doc. Ing. Daniel Langr, Ph.D.

Publikace

Ab initio translationally invariant nucleon-nucleus optical potentials

Autoři
Burrows, M.; Launey, K.D.; Mercenne, A.; Baker, R.B.; Sargsyan, G.H.; Dytrych, T.; Langr, D.
Rok
2024
Publikováno
PHYSICAL REVIEW C. 2024, 109 ISSN 2469-9985.
Typ
Článek
Anotace
We combine the ab initio symmetry-adapted no-core shell model (SA-NCSM) with the single-particle Green's function approach to construct optical potentials rooted in first principles. Specifically, we show that total cross sections and phase shifts for neutron elastic scattering from a 4He target with projectile energies between 0.5 and 10 MeV closely reproduce the experiment. In addition, we discuss an important new development that resolves a long-standing issue with spurious center-of-mass motion in the Green's function formalism for many-body approaches. The new development opens a path for first-principle predictions of cross sections for elastic scattering of single-nucleon projectiles, nucleon capture, and deuteron breakup reactions, feasible for a broad range of open-shell spherical and deformed nuclei in the SA-NCSM approach.

Coupling and recoupling coefficients for Wigner’s U(4) supermultiplet symmetry

Autoři
Dang, P.; Draayer, J.P.; Fen, P.; Dytrych, T.; Langr, D.; Kekejian, D.; Becker, K.S.; Thompson, N.
Rok
2024
Publikováno
The European Physical Journal Plus. 2024, 139 1-21. ISSN 2190-5444.
Typ
Článek
Anotace
A novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group—subgroup chains is presented. The canonical U(4) ⊃ U(3) ⊃ U(2) ⊃ U(1)coupling and recoupling coefficients are applicable to any system that possesses U(4) symmetry, while the physical U(4) ⊃ SUS(2)⊗SUT(2) coupling coefficients are more specific to nuclear structure studies that utilize Wigner’s supermultiplet symmetry concept. The procedure that is proposed sidesteps the use of binomial coefficients and alternating sum series and consequently enables fast and accurate computation of any and all U(4)-underpinned features. The inner multiplicity of a (S, T) pair within a single U(4) irreducible representation is obtained from the dimension of the null space of the SU(2) raising generators, while the resolution for the outer multiplicity follows from the work of Alex et al. on U(N). It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(4).

Parallel multithreaded deduplication of data sequences in nuclear structure calculations

Autoři
Langr, D.; Dytrych, T.
Rok
2024
Publikováno
International Journal of High Performance Computing Applications. 2024, 38(1), 5-16. ISSN 1094-3420.
Typ
Článek
Anotace
High performance computing (HPC) applications that work with redundant sequences of data can benefit from their deduplication. We study this problem on the symmetry-adapted no-core shell model (SA-NCSM), where redundant sequences of different kinds naturally emerge in the data of the basis of the Hilbert space physically relevant to a modeled nucleus. For a fast solution of this problem on multicore architectures, we propose and present three multithreaded algorithms, which employ either concurrent hash tables or parallel sorting methods. Furthermore, we present evaluation and comparison of these algorithms based on experiments performed with real-world SA-NCSM calculations. The results indicate that the fastest option is to use a concurrent hash table, provided that it supports sequences of data as a type of table keys. If such a hash table is not available, the algorithm based on parallel sorting is a viable alternative.

Uncertainty quantification of collective nuclear observables from the chiral potential parametrization

Autoři
Becker, K.S.; Launey, K.D.; Ekström, A.; Dytrych, T.; Langr, D.; Sargsyan, G.H.; Draayer, J.P.
Rok
2024
Publikováno
Physica Scripta. 2024, 99(12), 1-13. ISSN 0031-8949.
Typ
Článek
Anotace
We perform an uncertainty estimate of quadrupole moments and B(E2) transition rates that inform nuclear collectivity. In particular, we study the low-lying states of 6Li and 12C using the ab initio symmetry-adapted no-core shell model. For a narrow standard deviation of approximately 1% on the low-energy constants which parametrize high-precision chiral potentials, we find output standard deviations in the collective observables ranging from approximately 3-6%. The results mark the first step towards a rigorous uncertainty quantification of collectivity in nuclei that aims to account for all sources of uncertainty in ab initio descriptions of challenging collective and clustering observables.

