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http://hdl.handle.net/10397/93293
Title: | Overlapping domain decomposition based exponential time differencing methods for semilinear parabolic equations | Authors: | Li, X Ju, L Hoang, TTP |
Issue Date: | Mar-2021 | Source: | BIT. Numerical mathematics, Mar. 2021, v. 61, no. 1, p. 1-36 | Abstract: | The localized exponential time differencing method based on overlapping domain decomposition has been recently introduced and successfully applied to parallel computations for extreme-scale numerical simulations of coarsening dynamics based on phase field models. In this paper, we focus on numerical solutions of a class of semilinear parabolic equations with the well-known Allen–Cahn equation as a special case. We first study the semi-discrete system under the standard central difference spatial discretization and prove the equivalence between the monodomain problem and the corresponding multidomain problem obtained by the Schwarz waveform relaxation iteration. Then we develop the fully discrete localized exponential time differencing schemes and, by establishing the maximum bound principle, prove the convergence of the fully discrete localized solutions to the exact semi-discrete solution and the convergence of the iterative solutions. Numerical experiments are carried out to verify the theoretical results in one-dimensional space and test the convergence and accuracy of the proposed algorithms with different numbers of subdomains in two-dimensional space. | Keywords: | Convergence analysis Localized exponential time differencing Overlapping domain decomposition Parallel Schwarz iteration Semilinear parabolic equation Waveform relaxation |
Publisher: | Springer Netherlands | Journal: | BIT. Numerical mathematics | ISSN: | 0006-3835 | EISSN: | 1572-9125 | DOI: | 10.1007/s10543-020-00817-0 | Rights: | © Springer Nature B.V. 2020 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10543-020-00817-0 |
Appears in Collections: | Journal/Magazine Article |
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Li_Overlapping_Domain_Decomposition.pdf | Pre-Published version | 1.03 MB | Adobe PDF | View/Open |
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