论文标题
使用共轭梯度法的3D晶格空间中狄拉克方程的有效解决方案
An efficient solution for Dirac equation in 3D lattice space with the conjugate gradient method
论文作者
论文摘要
提出了一种具有过滤函数（PCG-F）的有效方法，预处理的共轭梯度方法，用于在3D晶格空间中用于迭代迭代方程。采用过滤函数以避免变化崩溃的问题，并引入动量依赖的预处理以促进迭代的效率。 PCG-F方法在用给定的球形和变形的木材势能求解DIRAC方程中得到了证明。 3D晶格空间中的逆哈密顿量方法和径向坐标空间中的射击方法给出的解决方案的精度很高。与现有的哈密顿反相比，目前的PCG-F方法在迭代的收敛中要快得多，尤其是对于变形电位而言。它还可以提供一种有希望的方法来在将来迭代地迭代地解决相对论的Hartree-Bogoliubov方程。
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.
