skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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 wave functions 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 this study presents calculations for nuclei with axial symmetry, including the ground state of spherical (magic or semimagic) 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.

Authors:
 [1];  [1];  [2];  [3]
  1. Univ. of Washington, Seattle, WA (United States). Dept. of Physics
  2. Univ. of Washington, Seattle, WA (United States). Dept. of Physics; Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
  3. Warsaw Univ. of Technology (Poland). Faculty of Physics; Univ. of Washington, Seattle, WA (United States). Dept. of Physics
Publication Date:
Research Org.:
Oak Ridge National Laboratory, Oak Ridge Leadership Computing Facility (OLCF); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1544399
Alternate Identifier(s):
OSTI ID: 1349702
Grant/Contract Number:  
FG02-97ER41014; AC05-00OR22725; AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 95; Journal Issue: 4; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English

Citation Formats

Jin, Shi, Bulgac, Aurel, Roche, Kenneth, and Wlazłowski, Gabriel. Coordinate-space solver for superfluid many-fermion systems with the shifted conjugate-orthogonal conjugate-gradient method. United States: N. p., 2017. Web. doi:10.1103/PhysRevC.95.044302.
Jin, Shi, Bulgac, Aurel, Roche, Kenneth, & Wlazłowski, Gabriel. Coordinate-space solver for superfluid many-fermion systems with the shifted conjugate-orthogonal conjugate-gradient method. United States. doi:10.1103/PhysRevC.95.044302.
Jin, Shi, Bulgac, Aurel, Roche, Kenneth, and Wlazłowski, Gabriel. Mon . "Coordinate-space solver for superfluid many-fermion systems with the shifted conjugate-orthogonal conjugate-gradient method". United States. doi:10.1103/PhysRevC.95.044302. https://www.osti.gov/servlets/purl/1544399.
@article{osti_1544399,
title = {Coordinate-space solver for superfluid many-fermion systems with the shifted conjugate-orthogonal conjugate-gradient method},
author = {Jin, Shi and Bulgac, Aurel and Roche, Kenneth and Wlazłowski, Gabriel},
abstractNote = {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 wave functions 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 this study presents calculations for nuclei with axial symmetry, including the ground state of spherical (magic or semimagic) 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.},
doi = {10.1103/PhysRevC.95.044302},
journal = {Physical Review C},
number = 4,
volume = 95,
place = {United States},
year = {2017},
month = {4}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: The ellipse contour $C$ : $z$($φ$) in Eq. (50) adopted to perform the contour integral. The thick solid line represents the positive energy continuum quasiparticle states with $E$ > -$μ$ , while the crosses represent the positive energy discrete bound quasiparticle states 0 < $E$i < -$μ$ .more » Density of integration points is larger for parts of the contour close to the real axis (depicted by blue and red colors), and decreases as we go far away from the real axis (depicted by green color).« less

Save / Share:

Works referenced in this record:

Stochastic estimation of nuclear level density in the nuclear shell model: An application to parity-dependent level density in 58 Ni
journal, February 2016


Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure
journal, August 2014


BiCGStab(?) for Families of Shifted Linear Systems
journal, April 2003


Energy Density Functional Approach to Superfluid Nuclei
journal, June 2003


Nuclear response in the continuum
journal, May 1975


Hartree-Fock-Bogolyubov description of nuclei near the neutron-drip line
journal, June 1984


Axially symmetric Hartree-Fock-Bogoliubov calculations for nuclei near the drip lines
journal, June 2003


Broyden's method in nuclear structure calculations
journal, July 2008


Fission fragment charge and mass distributions in Pu 239 ( n , f ) in the adiabatic nuclear energy density functional theory
journal, May 2016


An Efficient MAINV Preconditioned COCG Method for FEM Analysis of Millimeter Wave Filters
journal, January 2011

  • Li, Yue Hui; Nie, Zai Ping; Meng, Min
  • Journal of Infrared, Millimeter, and Terahertz Waves, Vol. 32, Issue 2
  • DOI: 10.1007/s10762-010-9761-6

Finite amplitude method applied to the giant dipole resonance in heavy rare-earth nuclei
journal, March 2016


A parallel method for large sparse generalized eigenvalue problems using a GridRPC system
journal, June 2008

  • Sakurai, Tetsuya; Kodaki, Yoshihisa; Tadano, Hiroto
  • Future Generation Computer Systems, Vol. 24, Issue 6
  • DOI: 10.1016/j.future.2008.01.002

Relativistic Coulomb Excitation within the Time Dependent Superfluid Local Density Approximation
journal, January 2015


Finite amplitude method for the solution of the random-phase approximation
journal, August 2007


Finite amplitude method in linear response TDDFT calculations
journal, September 2014


Preconditioning iterative algorithm for the electromagnetic scattering from a large cavity
journal, May 2009

  • Wang, Yingxi; Du, Kui; Sun, Weiwei
  • Numerical Linear Algebra with Applications, Vol. 16, Issue 5
  • DOI: 10.1002/nla.615

Coordinate space Hartree-Fock-Bogoliubov calculations for the zirconium isotope chain up to the two-neutron drip line
journal, May 2005


Large-amplitude motion in superfluid fermi droplets
journal, January 1990


A projection method for generalized eigenvalue problems using numerical integration
journal, October 2003


Solution of the Skyrme–HF+BCS equation on a 3D mesh, II: A new version of the Ev8 code
journal, February 2015


Finite-amplitude method for charge-changing transitions in axially deformed nuclei
journal, August 2014


Hartree-Fock-Bogoliubov descriptions of deformed weakly bound nuclei in large coordinate spaces
journal, November 2013


Microscopic calculation of Pu 240 scission with a finite-range effective force
journal, November 2009


Augmented Lagrangian method for constrained nuclear density functional theory
journal, August 2010


