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Efficient solution of lattice equations by the recovery method. I. Scalar elliptic problems


Babuska, I; Sauter, S (2004). Efficient solution of lattice equations by the recovery method. I. Scalar elliptic problems. Computing and Visualization in Science, 7(3-4):113-119.

Abstract

In this paper, an efficient solver for high-dimensional lattice equations will be introduced. We will present a new concept, the recovery method, to define a bilinear form on the continuous level which has equivalent energy as the original lattice equation. The finite element discretisation of the continuous bilinear form will lead to a stiffness matrix which serves as a quasi-optimal preconditioner for the lattice equations. Since a large variety of efficient solvers are available for linear finite element problems the new recovery method allows us to apply these solvers for unstructured lattice problems.

Abstract

In this paper, an efficient solver for high-dimensional lattice equations will be introduced. We will present a new concept, the recovery method, to define a bilinear form on the continuous level which has equivalent energy as the original lattice equation. The finite element discretisation of the continuous bilinear form will lead to a stiffness matrix which serves as a quasi-optimal preconditioner for the lattice equations. Since a large variety of efficient solvers are available for linear finite element problems the new recovery method allows us to apply these solvers for unstructured lattice problems.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:19 Feb 2018 20:33
Publisher:Springer
ISSN:1432-9360
Additional Information:The original publication is available at www.springerlink.com
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00791-004-0146-z
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1076.65097

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