Krylov subspace methods for the Dirac equation

The Lanczos algorithm is evaluated for solving the time-independent as well as the time-dependent Dirac equation with arbitrary electromagnetic fields. We demonstrate that the Lanczos algorithm can yield very precise eigenenergies and allows very precise time propagation of relativistic wave packets. The unboundedness of the Dirac Hamiltonian does not hinder the applicability of the Lanczos algorithm. As the Lanczos algorithm requires only matrix–vector products and inner products, which both can be efficiently parallelized, it is an ideal method for large-scale calculations. The excellent parallelization capabilities are demonstrated by a parallel implementation of the Dirac Lanczos propagator utilizing the Message Passing Interface standard.Program summaryProgram title: Dirac_LaczosCatalogue identifier: AEUY_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUY_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.: 526 428No. of bytes in distributed program, including test data, etc.: 2 181 729Distribution format: tar.gzProgramming language: C++11.Computer: Multi-core systems or cluster computers.Operating system: Any.Has the code been vectorized or parallelized?: Parallelized using MPI.RAM: Typically 10 megabyte to 1 gigabyte depending on the chosen problem sizeClassification: 2.7.External routines: Boost [1], LAPACK [2]Nature of problem:Solving the time-dependent Dirac equation in two spatial dimensionsSolution method:Lanczos propagatorRunning time:Depending on the problem size and computer hardware typically several minutes to several daysReferences:[1] Boost C++ Libraries, http://www.boost.org[2] LAPACK-Linear Algebra PACKage, http://www.netlib.org/lapack/