Multigrid method based on a space-time approach with standard coarsening for parabolic problems
| Autor: | Marcio Augusto Villela Pinto, Sebastião Romero Franco, Francisco J. Gaspar, Carmen Rodrigo |
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| Přispěvatelé: | Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Basis (linear algebra)
Discretization Applied Mathematics Space time Mathematical analysis Local Fourier analysis 010103 numerical & computational mathematics Space-time multigrid 01 natural sciences Backward Euler method Double discretization 010101 applied mathematics Computational Mathematics Operator (computer programming) Multigrid method Parabolic partial differential equations Time derivative Applied mathematics Heat equation 0101 mathematics Mathematics |
| Zdroj: | Applied Mathematics and Computation, 317, 1339-1351 |
| ISSN: | 0096-3003 |
| Popis: | In this work, a space-time multigrid method which uses standard coarsening in both temporal and spatial domains and combines the use of different smoothers is proposed for the solution of the heat equation in one and two space dimensions. In particular, an adaptive smoothing strategy, based on the degree of anisotropy of the discrete operator on each grid-level, is the basis of the proposed multigrid algorithm. Local Fourier analysis is used for the selection of the crucial parameter defining such an adaptive smoothing approach. Central differences are used to discretize the spatial derivatives and both implicit Euler and Crank–Nicolson schemes are considered for approximating the time derivative. For the solution of the second-order scheme, we apply a double discretization approach within the space-time multigrid method. The good performance of the method is illustrated through several numerical experiments. |
| Databáze: | OpenAIRE |
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