A Preconditioned COCG Method for Solving Complex Symmetric Linear Systems Arising from Scattering Problems
journal, January 2008

  • Li, L.; Huang, T. -Z.; Ren, Z. -G.
  • Journal of Electromagnetic Waves and Applications, Vol. 22, Issue 14-15
  • DOI: 10.1163/156939308787537793

Hartree-Fock-Bogoliubov calculations in coordinate space: Neutron-rich sulfur, zirconium, cerium, and samarium isotopes
journal, December 2003


Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.
journal, January 2012

  • Schunck, N.; Dobaczewski, J.; McDonnell, J.
  • Computer Physics Communications, Vol. 183, Issue 1
  • DOI: 10.1016/j.cpc.2011.08.013

Mean-field description of ground-state properties of drip-line nuclei: Pairing and continuum effects
journal, June 1996


Application of the imaginary time step method to the solution of the static Hartree-Fock problem
journal, June 1980


Linear algebraic calculation of the Green’s function for large-scale electronic structure theory
journal, April 2006


The nuclear density of states in the space of nuclear shapes
journal, September 1980


Pairing renormalization and regularization within the local density approximation
journal, April 2006


Pulsar glitches and restlessness as a hard superfluidity phenomenon
journal, July 1975


Application of the gradient method to Hartree-Fock-Bogoliubov theory
journal, July 2011


Vortex Pinning and Dynamics in the Neutron Star Crust
journal, November 2016


Nuclear ground-state properties from mean-field calculations
journal, September 2002

  • Dobaczewski, J.; Nazarewicz, W.; Stoitsov, M. V.
  • The European Physical Journal A, Vol. 15, Issue 1-2
  • DOI: 10.1140/epja/i2001-10218-8

Comment on “Spontaneous Fission: A Kinetic Approach”
journal, November 1997


Renormalization of the Hartree-Fock-Bogoliubov Equations in the Case of a Zero Range Pairing Interaction
journal, January 2002


Gamow Shell Model Description of Neutron-Rich Nuclei
journal, July 2002


Use of the discrete variable representation basis in nuclear physics
journal, May 2013


Odd-even mass differences from self-consistent mean field theory
journal, March 2009


Finite amplitude method for the quasiparticle random-phase approximation
journal, July 2011


Towards a universal nuclear density functional
journal, August 1998

  • Fayans, S. A.
  • Journal of Experimental and Theoretical Physics Letters, Vol. 68, Issue 3
  • DOI: 10.1134/1.567841

Eigenvalue computation in the 20th century
journal, November 2000

  • Golub, Gene H.; van der Vorst, Henk A.
  • Journal of Computational and Applied Mathematics, Vol. 123, Issue 1-2
  • DOI: 10.1016/S0377-0427(00)00413-1

Quasi-Minimal Residual Variants of the COCG and COCR Methods for Complex Symmetric Linear Systems in Electromagnetic Simulations
journal, December 2014

  • Gu, Xian-Ming; Huang, Ting-Zhu; Li, Liang
  • IEEE Transactions on Microwave Theory and Techniques, Vol. 62, Issue 12
  • DOI: 10.1109/TMTT.2014.2365472

The Lagrange-mesh method
journal, March 2015


Filter diagonalization of shell-model calculations
journal, August 2010


Numerical accuracy of mean-field calculations in coordinate space
journal, December 2015


Shifted Conjugate-Orthogonal–Conjugate-Gradient Method and Its Application to Double Orbital Extended Hubbard Model
journal, November 2008

  • Yamamoto, Susumu; Sogabe, Tomohiro; Hoshi, Takeo
  • Journal of the Physical Society of Japan, Vol. 77, Issue 11
  • DOI: 10.1143/JPSJ.77.114713

Self-consistent mean-field models for nuclear structure
journal, January 2003

  • Bender, Michael; Heenen, Paul-Henri; Reinhard, Paul-Gerhard
  • Reviews of Modern Physics, Vol. 75, Issue 1
  • DOI: 10.1103/RevModPhys.75.121

On the solution of the Hartree-Fock-Bogoliubov equations by the conjugate gradient method
journal, November 1995


Deformed coordinate-space Hartree-Fock-Bogoliubov approach to weakly bound nuclei and large deformations
journal, December 2008


Nuclear isotope shifts within the local energy-density functional approach
journal, August 2000


Skyrme interaction and nuclear matter constraints
journal, March 2012


Induced Fission of Pu 240 within a Real-Time Microscopic Framework
journal, March 2016


Isovector giant dipole resonance from the 3D time-dependent density functional theory for superfluid nuclei
journal, November 2011


A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stabilities
journal, May 1998


A study of the nuclear response function
journal, May 1975


A fast configuration space method for solving local Kohn–Sham equations
journal, September 2005


A filter diagonalization for generalized eigenvalue problems based on the Sakurai–Sugiura projection method
journal, February 2010

  • Ikegami, Tsutomu; Sakurai, Tetsuya; Nagashima, Umpei
  • Journal of Computational and Applied Mathematics, Vol. 233, Issue 8
  • DOI: 10.1016/j.cam.2009.09.029

A Petrov-Galerkin type method for solving Axk=b, where A is symmetric complex
journal, March 1990

  • van der Vorst, H. A.; Melissen, J. B. M.
  • IEEE Transactions on Magnetics, Vol. 26, Issue 2
  • DOI: 10.1109/20.106415

Coordinate-space solution of the Skyrme–Hartree–Fock– Bogolyubov equations within spherical symmetry. The program HFBRAD (v1.00)
journal, June 2005


Restarted GMRES for Shifted Linear Systems
journal, January 1998


Low-energy collective modes of deformed superfluid nuclei within the finite-amplitude method
journal, June 2013