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arXiv · 2007.09414

An efficient solution for Dirac equation in 3D lattice space with the conjugate gradient method

B. Li·Z. X. Ren·P. W. Zhao
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Abstract

An efficient method, preconditioned conjugate gradient method with a filtering function (PCG-F), is proposed for solving iteratively the Dirac equation in 3D lattice space for nuclear systems. The filtering function is adopted to avoid the variational collapsed problem and a momentum-dependent preconditioner is introduced to promote the efficiency of the iteration. The PCG-F method is demonstrated in solving the Dirac equation with given spherical and deformed Woods-Saxon potentials. The solutions given by the inverse Hamiltonian method in 3D lattice space and the shooting method in radial coordinate space are reproduced with a high accuracy. In comparison with the existing inverse Hamiltonian method, the present PCG-F method is much faster in the convergence of the iteration, in particular for deformed potentials. It may also provide a promising way to solve the relativistic Hartree-Bogoliubov equation iteratively in the future.

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B. Li, Z. X. Ren, P. W. Zhao. 2020-07-18. An efficient solution for Dirac equation in 3D lattice space with the conjugate gradient method. https://doi.org/10.1103/physrevc.102.044307

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