We describe the new version (v2.49t) of the code
hfodd which solves the nuclear Skyrme–Hartree–Fock (HF) or Skyrme–Hartree–Fock–Bogolyubov (HFB) problem by using the Cartesian deformed ...harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF
+
BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme–HFB code
hfbtho, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected.
Program title:
hfodd (v2.49t)
Catalogue identifier: ADFL_v3_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html
Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland
Licensing provisions: GNU General Public Licence v3
No. of lines in distributed program, including test data, etc.: 190 614
No. of bytes in distributed program, including test data, etc.: 985 898
Distribution format: tar.gz
Programming language: FORTRAN-90
Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT4, Cray XT5
Operating system: UNIX, LINUX, Windows XP
Has the code been vectorized or parallelized?: Yes, parallelized using MPI
RAM: 10 Mwords
Word size: The code is written in single-precision for the use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine.
Classification: 17.22
Catalogue identifier of previous version: ADFL_v2_2
Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 2361
External routines: The user must have access to
1.
the NAGLIB subroutine f02axe, or LAPACK subroutines zhpev, zhpevx, zheevr, or zheevd, which diagonalize complex hermitian matrices,
2.
the LAPACK subroutines dgetri and dgetrf which invert arbitrary real matrices,
3.
the LAPACK subroutines dsyevd, dsytrf and dsytri which compute eigenvalues and eigenfunctions of real symmetric matrices,
4.
the LINPACK subroutines zgedi and zgeco, which invert arbitrary complex matrices and calculate determinants,
5.
the BLAS routines dcopy, dscal, dgeem and dgemv for double-precision linear algebra and zcopy, zdscal, zgeem and zgemv for complex linear algebra, or provide another set of subroutines that can perform such tasks.
The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville:
http://netlib2.cs.utk.edu/.
Does the new version supersede the previous version?: Yes
Nature of problem: The nuclear mean field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree–Fock equations, even for heavy nuclei, and for various nucleonic (
n-particle–
n-hole) configurations, deformations, excitation energies, or angular momenta. Similarly, Local Density Approximation in the particle–particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree–Fock–Bogolyubov method.
Solution method: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean-field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in: J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166.
Reasons for new version: Version 2.49s of HFODD provides a number of new options such as the isospin mixing and projection of the Skyrme functional, the finite-temperature HF and HFB formalism and optimized methods to perform multi-constrained calculations. It is also the first version of HFODD to contain threading and parallel capabilities.
Summary of revisions:
1.
Isospin mixing and projection of the HF states has been implemented.
2.
The finite-temperature formalism for the HFB equations has been implemented.
3.
The Lipkin translational energy correction method has been implemented.
4.
Calculation of the shell correction has been implemented.
5.
The two-basis method for the solution to the HFB equations has been implemented.
6.
The Augmented Lagrangian Method (ALM) for calculations with multiple constraints has been implemented.
7.
The linear constraint method based on the cranking approximation of the RPA matrix has been implemented.
8.
An interface between HFODD and the axially-symmetric and parity-conserving code HFBTHO has been implemented.
9.
The mixing of the matrix elements of the HF or HFB matrix has been implemented.
10.
A parallel interface using the MPI library has been implemented.
11.
A scalable model for reading input data has been implemented.
12.
OpenMP pragmas have been implemented in three subroutines.
13.
The diagonalization of the HFB matrix in the simplex-breaking case has been parallelized using the ScaLAPACK library.
14.
Several little significant errors of the previous published version were corrected.
Running time: In serial mode, running 6 HFB iterations for
152Dy for conserved parity and signature symmetries in a full spherical basis of
N
=
14
shells takes approximately 8 min on an AMD Opteron processor at 2.6 GHz, assuming standard BLAS and LAPACK libraries. As a rule of thumb, runtime for HFB calculations for parity and signature conserved symmetries roughly increases as
N
7
, where
N is the number of full HO shells. Using custom-built optimized BLAS and LAPACK libraries (such as in the ATLAS implementation) can bring down the execution time by 60%. Using the threaded version of the code with 12 threads and threaded BLAS libraries can bring an additional factor 2 speed-up, so that the same 6 HFB iterations now take of the order of 2 min 30 s.
► This is version 249t of the code HFODD. ► This version contains new physics capabilities. ► Built-in parallel model (MPI and OpenMP) is now available. ► Portability and scalability has been improved.
