Stability of BDF-ADI Discretizations

Handle URI:
http://hdl.handle.net/10754/625356
Title:
Stability of BDF-ADI Discretizations
Authors:
Felício dos Reis, João Miguel ( 0000-0003-3763-4093 )
Abstract:
We present new results on absolute stability for BDF-ADI (Backward differentiation formula Alternating Direction Implicit) methods applied to a linear advection and diffusion equations. Unconditional absolute stability of the BDF2-ADI method is proven for advection and diffusion separately, as well as to the BDF3-ADI method for the purely-diffusive case. Conditional absolute stability of the BDF4-ADI is also proven for the purely-diffusive case, and stability regions for BDF3-ADI and BDF4- ADI are given in terms of the PDE coefficients and numerical parameters. Lastly, numerical experiments are presented to support the theoretical results and conjectures. These experiments also suggest future work.
Advisors:
Ketcheson, David I. ( 0000-0002-1212-126X )
Committee Member:
Keyes, David E. ( 0000-0002-4052-7224 ) ; Michels, Dominik L.; Loczi, Lajos ( 0000-0002-7999-5658 )
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
17-Aug-2017
Type:
Thesis
Appears in Collections:
Theses

Full metadata record

DC FieldValue Language
dc.contributor.advisorKetcheson, David I.en
dc.contributor.authorFelício dos Reis, João Miguelen
dc.date.accessioned2017-08-17T12:26:40Z-
dc.date.available2017-08-17T12:26:40Z-
dc.date.issued2017-08-17-
dc.identifier.urihttp://hdl.handle.net/10754/625356-
dc.description.abstractWe present new results on absolute stability for BDF-ADI (Backward differentiation formula Alternating Direction Implicit) methods applied to a linear advection and diffusion equations. Unconditional absolute stability of the BDF2-ADI method is proven for advection and diffusion separately, as well as to the BDF3-ADI method for the purely-diffusive case. Conditional absolute stability of the BDF4-ADI is also proven for the purely-diffusive case, and stability regions for BDF3-ADI and BDF4- ADI are given in terms of the PDE coefficients and numerical parameters. Lastly, numerical experiments are presented to support the theoretical results and conjectures. These experiments also suggest future work.en
dc.language.isoenen
dc.subjectNumerical analysisen
dc.subjectSplitting methodsen
dc.subjectBDF-ADIen
dc.subjectabsolute stabilityen
dc.subjectscour-cohn algorithmen
dc.titleStability of BDF-ADI Discretizationsen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen
dc.contributor.committeememberKeyes, David E.en
dc.contributor.committeememberMichels, Dominik L.en
dc.contributor.committeememberLoczi, Lajosen
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameMaster of Scienceen
dc.person.id144620en
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