Parallel Identification of Unique Sequences in Nuclear Structure Calculations

Autoři
Langr, D.; Dytrych, T.
Rok
2023
Publikováno
Parallel Processing and Applied Mathematics Part II. Springer, Cham, 2023. p. 357-369. Lecture Notes in Computer Science. vol. 13827. ISSN 0302-9743. ISBN 978-3-031-30444-6.
Typ
Stať ve sborníku
Anotace
Reducing the set of sequences into the set of sequences that are unique can save a lot of memory space in computer programs. We study this problem on the symmetry-adapted no-core shell model (SA-NCSM) nuclear structure calculations, where duplicated sequences of different kinds naturally emerge in the data of the basis of the Hilbert space physically relevant to a given nucleus. For a fast solution of this problem on multicore architectures, we propose and present a multithreaded algorithm suitable for high performance computing (HPC) environments. Furthermore, we provide an experimental evaluation of this algorithm and show that, in practice, it can significantly reduce the time required to identify unique sequences in a real-world application.

Ab initio View of Emergent Symplectic Symmetry and Its Crutial Role in Nuclear Dynamics

Autoři
Dytrych, T.; Launey, K.D.; Draayer, J.P.; Langr, D.
Rok
2022
Publikováno
Bulgarian Journal of Physics. 2022, 49(1), 37-46. ISSN 1310-0157.
Typ
Článek
Anotace
Results of large-scale first principle nuclear structure studies using the symmetry-adapted no-core shell model are reported. It is shown that nuclei up through the intermediate-mass region display highly regular and ubiquitous patterns of dominant nuclear shapes that vibrate and rotate. This emergent structure is tied to an approximate symplectic Sp (3, R) symmetry, and it is shown to determine dominant features of low-lying states, even in close-to-spherical nuclear states without any recognizable rotational properties.

CPP11sort: A parallel quicksort based on C++ threading

Autoři
Langr, D.; Schovánková, K.
Rok
2022
Publikováno
Concurrency and Computation: Practice and Experience. 2022, 34(4), 1-11. ISSN 1532-0626.
Typ
Článek
Anotace
A new efficient implementation of the multi-threaded quicksort algorithm called CPP11sort is presented. This implementation is built exclusively upon the threading primitives of the C++ programming language itself. The performance of CPP11sort is evaluated and compared with its mainstream competitors provided by GNU, Intel, and Microsoft. It is shown that out of the considered implementations, CPP11sort mostly yields the shortest sorting times and is the only one that is portable to any conforming C++ implementation without a need of external libraries or non-standard compiler extensions. The experimental evaluation with various input data distributions resulted in parallel speedup between 16.1 and 44.2 on a 56-core server and between 6.8 and 14.5 on a 10-core workstation with enabled hyper-threading.

Efficacy of the symmetry-adapted basis for ab initio nucleon-nucleus interactions for light- and intermediate-mass nuclei

Autoři
Mercenne, A.; Launey, K.D.; Dytrych, T.; Escher, J.E.; Quaglioni, S.; Sargsyan, G.H.; Langr, D.; Draayer, J.P.
Rok
2022
Publikováno
Computer Physics Communications. 2022, 280 1-11. ISSN 0010-4655.
Typ
Článek
Anotace
We study the efficacy of a new ab initio framework that combines the symmetry-adapted (SA) no-core shell-model approach with the resonating group method (RGM) for unified descriptions of nuclear structure and reactions. We obtain ab initio neutron-nucleus interactions for 4He, 16O, and 20Ne targets, starting with realistic nucleon-nucleon potentials. We discuss the effect of increasing model space sizes and symmetry-based selections on the SA-RGM norm and direct potential kernels, as well as on phase shifts, which are the input to calculations of cross sections. We demonstrate the efficacy of the SA basis and its scalability with particle numbers and model space dimensions, with a view toward ab initio descriptions of nucleon scattering and capture reactions up through the medium-mass region.

