The DEPOSIT computer code based on the low rank approximations

Mikhail S. Litsarev, Ivan V. Oseledets

Abstract: We present a new version of the DEPOSIT computer code based on the low rank approximations. This approach is based on the two dimensional cross decomposition of matrices and separated representations of analytical functions. The cross algorithm is available in the distributed package and can be used independently. All integration routines related to the computation of the deposited energy T ( b ) are implemented in a new way (low rank separated representation format on homogeneous meshes). By using this approach a bug in integration routines of previous version of the code was found and fixed in the current version. The total computational time was significantly accelerated and is about several minutes. New version program summary Program title: DEPOSIT 2014 Catalogue identifier: AENP_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AENP_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 182103 No. of bytes in distributed program, including test data, etc.: 1163484 Distribution format: tar.gz Programming language: C + + , Fortran. Computer: Any computer that can run C + + and Fortran compilers. Operating system: Any operating system with installed compilers mentioned above. Tested on Mac OS X 10.9 and Ubuntu 12.04. Has the code been vectorized or parallelized?: Due to the fast computation in the current implementation only a single-threaded version has been developed. Classification: 2.6, 4.10, 4.11, 19.1. External routines: BLAS, LAPACK and ALGLIB. The last one is included in the distribution. Catalogue identifier of previous version: AENP_v1_0 Journal reference of previous version: Comput. Phys. Comm. 184(2013) 432 Does the new version supersede the previous version?: Yes Nature of problem: For a given impact parameter b to calculate the deposited energy T ( b ) as a 3D integral over a coordinate space, and ionization probabilities P m ( b ) . For a given energy of the projectile to calculate the total and m -fold electron-loss cross sections using T ( b ) values on the whole b -mesh. Solution method: Calculation of the 3D-integral T ( b ) in all points of the b -mesh based on the low rank separated representations of matrices and tensors. For details, please see Ref. [1] Reasons for new version: The computation of the deposited energy T ( b ) integral is the slowest part of the program and should be done as fast as possible. To accelerate the program a new approach based on the low rank approximations was applied. It made computational scheme more stable and decreased the computational time by a factor of ∼ 10 3 . By means of this approach a bug in the integration routines was found and fixed for a special case of the energy gain. Summary of revisions: A two dimensional cross decomposition algorithm was developed as an independent module and was integrated with the energy gain Δ E . For the Slater density ρ ( r ) a separated representation via a sum of Gaussians was implemented. The calculation of three dimensional integrals T ( b ) was totally rewritten by using quadrature schemes based on the cross decomposition for energy gain and separated representations for Slater density. Details are reported in Ref. [1]. Running time: For a given energy the total and m -fold cross sections are calculated within about several minutes on a single-core.