Harbrecht, Helmut and Wendland, Wolfgang L. and Zorii, Natalia.
(2012)
* On Riesz minimal energy problems.*
Journal of mathematical analysis and applications, Vol. 393, H. 2 , S. 397–412.

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Official URL: http://edoc.unibas.ch/dok/A6002740

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## Abstract

In Rn, n⩾2, we study the constructive and numerical solution of minimizing the energy relative to the Riesz kernel , where 1>α>n, for the Gauss variational problem, considered for finitely many compact, mutually disjoint, boundaryless (n−1)-dimensional C∞-manifolds Γℓ, ℓ∈L, each Γℓ being charged with Borel measures with the sign αℓ≔±1 prescribed. We show that the Gauss variational problem over an affine cone of Borel measures can alternatively be formulated as a minimum problem over an affine cone of surface distributions belonging to the Sobolev–Slobodetski space H−ε/2(Γ), where ε≔α−1 and . This allows the application of simple layer boundary integral operators on Γ and, hence, a penalty approximation. A corresponding numerical method is based on the Galerkin–Bubnov discretization with piecewise constant boundary elements. Wavelet matrix compression is applied to sparsify the system matrix. To the discretized problem, a gradient-projection method is applied. Numerical results are presented to illustrate the approach.

Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht) |
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UniBasel Contributors: | Harbrecht, Helmut |

Item Type: | Article, refereed |

Article Subtype: | Research Article |

Publisher: | Elsevier |

ISSN: | 0022-247X |

Note: | Publication type according to Uni Basel Research Database: Journal article |

Last Modified: | 08 Nov 2012 16:22 |

Deposited On: | 08 Nov 2012 16:14 |

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