Fast low-rank approximations of multidimensional integrals in ion-atomic collisions modelling
This work addresses a computational bottleneck in energy deposition modeling for ion-atomic collisions, offering a practical speedup for a specific physics simulation.
The paper proposes a low-rank separated approximation technique for computing 3D integrals in ion-atomic collision models, achieving a 1000x speedup over spectral quadratures used in the original DEPOSIT code.
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.