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arXiv · 1301.1171

Fast cubature of volume potentials over rectangular domains

Flavia Lanzara·Vladimir Maz'ya·Gunther Schmidt
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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 $O(h^6)$ up to dimension $10^8$.

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Flavia Lanzara, Vladimir Maz'ya, Gunther Schmidt. 2013-01-07. Fast cubature of volume potentials over rectangular domains. https://arxiv.org/abs/1301.1171

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