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Manuscript Title: Collisions of electrons with hydrogen atoms II. Low-energy program using the method of the exterior complex scaling
Authors: Jakub Benda, Karel Houfek
Program title: hex-ecs
Catalogue identifier: AETI_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 185(2014)2903
Programming language: C++11.
Computer: Any.
Operating system: Any system with a C++11 compiler (e.g. GCC 4.8.1; tested on OpenSUSE 13.1 and Windows 8).
Has the code been vectorised or parallelized?: Parallelized by OpenMP and MPI.
RAM: Depending on input; 4.9 GiB for the test run.
Keywords: Electron-hydrogen scattering, Exterior complex scaling.
Classification: 2.4.

External routines: GSL [1], HDF5 [2], UMFPACK [3], FFTW3 [4], optionally with OpenBLAS [5].

Nature of problem:
Solution of the two-particle Schrödinger equation in central field.

Solution method:
The two-electron states are expanded into angular momentum eigenstates, which gives rise to the coupled bi-radial equations. The bi-radially dependent solution is then represented in a B-spline basis, which transforms the set of equations into a large matrix equation in this basis. The boundary condition is of Dirichlet type, thanks to the use of the exterior complex scaling method, which extends the coordinates into the complex plane. The matrix equation is then solved by preconditioned conjugate gradients.

Running time:
Depending on input; 16 mins for the test run on Intel i3 3.07 GHz processor (2 threads).

[1] M. Galassi, et al., GNU Scientific Library: Reference Manual, Network Theory Ltd., 2003.
[2] The HDF Group, Hierarchical Data Format, version 5 (1997-2014), http://www.hdfgroup.org/HDF5/.
[3] T. A. Davis, ACM Trans. Math. Softw. 30 (2004) 196-199.
[4] M. Frigo, Steven, G. Johnson, Proceedings of the IEEE (2005) 216-231.
[5] Z. Xianyi, W. Qian, Z. Yunquan, 2012 IEEE 18th International Conference on Parallel and Distributed Systems (ICPADS), 17-19 Dec. 2012.