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Fast cubature of volume potentials over rectangular domains by approximate approximations
University of Roma La Sapienza, Italy .
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
Weierstrass Institute Appl Anal and Stochast, Germany .
2014 (English)In: Applied and Computational Harmonic Analysis, ISSN 1063-5203, E-ISSN 1096-603X, Vol. 36, no 1, 167-182 p.Article in journal (Refereed) Published
Abstract [en]

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).

Place, publisher, year, edition, pages
Elsevier , 2014. Vol. 36, no 1, 167-182 p.
Keyword [en]
Multi-dimensional convolution, Advection-diffusion potential, Separated representation, Higher dimensions
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-102767DOI: 10.1016/j.acha.2013.06.003ISI: 000327920000009OAI: diva2:683931
Available from: 2014-01-07 Created: 2013-12-26 Last updated: 2014-01-07

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Maz´ya, Vladimir
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Mathematics and Applied MathematicsThe Institute of Technology
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