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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.

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Metadaten
Author:Stefan-Alexander SchneiderORCiDGND
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
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