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Sobolev gradient preconditioning for the electrostatic potential equation

✍ Scribed by J. Karátson; L. Lóczi

Book ID
104007699
Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
611 KB
Volume
50
Category
Article
ISSN
0898-1221

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✦ Synopsis

Sobolev gradient type preconditioning is proposed for the numerical solution of the electrostatic potential equation. A constructive representation of the gradients leads to efficient Laplacian preconditioners in the iteration thanks to the available fast Poisson solvers. Convergence is then verified for the corresponding sequence in Sobolev space, implying mesh independent convergence results for the discretized problems. A particular study is devoted to the case of a ball: due to the radial symmetry of this domain, a direct realization without discretization is feasible. The simplicity of the algorithm and the fast linear convergence are finally illustrated in a numerical test example. ~) 2005 Elsevier Ltd. All rights reserved.

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