Convergence analysis for parallel‐in‐time solution of hyperbolic systems
| العنوان: | Convergence analysis for parallel‐in‐time solution of hyperbolic systems |
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| المؤلفون: | Hans De Sterck, Stephanie Friedhoff, Scott MacLachlan, Alexander J. M. Howse |
| المصدر: | Numerical Linear Algebra with Applications. 27 |
| بيانات النشر: | Wiley, 2019. |
| سنة النشر: | 2019 |
| مصطلحات موضوعية: | Algebra and Number Theory, Partial differential equation, Spacetime, Applied Mathematics, Parareal, 010103 numerical & computational mathematics, Symbolic computation, 01 natural sciences, 010101 applied mathematics, symbols.namesake, Multigrid method, Fourier transform, Convergence (routing), symbols, Applied mathematics, 0101 mathematics, Mathematics, Ansatz |
| الوصف: | Parallel-in-time algorithms have been successfully employed for reducing time-to-solution of a variety of partial differential equations, especially for diffusive (parabolic-type) equations. A major failing of parallel-in-time approaches to date, however, is that most methods show instabilities or poor convergence for hyperbolic problems. This paper focuses on the analysis of the convergence behavior of multigrid methods for the parallel-in-time solution of hyperbolic problems. Three analysis tools are considered that differ, in particular, in the treatment of the time dimension: (1) space-time local Fourier analysis, using a Fourier ansatz in space and time, (2) semi-algebraic mode analysis, coupling standard local Fourier analysis approaches in space with algebraic computation in time, and (3) a two-level reduction analysis, considering error propagation only on the coarse time grid. In this paper, we show how insights from reduction analysis can be used to improve feasibility of the semi-algebraic mode analysis, resulting in a tool that offers the best features of both analysis techniques. Following validating numerical results, we investigate what insights the combined analysis framework can offer for two model hyperbolic problems, the linear advection equation in one space dimension and linear elasticity in two space dimensions. |
| تدمد: | 1099-1506 1070-5325 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::bdc35922a3f743503916d6e84cb931e8 https://doi.org/10.1002/nla.2271 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi...........bdc35922a3f743503916d6e84cb931e8 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 10991506 10705325 |
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