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
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OOSHDU.10155/196 |
| Date | 01 August 2011 |
| Creators | Dubitski, Alexander |
| Contributors | Van Veen, Lennaert |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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