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 matrixvector 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 title: Dirac_Laczos Catalogue identifier: AEUY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUY_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 526428 No. of bytes in distributed program, including test data, etc.: 2181729 Distribution format: tar.gz Programming 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 size Classification: 2.7. External routines: Boost [1], LAPACK [2] Nature of problem: Solving the time-dependent Dirac equation in two spatial dimensions Solution method: Lanczos propagator Running time: Depending on the problem size and computer hardware typically several minutes to several days References: [1] Boost C++ Libraries, http://www.boost.org [2] LAPACK-Linear Algebra PACKage, http://www.netlib.org/lapack/
krylov subspace methods dirac equation lanczos algorithm