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On Riesz minimal energy problems

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)
UniBasel Contributors:Harbrecht, Helmut
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
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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