Impact of Clustering on the 8Li β Decay and Recoil Form Factors

Autoři
Sargsyan, G.H.; Launey, K.D.; Burkey, M.T.; Gallant, A.T.; Scielzo, N.D.; Savard, G.; Mercenne, A.; Dytrych, T.; Langr, D.; Varriano, L.; Longfellow, B.; Hirsh, T.Y.; Draayer, J.P.
Rok
2022
Publikováno
Physical Review Letters. 2022, 128 202503-1-202503-7. ISSN 0031-9007.
Typ
Článek
Anotace
We place unprecedented constraints on recoil corrections in the β decay of 8Li, by identifying a strong correlation between them and the 8Li ground state quadrupole moment in large-scale ab initio calculations. The results are essential for improving the sensitivity of high-precision experiments that probe the weak interaction theory and test physics beyond the standard model. In addition, our calculations predict a 2+ state of the α+α system that is energetically accessible to β decay but has not been observed in the experimental 8Be energy spectrum, and has an important effect on the recoil corrections and β decay for the A=8 systems. This state and an associated 0+ state are notoriously difficult to model due to their cluster structure and collective correlations, but become feasible for calculations in the ab initio symmetry-adapted no-core shell-model framework.

SU3lib: A C++ library for accurate computation of Wigner and Racah coefficients of SU(3)

Autoři
Dytrych, T.; Langr, D.; Draayer, J.P.; Launey, K.D.; Gazda, D.
Rok
2021
Publikováno
Computer Physics Communications. 2021, 269 1-6. ISSN 0010-4655.
Typ
Článek
Anotace
We present the C++ library SU3lib for accurate computation of SU(3) Wigner coupling and Racah recoupling coefficients. It is built on the efficient mathematical algorithm originally proposed by Draayer and Akiyama [1]. The presented library extends the reach of this algorithm towards large SU(3) irreducible representations and outer multiplicities that were heretofore inaccessible due to floating-point precision errors. As large irreducible representations of SU(3) play an important role in medium- and heavy-mass atomic nuclei, SU3lib expands the scope of approaches to nuclear structure and reactions that rely on available SU(3) coupling-recoupling coefficients.

Transformation of a nucleon-nucleon potential operator into its SU(3) tensor form using GPUs

Autoři
Oberhuber, T.; Langr, D.; Dytrych, T.; Draayer, J.P.; Launey, K.D.
Rok
2021
Publikováno
Discrete and Continuous Dynamical Systems. Series S. 2021, 14(3), 1111-1122. ISSN 1937-1632.
Typ
Článek
Anotace
Starting from the matrix elements of a nucleon-nucleon potential operator provided in a basis of spherical harmonic oscillator functions, we present an algorithm for expressing a given potential operator in terms of irreducible tensors of the SU(3) and SU(2) groups. Further, we introduce a GPU-based implementation of the latter and investigate its performance compared with a CPU-based version of the same. We find that the CUDA implementation delivers speedups of 2.27x – 5.93x.

Physics of nuclei: Key role of an emergent symmetry

Autoři
Dytrych, T.; Launey, K.D.; Draayer, J.P.; Rowe, D.; Wood, J.; Rosensteel, G.; Bahri, C.; Langr, D.; Baker, R.B.
Rok
2020
Publikováno
Physical Review Letters. 2020, 124(4), ISSN 0031-9007.
Typ
Článek
Anotace
We show through first-principle nuclear structure calculations that the special nature of the strong nuclear force determines highly regular patterns heretofore unrecognized in nuclei that can be tied to an emergent approximate symmetry. This symmetry is remarkably ubiquitous and mathematically tracks with a symplectic symmetry group. This, in turn, has important implications for understanding the physics of nuclei: we find that nuclei are made of only a few equilibrium shapes, deformed or not, with associated vibrations and rotations. It also opens the path for ab initio large-scale modeling of open-shell intermediate-mass nuclei without the need for renormalized interactions and effective charges.

Reducing the Impact of Intensive Dynamic Memory Allocations in Parallel Multi-Threaded Programs

Autoři
Langr, D.; Kočička, M.
Rok
2020
Publikováno
IEEE Transactions on Parallel and Distributed Systems. 2020, 31(5), 1152-1164. ISSN 1045-9219.
Typ
Článek
Anotace
Frequent dynamic memory allocations (DyMAs) can significantly hinder the scalability of parallel multi-threaded programs. As the number of threads grows, DyMAs can even become the main performance bottleneck. We introduce modern tools and methods for evaluating the impact of DyMAs and present techniques for its reduction, which include scalable heap implementations, small buffer optimization, and memory pooling. Additionally, we provide a survey of state-of-the-art implementations of these techniques and study them experimentally by using a benchmark program, server simulator software, and a real-world high-performance computing application. As a result, we show that relatively small modifications in parallel program’s source code or a way of its execution may substantially reduce the runtime overhead associated with the use of dynamic data structures.

