Fast cubature of volume potentials over rectangular domains by approximate approximations
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
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.
Multi-dimensional convolution, Advection-diffusion potential, Separated representation, Higher dimensions
IdentifiersURN: urn:nbn:se:liu:diva-102767DOI: 10.1016/j.acha.2013.06.003ISI: 000327920000009OAI: oai:DiVA.org:liu-102767DiVA: diva2:683931