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

SUMMARY An efficient technique based on low-rank separated approxim ations is proposed for computation of threedimensional 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. Copyright c 0000 John Wiley & Sons, Ltd.

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