Application of the gradient method to Hartree-Fock-Bogoliubov theory

Robledo, L. M.; Bertsch, G. F.

doi:10.1103/physrevc.84.014312

Cited by 107 publications

(163 citation statements)

References 23 publications

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“…The evaluation of the nuclear DFT is numerically demanding, particularly if one considers large fermionic systems in three dimensions and large deformations, without any symmetry constraints. Over the years many iterative approaches for solving the HFB equations have been proposed, including successive diagonalizations of the HFB or HF+BCS matrices, imaginary time evolu- * js1421@uw.edu † bulgac@uw.edu ‡ kenneth.roche@pnl.gov § gabrielw@if.pw.edu.pl tion [12,13], and gradient methods [14,15], which typically need significant memory requirements and operations of complexity O(N 3 ), where N is the dimension of the HFB matrix. For a review of modern diagonalization software, see Ref.…”

Section: Introductionmentioning

confidence: 99%

Coordinate-space solver for superfluid many-fermion systems with the shifted conjugate-orthogonal conjugate-gradient method

et al. 2017

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Self-consistent approaches to superfluid many-fermion systems in three-dimensions (and their subsequent use in time-dependent studies) require a large number of diagonalizations of very large dimension Hermitian matrices, which results in enormous computational costs. We present an approach based on the shifted conjugate-orthogonal conjugate-gradient (COCG) Krylov method for the evaluation of the Green's function, from which we subsequently extract various densities (particle number, spin, current, kinetic energy, anomalous, etc.) of a nuclear system. The approach eschews the determination of the quasiparticle wavefunctions and their corresponding quasiparticle energies, which never explicitly appear in the construction of a single-particle Hamiltonian or needed for the calculation of various static nuclear properties, which depend only on densities. As benchmarks we present calculations for nuclei with axial symmetry, including the ground state of spherical (magic or semi-magic) and axially deformed nuclei, the saddle-point in the 240 Pu constrained fission path, and a vortex in the neutron star crust and demonstrate the superior efficiency of the shifted COCG Krylov method over traditional approaches.

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Section: Introductionmentioning

confidence: 99%

Coordinate-space solver for superfluid many-fermion systems with the shifted conjugate-orthogonal conjugate-gradient method

et al. 2017

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“…The nonlinear HFB equation is solved using the gradient method [80] and taking into account approximately secondorder curvature effects [69,81]. The HFB quasiparticle creation and annihilation operators are expanded in a harmonic oscillator (HO) basis and special attention is paid to the convergence of the results with the basis size (see Appendix A for further details).…”

Section: Theorymentioning

confidence: 99%

Microscopic description of cluster radioactivity in actinide nuclei

2011

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Cluster radioactivity is the emission of a fragment heavier than an α particle and lighter than mass 50. The range of clusters observed in experiments goes from 14 C to 32 Si while the heavy mass residue is always a nucleus in the neighborhood of the doubly-magic 208 Pb nucleus. Cluster radioactivity is described in this paper as very asymmetric nuclear fission. A new fission valley leading to a decay with large fragment mass asymmetry matching the cluster radioactivity products is found. The mass octupole moment is found to be more convenient than the standard quadrupole moment as the parameter driving the system to fission. The mean-field Hartree-Fock-Bogoliubov theory with the phenomenological Gogny interaction has been used to compute the cluster emission properties of a wide range of even-even actinide nuclei from 222 Ra to 242 Cm, where emission of the clusters has been experimentally observed. Computed half-lives for cluster emission are compared with experimental results. The noticeable agreement obtained between the predicted properties of cluster emission (namely, cluster masses and emission half-lives) and the measured data confirms the validity of the proposed methodology in the analysis of the phenomenon of cluster radioactivity. A continuous fission path through the scission point has been described using the neck parameter constraint.

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“…The iterative scheme described in Ref. [17] utilises a preconditioning of quasiparticle wave functions in a gradient-based scheme to solve the HFB equations in that basis. In a representation like ours, the cost per iteration of preconditioning the states is much larger than that of preconditioning the potentials as it requires a much larger number of applications of derivative operators.…”

Section: Comments On Some Alternative Approachesmentioning

confidence: 99%

“…The matrix elements of Gaussian forces then take a separable form which allows for very reasonable precision at moderate computational cost. Such representation in general favours iteration algorithms that evolve directly the Thouless matrix representing the HFB state [15,16,17] instead of the strategy we will discuss below. For effective Hamiltonians that cannot be easily mapped on Gaussians, however, the advantages of using a HO basis are less evident.…”

Section: Introductionmentioning

confidence: 99%

Iterative approaches to the self-consistent nuclear energy density functional problem

2019

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Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing solvers can become very slow, and their performance dependent on manual fine-tuning of numerical parameters. In addition, convergence can sensitively depend on particularities of the EDF's parametrisation under consideration. Using the widely-used Skyrme EDF as an example, we investigate the impact of the parametrisation of the EDF, both in terms of the operator structures present and the size of coupling constants, on the convergence of numerical solvers. We focus on two aspects of the self-consistency cycle, which are the diagonalisation of a fixed single-particle Hamiltonian on one hand and the evolution of the mean-field densities and potentials on the other. Throughout the article we use a coordinate-space representation, for which the behaviour of algorithms can be straightforwardly analysed. We propose two algorithmic improvements that are easily implementable in existing solvers, heavy-ball dynamics and potential preconditioning. We demonstrate that these methods can be made virtually parameter-free, requiring no manual fine-tuning to achieve near-optimal performance except for isolated cases. The combination of both methods decreases substantially the CPU time required to obtain converged results. The improvements are illustrated for the MOCCa code that solves the self-consistent HFB problem in a 3d coordinate space representation for parametrisations of the standard Skyrme EDF at next-to-leading order in gradients and its extension to next-to-next-to-leading order.

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Application of the gradient method to Hartree-Fock-Bogoliubov theory

Cited by 107 publications

References 23 publications

Coordinate-space solver for superfluid many-fermion systems with the shifted conjugate-orthogonal conjugate-gradient method

Coordinate-space solver for superfluid many-fermion systems with the shifted conjugate-orthogonal conjugate-gradient method

Microscopic description of cluster radioactivity in actinide nuclei

Iterative approaches to the self-consistent nuclear energy density functional problem

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