Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

Pethiyagoda, Ravindra, McCue, Scott W., Moroney, Timothy J., & Back, Julian M. (2014) Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns. Journal of Computational Physics, 269, pp. 297-313.

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The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

Impact and interest:

4 citations in Scopus
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3 citations in Web of Science®

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ID Code: 69016
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: free surface flows, nonlinear gravity waves, Kelvin ship wave patterns, boundary integral method, Jacobian-free Newton-Krylov method, Preconditioner, GPU acceleration
DOI: 10.1016/j.jcp.2014.03.024
ISSN: 0021-9991
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Theoretical and Applied Mechanics (010207)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
Divisions: Current > Institutes > Institute for Future Environments
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 Elsevier Inc. All rights reserved.
Copyright Statement: This is the author’s version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational Physics, [Volume 269, (15 July 2014)] DOI: 10.1016/j.jcp.2014.03.024
Deposited On: 23 Mar 2014 22:14
Last Modified: 04 Aug 2016 01:21

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