Fast cubature of volume potentials over rectangular domains

2013/01/07 by Flavia Lanzara, Lanzara, Flavia, Maz'ya, Vladimir +1
Engineering · Mathematics · Physics and Astronomy · #41A30 #41A63 #65-05 #65D32 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1301.1171

openalex publication_date 2013/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In the present paper we study high-order cubature formulas for the computation of advection-diffusion potentials over boxes. 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. For densities with separated approximation, we derive a tensor product representation of the integral operator which admits efficient cubature procedures in very high dimensions. Numerical tests show that these formulas are accurate and provide approximation of order O(h⁶) up to dimension 10⁸.

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