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

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.

arXiv comment18 pages, 7 figures

References in corpus (40)

• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• New parametrization for the nuclear covariant energy density functional with point-coupling interaction
• Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
• Relativistic Nuclear Energy Density Functionals: adjusting parameters to binding energies
• New effective interactions in RMF theory with non-linear terms and density-dependent meson-nucleon coupling
• A Giant Halo at the Neutron Drip Line
• Neutron halo in deformed nuclei
• The limits of the nuclear landscape explored by the relativistic continuum Hatree-Bogoliubov theory
• Spherical Relativistic Hartree theory in a Woods-Saxon basis
• Progress on tilted axis cranking covariant density functional theory for nuclear magnetic and antimagnetic rotation
• Halos in medium-heavy and heavy nuclei with covariant density functional theory in continuum
• The TDHF Code Sky3D
• Potential Energy Surfaces of Actinide Nuclei from a Multi-dimensional Constraint Covariant Density Functional Theory: Barrier Heights and Saddle Point Shapes
• Deformed relativistic Hartree Bogoliubov theory in continuum
• Finite amplitude method for the RPA solution
• Multidimensionally-constrained relativistic mean field models and potential energy surfaces of actinide nuclei
• Anomaly in the charge radii of Pb isotopes
• Relativistic Hartree-Fock-Bogoliubov theory with Density Dependent Meson-Nucleon Couplings
• Multidimensionally-constrained covariant density functional theories --- nuclear shapes and potential energy surfaces
• Rod-shaped Nuclei at Extreme Spin and Isospin
• Shrunk halo and quenched shell gap at $N=16$ in ${}^{22}$C: Inversion of $sd$ states and deformation effects
• Nuclear halo structure and pseudo-spin symmetry
• Covariant density functional theory: Reexamining the structure of superheavy nuclei
• Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods
• Stability of the linear chain structure for ${}^{12}$C in covariant density functional theory on a 3D lattice
• Tetrahedral shapes of neutron-rich Zr isotopes from multidimensionally-constrained relativistic Hartree-Bogoliubov model
• Effects of pairing, continuum, and deformation on particles in the classically forbidden regions for Mg isotopes
• Time-dependent HF approach to SHE dynamics
• Isotopic trends of quasifission and fusion-fission in the reactions ${}^{48}$Ca+${}^{239,244}$Pu
• Dynamics of the linear-chain alpha cluster in microscopic time-dependent relativistic density functional theory
• Three-dimensional mesh calculations for covariant density functional theory
• Ground state properties and potential energy surfaces of ${}^{270}$Hs from multidimensionally-constrained relativistic mean field model
• Toward a bridge between relativistic and nonrelativistic density functional theories for nuclei
• Superheavy nuclei in microscopic collective Hamiltonian approach: the impact of beyond mean field correlations on the ground state and fission properties
• Toroidal states in ${}^{28}$Si with covariant density functional theory in 3D lattice space
• Avoid the Tsunami of the Dirac sea in the Imaginary Time Step method
• Iterative solution of a Dirac equation with inverse Hamiltonian method
• Single particle in a reflection-asymmetric potential
• Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory
• Application of the inverse Hamiltonian method to Hartree-Fock-Bogoliubov calculations