Space-Efficient k-d Tree-Based Storage Format for Sparse Tensors

Autoři
Rok
2020
Publikováno
Proceedings of the 29th International Symposium on High-Performance Parallel and Distributed Computing. New York: Association for Computing Machinery, 2020. p. 29-33. HPDC ’20. ISBN 978-1-4503-7052-3.
Typ
Stať ve sborníku
Anotace
Computations with tensors are widespread in many scientific areas. Usually, the used tensors are very large but sparse, i.e., the vast majority of their elements are zero. The space complexity of sparse tensor storage formats varies significantly. For overall efficiency, it is important to reduce the execution time and additional space requirements of the initial preprocessing (i.e., converting tensors from common storage formats to the given internal format). The main contributions of this paper are threefold. Firstly, we present a new storage format for sparse tensors, which we call the succinct k-d tree-based tensor (SKTB) format. We compare the space complexity of common tensor storage formats and of the SKTB format and demonstrate the viability of using a tree as a data structurefor sparse tensors. Secondly, we present a parallel space-efficient algorithm for converting tensors to the SKTB format. Thirdly, we demonstrate the computational efficiency of the proposed format in sparse tensor-vector multiplication.

Accelerating Many-Nucleon Basis Generation for High Performance Computing Enabled Ab Initio Nuclear Structure Studies

Autoři
Langr, D.; Dytrych, T.; Launey, K.D.; Draayer, J.P.
Rok
2019
Publikováno
International Journal of High Performance Computing Applications. 2019, 33(3), 522-533. ISSN 1094-3420.
Typ
Článek
Anotace
We present the problem of generating a many-nucleon basis in SU(3)-scheme for ab initio nuclear structure calculations in a symmetry-adapted no-core shell model (SA-NCSM) framework. We first discuss and analyze the basis construction algorithm whose baseline implementation quickly becomes a significant bottleneck for large model spaces and heavier nuclei. The outcomes of this analysis are utilized to propose a new scalable version of the algorithm. Its performance is consequently studied empirically using the Blue Waters supercomputer. The measurements show significant acceleration achieved with over two orders of magnitude speedups realized for larger model spaces.

Efficient Algorithm for Representations of U(3) in U(N)

Autoři
Langr, D.; Dytrych, T.; Draayer, J.P.; Launey, K.D.; Tvrdík, P.
Rok
2019
Publikováno
Computer Physics Communications. 2019, 244 442-447. ISSN 0010-4655.
Typ
Článek
Anotace
An efficient algorithm for enumerating representations of U(3) that occur in a representation of the unitary group U(N) is introduced. The algorithm is applicable to U(N) representations associated with a system of identical fermions (protons, neutrons, electrons, etc.) distributed among the N=(eta+1)(eta+2)/2 degenerate eigenstates of the etath level of the three-dimensional harmonic oscillator. A C++ implementation of the algorithm is provided and its performance evaluated. The implementation can employ OpenMP threading for use in parallel applications.

Importance Basis Truncation in the Symmetry-adapted No-core Shell Model

Autoři
Knapp, F.; Dytrych, T.; Langr, D.; Oberhuber, T.
Rok
2019
Publikováno
Acta Physica Polonica B. 2019, 50(3), 541-547. ISSN 0587-4254.
Typ
Článek
Anotace
We apply the importance-truncation procedure in the framework of the ab initio symmetry-adapted no-core shell model. We study efficacy of this new method for the description of energies and E2 transitions of the ground-state rotational band in 12C. We demonstrate that the coupling SU(3)-scheme basis with the perturbative relevance estimate leads to a dramatic reduction in dimensionality of the nuclear eigenvalue problem.

Analysis of Memory Footprints of Sparse Matrices Partitioned Into Uniformly-Sized Blocks

Rok
2018
Publikováno
Scalable Computing: Practice and Experience. 2018, 19(3), 275-291. ISSN 1895-1767.
Typ
Článek
Anotace
The presented study analyses memory footprints of 563 representative benchmark sparse matrices with respect to their partitioning into uniformly-sized blocks. Different block sizes and different ways of storing blocks in memory are considered and statistically evaluated. Memory footprints of partitioned matrices are then compared with their lower bounds and CSR, index-compressed CSR, and EBF storage formats. The results show that block-based storage formats may significantly reduce memory footprints of sparse matrices arising from a wide range of application domains. Additionally, measured consistency of results is presented and discussed, benefits of individual formats for storing blocks are evaluated, and an analysis of best-case and worst-case matrices is provided for in-depth understanding of causes of memory savings of block-based formats.

