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.
On the fast computation of high dimensional volume potentials / Lanzara, Flavia; V., Maz'Ya; G., Schmidt. - In: MATHEMATICS OF COMPUTATION. - ISSN 0025-5718. - STAMPA. - 80:274(2011), pp. 887-904. [10.1090/s0025-5718-2010-02425-1]
On the fast computation of high dimensional volume potentials
LANZARA, Flavia;
2011
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
