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Title: | Parallel-in-Time High-Order Multiderivative IMEX Solvers | Authors: | SCHUETZ, Jochen Seal, David C. ZEIFANG, Jonas |
Issue Date: | 2022 | Publisher: | SPRINGER/PLENUM PUBLISHERS | Source: | Journal of Scientific Computing, 90 (1) (Art N° 54) | Abstract: | In this work, we present a novel class of high-order time integrators for the numerical solution of ordinary differential equations. These integrators are of the two-derivative type, i.e., they take into account not only the first, but also the second temporal derivative of the unknown solution. While being motivated by two-derivative Runge-Kutta schemes, the methods themselves are of the predictor-corrector type, constructed in such a way that time-parallelism through pipelining is possible. This means that predictor and corrector steps can be computed simultaneously on different processors. Two variants are shown, the second-one being of Gauss-Seidel-type and hence having lower storage requirements. It turns out that this second variant is not only low-storage, but also performs better in numerical simulations. The algorithms presented can be cast as implicit two-step-two-derivative-multi-stage methods for which we present a detailed mathematical convergence analysis. Subsequently, numerical results are shown, demonstrating first the algorithms' ability to cope with very stiff equations and showing up to eighth order of accuracy. Following, the parallel-in-time capabilities are illustrated. We conclude that the class of methods is very well-suited if the time parallelization of very stiff equations is an option. | Notes: | Schutz, J (corresponding author), Univ Hasselt, Fac Sci, Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium.; Schutz, J (corresponding author), Univ Hasselt, Data Sci Inst, Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium. jochen.schuetz@uhasselt.be; seal@usna.edu; jonas.zeifang@uhasselt.be |
Keywords: | Multiderivative;IMEX;Parallelism in time;Time integration | Document URI: | http://hdl.handle.net/1942/36383 | ISSN: | 0885-7474 | e-ISSN: | 1573-7691 | DOI: | 10.1007/s10915-021-01733-3 | ISI #: | 000731291000005 | Rights: | The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2023 |
Appears in Collections: | Research publications |
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paper.pdf | Peer-reviewed author version | 889.79 kB | Adobe PDF | View/Open |
Parallel-in-Time High-Order Multiderivative IMEX Solvers.pdf Restricted Access | Published version | 1.27 MB | Adobe PDF | View/Open Request a copy |
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