### 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 language | English |
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Pages (from-to) | 1093-1104 |

Number of pages | 12 |

Journal | Computers and Mathematics with Applications |

Volume | 50 |

Issue number | 7 |

DOIs | |

Publication status | Published - Oct 2005 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modelling and Simulation

### Cite this

*Computers and Mathematics with Applications*,

*50*(7), 1093-1104. https://doi.org/10.1016/j.camwa.2005.08.011

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

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 50, no. 7, pp. 1093-1104. https://doi.org/10.1016/j.camwa.2005.08.011

}

TY - JOUR

T1 - Sobolev gradient preconditioning for the electrostatic potential equation

AU - Karátson, J.

AU - Lóczi, L.

PY - 2005/10

Y1 - 2005/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=26444531625&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26444531625&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2005.08.011

DO - 10.1016/j.camwa.2005.08.011

M3 - Article

AN - SCOPUS:26444531625

VL - 50

SP - 1093

EP - 1104

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 7

ER -