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Efficient solution of anisotropic lattice equations by the recovery method


Babuska, I; Sauter, S (2008). Efficient solution of anisotropic lattice equations by the recovery method. SIAM Journal on Scientific Computing (SISC), 30(5):2386-2404.

Abstract

In a recent paper, the authors introduced the recovery method (local energy matching principle) for solving large systems of lattice equations. The idea is to construct a partial differential equation along with a finite element discretization such that the arising system of linear equations has equivalent energy as the original system of lattice equations. Since a vast variety of efficient solvers is available for solving large systems of finite element discretizations of elliptic PDEs, these solvers may serve as preconditioners for the system of lattice equations. In this paper, we will focus on both the theoretical and the numerical dependence of the method on various mesh-dependent parameters, which can be easily computed and monitored during the solution process. Systematic parameter tests have been performed which underline (a) the robustness and the efficiency of the recovery method and (b) the reliability of the control parameters, which are computed in a preprocessing step to predict the performance of the preconditioner based on the recovery method.

Abstract

In a recent paper, the authors introduced the recovery method (local energy matching principle) for solving large systems of lattice equations. The idea is to construct a partial differential equation along with a finite element discretization such that the arising system of linear equations has equivalent energy as the original system of lattice equations. Since a vast variety of efficient solvers is available for solving large systems of finite element discretizations of elliptic PDEs, these solvers may serve as preconditioners for the system of lattice equations. In this paper, we will focus on both the theoretical and the numerical dependence of the method on various mesh-dependent parameters, which can be easily computed and monitored during the solution process. Systematic parameter tests have been performed which underline (a) the robustness and the efficiency of the recovery method and (b) the reliability of the control parameters, which are computed in a preprocessing step to predict the performance of the preconditioner based on the recovery method.

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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
Uncontrolled Keywords:lattice equations, recovery method, preconditioning
Language:English
Date:3 July 2008
Deposited On:05 Jan 2009 13:28
Last Modified:05 Apr 2016 12:39
Publisher:Society for Industrial and Applied Mathematics (SIAM)
ISSN:1064-8275
Additional Information:Copyright © 2008, Society for Industrial and Applied Mathematics
Publisher DOI:https://doi.org/10.1137/070690717

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