WIAS Preprint No. 1767, (2013)

Fast cubature of volume potentials over rectangular domains


  • Lanzara, Flavia
  • Maz'ya, Vladimir
  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 65D32 65-05 41A30 41A63


  • Multi-dimensional convolution, advection-diffusion potential, tensor product representation, higher dimensions


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.

Appeared in

  • Appl. Comput. Harmon. Anal., 36 (2014) pp. 167--182 with modified title: Fast cubature of volume potentials over rectangular domains by approximate approximations

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