Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605197 | Applied and Computational Harmonic Analysis | 2014 | 16 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
F. Lanzara, V. Mazʼya, G. Schmidt,