Abstract
SummaryAn 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 40003 that 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 103 faster than spectral quadratures in spherical coordinates used in the original DEPOSIT code. The approach can be generalized to other multidimensional problems in physics. Copyright © 2015 John Wiley & Sons, Ltd.
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