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Properties of strongly interacting, two-component finite Fermi systems are discussed within the recently developed coordinate-space Hartree-Fock-Bogoliubov (HFB) code HFB-AX. This solver is capable ...of treating the salient features of weakly bound and extremely deformed systems. Two illustrative examples are presented: i) neutron-rich deformed Mg isotopes, and ii) spin-polarized atomic condensates in a strongly deformed harmonic trap.
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The UNEDF SciDAC project to develop and optimize the energy density functional for atomic nuclei using state-of-the art computational infrastructure is briefly described. The ultimate goal is to ...replace current phenomenological models of the nucleus with a well-founded microscopic theory with minimal uncertainties, capable of describing nuclear data and extrapolating to unknown regions.
The demands of cutting-edge science are driving the need for larger and faster computing resources. With the rapidly growing scale of computing systems and the prospect of technologically disruptive ...architectures to meet these needs, scientists face the challenge of effectively using complex computational resources to advance scientific discovery. Multi-disciplinary collaborating networks of researchers with diverse scientific backgrounds are needed to address these complex challenges. The UNEDF SciDAC collaboration of nuclear theorists, applied mathematicians, and computer scientists is developing a comprehensive description of nuclei and their reactions that delivers maximum predictive power with quantified uncertainties. This paper describes UNEDF and identifies attributes that classify it as a successful computational collaboration. We illustrate significant milestones accomplished by UNEDF through integrative solutions using the most reliable theoretical approaches, most advanced algorithms, and leadership-class computational resources.
We describe the new version (v2.40h) of the code hfodd which solves the nuclear Skyrme–Hartree–Fock or Skyrme–Hartree–Fock–Bogolyubov problem by using the Cartesian deformed harmonic-oscillator ...basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree–Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for state-dependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the DT2h transformations and rotations of wave functions, (ix) quasiparticle blocking for the HFB solutions in odd and odd–odd nuclei, (x) the Broyden method to accelerate the convergence, (xi) the Lipkin–Nogami method to treat pairing correlations, (xii) the exact Coulomb exchange term, (xiii) several utility options, and we have corrected three insignificant errors.
Program title: HFODD (v2.40h)
Catalogue identifier: ADFL_v2_2
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v2_2.html
Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 79 618
No. of bytes in distributed program, including test data, etc.: 372 548
Distribution format: tar.gz
Programming language: FORTRAN-77 and Fortran-90
Computer: Pentium-III, AMD-Athlon, AMD-Opteron
Operating system: UNIX, LINUX, Windows XP
Has the code been vectorised or parallelized?: Yes, vectorised
RAM: 10 Mwords
Word size: The code is written in single-precision for use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine.
Classification: 17.22
Catalogue identifier of previous version: ADFL_v2_1
Journal reference of previous version: Comput. Phys. Commun. 167 (2005) 214
External routines: Lapack (http://www.netlib.org/lapack/), Blas (http://www.netlib.org), linpack (http://www.netlib/linpack/)
Does the new version supersede the previous version?: Yes
Nature of problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree–Fock equations, even for heavy nuclei, and for various nucleonic (n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle–particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree–Fock–Bogolyubov method.
Solution method: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in 1.
Summary of revisions:1.Projection on good angular momentum (for the Hartree–Fock states) has been implemented.2.Calculation of the GCM kernels has been implemented.3.Calculation of matrix elements of the Yukawa interaction has been implemented.4.The BCS solutions for state-dependent pairing gaps have been implemented.5.The HFB solutions for broken simplex symmetry have been implemented.6.Calculation of Bohr deformation parameters has been implemented.7.Constraints on the Schiff moments and scalar multipole moments have been implemented.8.The DT2h transformations and rotations of wave functions have been implemented.9.The quasiparticle blocking for the HFB solutions in odd and odd–odd nuclei has been implemented.10.The Broyden method to accelerate the convergence has been implemented.11.The Lipkin–Nogami method to treat pairing correlations has been implemented.12.The exact Coulomb exchange term has been implemented.13.Several utility options have been implemented.14.Three insignificant errors have been corrected.
Restrictions: The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required.
Unusual features: The user must have access to1.an implementation of the BLAS (Basic Linear Algebra Subroutines),2.the NAGLIB subroutine F02AXE, or LAPACK subroutines ZHPEV, ZHPEVX, or ZHEEVR, which diagonalize complex Hermitian matrices, and3.the LINPACK subroutines ZGEDI and ZGECO, which invert arbitrary complex matrices and calculate determinants or provide another set of subroutines that can perform such a tasks. The LAPACK and LINPACK subroutines and an unoptimized version of the BLAS can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://www.netlib.org/.
