Accurate computation of the high dimensional diffraction potential over hyper-rectangles
Numerical Analysis
2019-10-29 v1
Abstract
We propose a fast method for high order approximation of potentials of the Helmholtz type operator Delta+kappa^2 over hyper-rectangles in R^n. By using the basis functions introduced in the theory of approximate approximations, the cubature of a potential is reduced to the quadrature of one-dimensional integrals with separable integrands. Then a separated representation of the density, combined with a suitable quadrature rule, leads to a tensor product representation of the integral operator. Numerical tests show that these formulas are accurate and provide approximations of order 6 up to dimension 100 and kappa^2=100.
Cite
@article{arxiv.1812.01338,
title = {Accurate computation of the high dimensional diffraction potential over hyper-rectangles},
author = {Flavia Lanzara and Vladimir Maz'ya and Gunther Schmidt},
journal= {arXiv preprint arXiv:1812.01338},
year = {2019}
}