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An efficient method, preconditioned conjugate gradient method with afiltering function (PCG-F), is proposed for solving iteratively the Diracequation in 3D lattice space for nuclear systems. The filtering function isadopted to avoid the variational collapsed problem and a momentum-dependentpreconditioner is introduced to promote the efficiency of the iteration. ThePCG-F method is demonstrated in solving the Dirac equation with given sphericaland deformed Woods-Saxon potentials. The solutions given by the inverseHamiltonian method in 3D lattice space and the shooting method in radialcoordinate space are reproduced with a high accuracy. In comparison with theexisting inverse Hamiltonian method, the present PCG-F method is much faster inthe convergence of the iteration, in particular for deformed potentials. It mayalso provide a promising way to solve the relativistic Hartree-Bogoliubovequation iteratively in the future.

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