conductionen_US
dc.subjectPartial Differential Equation (PDE)en_US
dc.subjectTruncation Error (TR)en_US
dc.titleFinite difference schemes for heat conduction analysis in integrated circuit design and manufacturingen_US
dc.typeArticleen_US
dc.identifier.emailWong, N:nwong@eee.hku.hken_US
dc.identifier.emailLam, EY:elam@eee.hku.hken_US
dc.identifier.authorityWong, N=rp00190en_US
dc.identifier.authorityLam, EY=rp00131en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1002/cta.675en_US
dc.identifier.scopuseid_2-s2.0-80053208946en_US
dc.identifier.hkuros200962-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-80053208946&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume39en_US
dc.identifier.issue9en_US
dc.identifier.spage905en_US
dc.identifier.epage921en_US
dc.identifier.isiWOS:000295231500002-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridShen, Y=12804295400en_US
dc.identifier.scopusauthoridWong, N=35235551600en_US
dc.identifier.scopusauthoridLam, EY=7102890004en_US
dc.identifier.scopusauthoridKoh, CK=7201749804en_US

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