An efficient method, the preconditioned conjugate gradient method with a filtering function (PCG-F), is proposed for solving iteratively the Dirac equation in three-dimensional (3D) lattice space for nuclear systems by defining a variational subspace, in which the positive-energy solutions are minima rather than saddle points as in the full variational space. This allows one to obtain the single nucleon energies and wave functions of the Dirac equation in 3D lattice space efficiently. The PCG-F method is demonstrated to solve 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 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.

• Received 15 June 2020
• Revised 4 September 2020
• Accepted 23 September 2020

DOI:https://doi.org/10.1103/PhysRevC.102.044307