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...
Saved in:
| Published in: | SIAM journal on scientific and statistical computing Vol. 2; no. 2; pp. 198 - 206 |
|---|---|
| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Philadelphia
Society for Industrial and Applied Mathematics
01.06.1981
|
| Subjects: | |
| ISSN: | 0196-5204, 1064-8275, 2168-3417, 1095-7197 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 |
| ISSN: | 0196-5204 1064-8275 2168-3417 1095-7197 |
| DOI: | 10.1137/0902017 |