A parallel adaptive method for pseudo-arclength continuation

We parallelize the pseudo-arclength continuation method for solving nonlinear systems of equations. Pseudo-arclength continuation is a predictor-corrector method where the correction step consists of solving a linear system of algebraic equations. Our algorithm parallelizes adaptive step-length sele...

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Bibliographic Details
Main Author: Dubitski, Alexander
Other Authors: Van Veen, Lennaert
Language:en
Published: 2011
Subjects:
HPC
Online Access:http://hdl.handle.net/10155/196
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spelling ndltd-LACETR-oai-collectionscanada.gc.ca-OOSHDU.10155-1962013-04-17T04:05:44ZA parallel adaptive method for pseudo-arclength continuationDubitski, AlexanderHPCArclengthParallelComputingWe parallelize the pseudo-arclength continuation method for solving nonlinear systems of equations. Pseudo-arclength continuation is a predictor-corrector method where the correction step consists of solving a linear system of algebraic equations. Our algorithm parallelizes adaptive step-length selection and inexact prediction. Prior attempts to parallelize pseudo-arclength continuation are typically based on parallelization of the linear solver which leads to completely solver-dependent software. In contrast, our method is completely independent of the internal solver and therefore applicable to a large domain of problems. Our software is easy to use and does not require the user to have extensive prior experience with High Performance Computing; all the user needs to provide is the implementation of the corrector step. When corrector steps are costly or continuation curves are complicated, we observe up to sixty percent speed up with moderate numbers of processors. We present results for a synthetic problem and a problem in turbulence.UOITVan Veen, Lennaert2011-11-28T16:09:59Z2011-11-28T16:09:59Z2011-08-01Thesishttp://hdl.handle.net/10155/196en
collection NDLTD
language en
sources NDLTD
topic HPC
Arclength
Parallel
Computing
spellingShingle HPC
Arclength
Parallel
Computing
Dubitski, Alexander
A parallel adaptive method for pseudo-arclength continuation
description We parallelize the pseudo-arclength continuation method for solving nonlinear systems of equations. Pseudo-arclength continuation is a predictor-corrector method where the correction step consists of solving a linear system of algebraic equations. Our algorithm parallelizes adaptive step-length selection and inexact prediction. Prior attempts to parallelize pseudo-arclength continuation are typically based on parallelization of the linear solver which leads to completely solver-dependent software. In contrast, our method is completely independent of the internal solver and therefore applicable to a large domain of problems. Our software is easy to use and does not require the user to have extensive prior experience with High Performance Computing; all the user needs to provide is the implementation of the corrector step. When corrector steps are costly or continuation curves are complicated, we observe up to sixty percent speed up with moderate numbers of processors. We present results for a synthetic problem and a problem in turbulence. === UOIT
author2 Van Veen, Lennaert
author_facet Van Veen, Lennaert
Dubitski, Alexander
author Dubitski, Alexander
author_sort Dubitski, Alexander
title A parallel adaptive method for pseudo-arclength continuation
title_short A parallel adaptive method for pseudo-arclength continuation
title_full A parallel adaptive method for pseudo-arclength continuation
title_fullStr A parallel adaptive method for pseudo-arclength continuation
title_full_unstemmed A parallel adaptive method for pseudo-arclength continuation
title_sort parallel adaptive method for pseudo-arclength continuation
publishDate 2011
url http://hdl.handle.net/10155/196
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