Fast low-rank approximations of multidimensional integrals in ion-atomic collisions modelling

TL;DR

This paper introduces a low-rank approximation method that significantly accelerates the computation of three-dimensional integrals in ion-atomic collision models, reducing complexity and computational time.

Contribution

The paper presents a novel low-rank separated approximation technique that improves efficiency in computing multidimensional integrals in physics simulations.

Findings

Algorithm is 1000 times faster than traditional spectral quadratures.

Method reduces computational complexity for multidimensional integrals.

Approach can be generalized to other physics problems.

Abstract

An efficient technique based on low-rank separated approximations is proposed for computation of three-dimensional integrals arising in the energy deposition model that describes ion-atomic collisions. Direct tensor-product quadrature requires grids of size $4000^3$ which is unacceptable. Moreover, several of such integrals have to be computed simultaneously for different values of parameters. To reduce the complexity, we use the structure of the integrand and apply numerical linear algebra techniques for the construction of low-rank approximation. The resulting algorithm is $10^3$ faster than spectral quadratures in spherical coordinates used in the original DEPOSIT code. The approach can be generalized to other multidimensional problems in physics.