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ON THE FAST COMPUTATION OF HIGH DIMENSIONAL VOLUME POTENTIALS
University Roma La Sapienza.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Weierstrass Institute Appl Anal and Stochast.
2011 (English)In: MATHEMATICS OF COMPUTATION, ISSN 0025-5718, Vol. 80, no 274, 887-904 p.Article in journal (Refereed) Published
Abstract [en]

A fast method of an arbitrary high order for approximating volume potentials is proposed, which is effective also in high dimensional cases. Basis functions introduced in the theory of approximate approximations are used. Results of numerical experiments, which show approximation order O(h(8)) for the Newton potential in high dimensions, for example, for n = 200 000, are provided. The computation time scales linearly in the space dimension. New one-dimensional integral representations with separable integrands of the potentials of advection-diffusion and heat equations are obtained.

Place, publisher, year, edition, pages
American Mathematical Society , 2011. Vol. 80, no 274, 887-904 p.
National Category
Medical and Health Sciences
Identifiers
URN: urn:nbn:se:liu:diva-67302DOI: 10.1090/S0025-5718-2010-02425-1ISI: 000288587600011OAI: oai:DiVA.org:liu-67302DiVA: diva2:409399
Available from: 2011-04-08 Created: 2011-04-08 Last updated: 2014-10-23

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Maz´ya, Vladimir

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