On the fast computation of high dimensional volume potentials

Details On the fast computation of high dimensional volume potentials On the fast computation of high dimensional volume potentials

2009-11-02

arxiv.org/abs/0911.0443v1

Mathematics

Numerical Analysis

19 pages

Scientific paper

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.

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