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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Non-iterative parallel Schwarz algorithms based on overlapping domain decomposition for parabolic partial differential equations
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by Danping Yang PDF
Math. Comp. 86 (2017), 2687-2718 Request permission

Abstract:

Two non-iterative parallel Schwarz algorithms (NIPSA) are presented to solve initial-boundary value problems of parabolic partial differential equations of second order. Algorithms are based on an overlapping domain decomposition and are fully parallel. A new idea is to introduce a partition of unity to distribute reasonably residuals of systems into sub-domains in the first algorithm and to sum weighted local corrections of solutions on sub-domains in the second one. Theoretical analysis shows that the algorithms have very good approximate property. At each time step, no iteration is required to reach the optimal order accuracy in $L^2$-norm. As well small overlapping can be used under some conditions for domain decomposition. Numerical results are also reported, which verify the theoretical analysis.
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Additional Information
  • Danping Yang
  • Affiliation: Department of Mathematics, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, and NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, East China Normal University, Shanghai, 200062, People’s Republic of China
  • MR Author ID: 238349
  • Email: dpyang@math.ecnu.edu.cn
  • Received by editor(s): February 5, 2014
  • Received by editor(s) in revised form: March 17, 2015, and July 7, 2015
  • Published electronically: May 11, 2017
  • Additional Notes: This research was supported partially by the National Natural Science Foundation of China under the grants 11571115 and 11171113 and by the Science and Technology Commission of Shanghai Municipality, grant No. 13dz2260400.
  • © Copyright 2017 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 2687-2718
  • MSC (2010): Primary 65N30, 65F10
  • DOI: https://doi.org/10.1090/mcom/3102
  • MathSciNet review: 3667021