Sparse Grid and Extrapolation Methods for Parabolic Problems
- Sparse grids are a recently introduced new technique for discretizing partial differential equations having a very favorable complexity in the number of unknowns for higher dimensional problems. Therefore, sparse grids are especially attractive for instationary equations when time is treated as an additional dimension. The paper will introduce the sparse grid finite element technique and the sparse grid combination technique which can be interpreted as a multivariate extrapolation method. The conceps are closely related to the multilevel principle so that multigrid methods and multilevel preconditioning strategies are the natural solvers. Thus the overall solution process has optimal complexity. Furthermore, the combination technique is easily parallelizable and applicable to nonlinear problems, like the Richardson equation. Besides an introduction of the algorithms with their basic analysis we will present numerical tests for a suite of characteristic model problems.
Author: | Stefan-Alexander SchneiderORCiDGND |
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Identifier: | 0-7923-2936-8 OPAC HS OPAC extern |
Parent Title (English): | Computational methods in water resources X. Volume 2 |
Subtitle (English): | edited proceedings of the Tenth International Conference on Computational methods in Water Resources, held at Universität Heidelberg, Germany, Jul. 1994 |
Publisher: | Kluwer Academic Publishers |
Place of publication: | Dordrecht; Boston; London |
Document Type: | conference proceeding (article) |
Conference: | Tenth International Conference on Computational methods in Water Resources, Heidelberg, Juli 1994 |
Language: | English |
Year of first Publication: | 1994 |
Number of pages: | 9 Seiten |
First Page: | 1383 |
Last Page: | 1391 |
Institutes: | Fakultät Elektrotechnik |
Publication Lists: | Schneider, Stefan-Alexander |
Publication reviewed: | begutachtet |
Release Date: | 2021/06/14 |