Accurate computation of the high dimensional diffraction potential over hyper-rectangles

2018/12/04 by Flavia Lanzara, Lanzara, Flavia, Vladimir Maz’ya +3
Materials Science · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Metamaterials and Metasurfaces Applications #Numerical Analysis (math.NA) #Optical Coatings and Gratings

paper · pdf · doi:10.48550/arxiv.1812.01338

openalex publication_date 2018/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We propose a fast method for high order approximation of potentials of the Helmholtz type operator Delta+kappa² over hyper-rectangles in Rⁿ. 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 kappa²=100.

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