Running time: One Hartree–Fock iteration for the superdeformed, rotating, parity conserving state of 15266Dy86 takes about six seconds on the AMD-Athlon 1600+ processor. Starting from the Woods–Saxon wave functions, about fifty iterations are required to obtain the energy converged within the precision of about 0.1 keV. In the case where every value of the angular velocity is converged separately, the complete superdeformed band with precisely determined dynamical moments J(2) can be obtained in forty minutes of CPU time on the AMD-Athlon 1600+ processor. This time can be often reduced by a factor of three when a self-consistent solution for a given rotational frequency is used as a starting point for a neighboring rotational frequency.
References:1J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166.
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The fast computation of the Gauss hypergeometric function
F
1
2
with all its parameters complex is a difficult task. Although the
F
1
2
function verifies numerous analytical properties involving ...power series expansions whose implementation is apparently immediate, their use is thwarted by instabilities induced by cancellations between very large terms. Furthermore, small areas of the complex plane, in the vicinity of
z
=
e
±
i
π
3
, are inaccessible using
F
1
2
power series linear transformations. In order to solve these problems, a generalization of R.C. Forrey's transformation theory has been developed. The latter has been successful in treating the
F
1
2
function with real parameters. As in real case transformation theory, the large canceling terms occurring in
F
1
2
analytical formulas are rigorously dealt with, but by way of a new method, directly applicable to the complex plane. Taylor series expansions are employed to enter complex areas outside the domain of validity of power series analytical formulas. The proposed algorithm, however, becomes unstable in general when
|
a
|
,
|
b
|
,
|
c
|
are moderate or large. As a physical application, the calculation of the wave functions of the analytical Pöschl–Teller–Ginocchio potential involving
F
1
2
evaluations is considered.
Program title: hyp_2F1, PTG_wf
Catalogue identifier: AEAE_v1_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/AEAE_v1_0.html
Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence,
http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 6839
No. of bytes in distributed program, including test data, etc.: 63 334
Distribution format: tar.gz
Programming language: C++, Fortran 90
Computer: Intel i686
Operating system: Linux, Windows
Word size: 64 bits
Classification: 4.7
Nature of problem: The Gauss hypergeometric function
F
1
2
, with all its parameters complex, is uniquely calculated in the frame of transformation theory with power series summations, thus providing a very fast algorithm. The evaluation of the wave functions of the analytical Pöschl–Teller–Ginocchio potential is treated as a physical application.
Solution method: The Gauss hypergeometric function
F
1
2
verifies linear transformation formulas allowing consideration of arguments of a small modulus which then can be handled by a power series. They, however, give rise to indeterminate or numerically unstable cases, when
b
−
a
and
c
−
a
−
b
are equal or close to integers. They are properly dealt with through analytical manipulations of the Lanczos expression providing the Gamma function. The remaining zones of the complex plane uncovered by transformation formulas are dealt with Taylor expansions of the
F
1
2
function around complex points where linear transformations can be employed. The Pöschl–Teller–Ginocchio potential wave functions are calculated directly with
F
1
2
evaluations.
Restrictions: The algorithm provides full numerical precision in almost all cases for
|
a
|
,
|
b
|
, and
|
c
|
of the order of one or smaller, but starts to be less precise or unstable when they increase, especially through
a,
b, and
c imaginary parts. While it is possible to run the code for moderate or large
|
a
|
,
|
b
|
, and
|
c
|
and obtain satisfactory results for some specified values, the code is very likely to be unstable in this regime.
Unusual features: Two different codes, one for the hypergeometric function and one for the Pöschl–Teller–Ginocchio potential wave functions, are provided in C++ and Fortran 90 versions.
Running time: 20,000
F
1
2
function evaluations take an average of one second.
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We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed ...harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite temperature formalism for the HFB and HF+BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected.
Full text
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
We overview the methodology behind the large-scale mass table calculations based on the nuclear density functional theory (DFT) with Skyrme energy density functionals (EDFs). The calculations ...employing massively parallel computers are done in a large configuration space of an axially deformed harmonic oscillator. Nuclear mass tables tabulating global nuclear properties such as binding energies, radii, shape deformations, and pairing gaps are obtained for several Skyrme EDFs augmented by a mixed-type pairing functional, using an approximate particle number projection before variation. Specialty visualization tools have been developed to analyze the results. As an illustrative example of our current capabilities, we show some results for a wide range of even-even nuclei with Z ≤ 120 and N ≤ 300.
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