Work

Fast cubature of volume potentials over rectangular domains

Year: 2013

Type: preprint

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 $10^8$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1301.1171

Authors: Lanzara, Flavia, Maz'ya, Vladimir, Schmidt, Gunther

Institutions: Sapienza University of Rome, Linköping University, University of Liverpool, Weierstrass Institute for Applied Analysis and Stochastics

Language: English

Topic: Mathematical Approximation and Integration

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2109256382

Cites: 10

Cited by:

Related to: 10