Percutaneous coronary interventions for chronic total occlusions

Abstract

While collisions of electrons with hydrogen atoms pose a well studied and in some sense closed problem, there is still no free computer code ready for “production use”, that would enable applied researchers to generate necessary data for arbitrary impact energies and scattering transitions directly if absent in on-line scattering databases. This is the second article on the Hex program package, which describes a new computer code that is, with a little setup, capable of solving the scattering equations for energies ranging from a fraction of the ionization threshold to approximately 100 eV or more, depending on the available computational resources. The program implements the exterior complex scaling method in the B-spline basis.Program title: hex-ecsCatalogue identifier: AETI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETI_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 44 440No. of bytes in distributed program, including test data, etc.: 322 643Distribution format: tar.gzProgramming 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 vectorized or parallelized?: Parallelized by OpenMP and MPI.RAM: Depending on input; 4.9 GiB for the test run.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 min for the test run on Intel i3 3.07 GHz processor (2 threads).