Krylov subspace methods for the Dirac equation

Beerwerth, Randolf; Bauke, Heiko

doi:10.1016/j.cpc.2014.11.008

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Krylov subspace methods for the Dirac equation

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Beerwerth, Randolf
Division Prof. Dr. Christoph H. Keitel, MPI for Nuclear Physics, Max Planck Society;

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Bauke, Heiko
Division Prof. Dr. Christoph H. Keitel, MPI for Nuclear Physics, Max Planck Society;

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http://www.sciencedirect.com/science/article/pii/S0010465514003804
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Citation

Beerwerth, R., & Bauke, H. (2014). Krylov subspace methods for the Dirac equation. Computer Physics Communications, 188, 189-197. doi:10.1016/j.cpc.2014.11.008.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0024-99CA-B

Abstract

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.