Sobolev gradient preconditioning for the electrostatic potential equation

J. Karátson, L. Lóczi

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1093-1104
Number of pages12
JournalComputers and Mathematics with Applications
Volume50
Issue number7
DOIs
Publication statusPublished - Oct 2005

Fingerprint

Sobolev Gradient
Sobolev spaces
Preconditioning
Electrostatics
Radial Symmetry
Linear Convergence
Preconditioner
Convergence Results
Sobolev Spaces
Simplicity
Siméon Denis Poisson
Ball
Discretization
Numerical Solution
Mesh
Gradient
Iteration

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation

Cite this

Sobolev gradient preconditioning for the electrostatic potential equation. / Karátson, J.; Lóczi, L.

In: Computers and Mathematics with Applications, Vol. 50, No. 7, 10.2005, p. 1093-1104.

Research output: Contribution to journalArticle

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