New version of hex-ecs, the B-spline implementation of exterior complex scaling method for solution of electron–hydrogen scattering

Published: 13 June 2016| Version 1 | DOI: 10.17632/6yfwt8psxx.1


We provide an updated version of the program hex-ecs originally presented in Comput. Phys. Commun. 185 (2014) 2903–2912. The original version used an iterative method preconditioned by the incomplete LU factorization (ILU), which–though very stable and predictable–requires a large amount of working memory. In the new version we implemented a “separated electrons” (or “Kronecker product approximation”, KPA) preconditioner as suggested by Bar-On et al., Appl. Num. Math. 33 (2000) 95–104. This preconditioner has much lower memory requirements, though in return it requires more iterations to reach converged results. By careful choice between ILU and KPA preconditioners one is able to extend the computational feasibility to larger calculations. Secondly, we added the option to run the KPA preconditioner on an OpenCL device (e.g. GPU). GPUs have generally better memory access times, which speeds up particularly the sparse matrix multiplication. The original version of this program (AETI_v1_0) may be found at



Natural Sciences