PIMS/CSC Weekly Seminar: Dhavide Aruliah, University of Ontario Institute of Technology
Topic
A Parallel Adaptive Method for Pseudo-Arclength Continuation
Speakers
Details
ABSTRACT: Pseudo-arclength continuation is a well-established framework for generating a curve of numerical solutions of nonlinear equations.
The usual predictor-corrector scheme uses a prediction of a prescribed step-length along a tangent direction followed by correction steps (typically using Newton's method) in a hyperplane containing the prediction point. In many complicated high-dimensional systems, the corrections steps can be extremely costly to compute; as a result, the step-length of the original prediction step must be chosen carefully to avoid prohibitively many failed steps and corresponding wasted CPU cycles. In this talk, we present a parallel method for adapting the step-length of pseudo-arclength continuation. Our method employs several predictor-corrector sequences run concurrently on distinct processors with differing step-lengths. Our parallel framework permits intermediate results of unconverged correction sequences to seed new predictor-corrector sequences with longer step-lengths; the goal is to amortise the cost of corrector steps to make further progress along the underlying numerical curve. We describe the essence of the parallel algorithm and provide evidence from numerical experiments to support its efficacy. Results from numerical experiments suggest that a three-fold speed-up is attainable when the continuation curve sought has great topological complexity and the corrector steps require significant processor time. Our implementation can be used without extensive experience with High-Performance Computing (HPC); users need only supply a routine for computing the corrector steps. This is joint work with Alexander Dubitski (UOIT) and Lennaert van Veen (UOIT).
The usual predictor-corrector scheme uses a prediction of a prescribed step-length along a tangent direction followed by correction steps (typically using Newton's method) in a hyperplane containing the prediction point. In many complicated high-dimensional systems, the corrections steps can be extremely costly to compute; as a result, the step-length of the original prediction step must be chosen carefully to avoid prohibitively many failed steps and corresponding wasted CPU cycles. In this talk, we present a parallel method for adapting the step-length of pseudo-arclength continuation. Our method employs several predictor-corrector sequences run concurrently on distinct processors with differing step-lengths. Our parallel framework permits intermediate results of unconverged correction sequences to seed new predictor-corrector sequences with longer step-lengths; the goal is to amortise the cost of corrector steps to make further progress along the underlying numerical curve. We describe the essence of the parallel algorithm and provide evidence from numerical experiments to support its efficacy. Results from numerical experiments suggest that a three-fold speed-up is attainable when the continuation curve sought has great topological complexity and the corrector steps require significant processor time. Our implementation can be used without extensive experience with High-Performance Computing (HPC); users need only supply a routine for computing the corrector steps. This is joint work with Alexander Dubitski (UOIT) and Lennaert van Veen (UOIT).
Additional Information
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Dhavide Aruliah (University of Ontario Institute of Technology, Oshawa, ON, Canada)
Dhavide Aruliah (University of Ontario Institute of Technology, Oshawa, ON, Canada)