ON THE FAST COMPUTATION OF HIGH DIMENSIONAL VOLUME POTENTIALS
2011 (English)In: MATHEMATICS OF COMPUTATION, ISSN 0025-5718, Vol. 80, no 274, 887-904 p.Article in journal (Refereed) Published
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.
Medical and Health Sciences
IdentifiersURN: urn:nbn:se:liu:diva-67302DOI: 10.1090/S0025-5718-2010-02425-1ISI: 000288587600011OAI: oai:DiVA.org:liu-67302DiVA: diva2:409399