Fast Numerical Solution of Time-Periodic Parabolic Problems by a Multigrid Method
The discrete solutions of parabolic problems subject to the condition $y( \cdot ,T) = y( \cdot ,0)$ of time periodicity are solutions of large sparse systems. In this paper we propose a multigrid algorithm. It is a very fast iterative method. The algorithm can easily be generalized to nonlinear prob...
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| Vydáno v: | SIAM journal on scientific and statistical computing Ročník 2; číslo 2; s. 198 - 206 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Philadelphia
Society for Industrial and Applied Mathematics
01.06.1981
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| Témata: | |
| ISSN: | 0196-5204, 1064-8275, 2168-3417, 1095-7197 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | The discrete solutions of parabolic problems subject to the condition $y( \cdot ,T) = y( \cdot ,0)$ of time periodicity are solutions of large sparse systems. In this paper we propose a multigrid algorithm. It is a very fast iterative method. The algorithm can easily be generalized to nonlinear problems and to conditions of the type $y( \cdot ,0) = A(y( \cdot ,T))$ ($A$ is a nonlinear mapping). The computational work for solving the periodic problem is of the same order as the work for solving an initial value problem ($y( \cdot ,0)$ given). Numerical results are reported for a linear and a nonlinear example. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 |
| ISSN: | 0196-5204 1064-8275 2168-3417 1095-7197 |
| DOI: | 10.1137/0902017 |