Efficient Parallel Generation of Many-Nucleon Basis for Large-Scale Ab Initio Nuclear Structure Calculations

Autoři
Langr, D.; Dytrych, T.; Oberhuber, T.; Knapp, F.
Rok
2018
Publikováno
Parallel Processing and Applied Mathematics Part II.. Cham: Springer International Publishing AG, 2018. p. 341-350. Lecture Notes in Computer Science. vol. 10778. ISSN 0302-9743. ISBN 978-3-319-78053-5.
Typ
Stať ve sborníku
Anotace
We address the problem of generating a many-nucleon basis for ab initio nuclear structure modeling, which quickly becomes a significant runtime bottleneck for large model spaces. We first analyze the original basis generation algorithm, which does not employ multi-threading parallel paradigm. Based on the analysis, we propose and empirically evaluate a new efficient scalable basis generation algorithm. We report a reduction of basis generation runtime by a factor of 42 on the Blue Waters supercomputer and by two orders of magnitude on our test-bed computer system with Broadwell CPUs.

Importance Truncation in the SU(3) Symmetry-adapted No-core Shell Model

Autoři
Knapp, F.; Dytrych, T.; Langr, D.; Oberhuber, T.
Rok
2018
Publikováno
Proceedings of the XXIV Nuclear Physics Workshop. Kraków: Jagiellonian University, 2018. p. 65-72. Acta Physica Polonica B Proceedings Supplement. vol. 11. ISSN 1899-2358.
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Stať ve sborníku
Anotace
We apply, for the first time, the importance-truncation (IT) procedure based on the many-body perturbation theory for the multi-shell SU(3) scheme basis of the ab initio symmetry-adapted no-core shell model (SA-NCSM). It is shown that the IT method can yield a quantitative justification for the symmetry-based truncation of the SA-NCSM approach. Furthermore, we demonstrate that the IT algorithm can be applied in a symmetry-truncated model space and it leads to even more dramatic reduction in dimensionality of the nuclear eigenvalue problem.

Multilayer Approach for Joint Direct and Transposed Sparse Matrix Vector Multiplication for Multithreaded CPUs

Autoři
Šimeček, I.; Langr, D.; Kotenkov, I.
Rok
2018
Publikováno
Parallel Processing and Applied Mathematics Part I.. Cham: Springer International Publishing AG, 2018. p. 47-56. Lecture Notes in Computer Science. vol. 10777. ISSN 0302-9743. ISBN 978-3-319-78023-8.
Typ
Stať ve sborníku
Anotace
One of the most common operations executed on modern high-perfor\-mance computing systems is multiplication of a sparse matrix by a dense vector within a shared-memory computational node. Strongly related but far less studied problem is joint direct and transposed sparse matrix-vector multiplication, which is widely needed by certain types of iterative solvers. We propose a multilayer approach for joint sparse multiplication that balances the workload of threads. Measurements prove that our algorithm is scalable and achieve high computational performance for multiple benchmark matrices that arise from various scientific and engineering disciplines.

On Memory Footprints of Partitioned Sparse Matrices

Rok
2017
Publikováno
Proceedings of the 2017 Federated Conference on Computer Science and Information Systems. Katowice: Polish Information Processing Society, 2017. p. 513-521. Annals of Computer Science and Information Systems. vol. 11. ISSN 2300-5963. ISBN 978-83-946253-7-5.
Typ
Stať ve sborníku
Anotace
The presented study analyses 563 representative benchmark sparse matrices with respect to their partitioning into uniformly-sized blocks. The aim is to minimize memory footprints of matrices. Different block sizes and different ways of storing blocks in memory are considered and statistically evaluated. Memory footprints of partitioned matrices are additionally compared with lower bounds and the CSR storage format. The average measured memory savings against CSR in case of single and double precision are 42.3 and 28.7 percents, respectively. The corresponding worst-case savings are 25.5 and 17.1 percents. Moreover, memory footprints of partitioned matrices were in average 5 times closer to their lower bounds than CSR. Based on the obtained results, we provide generic suggestions for efficient partitioning and storage of sparse matrices in a computer memory.

AQsort: Scalable Multi-Array In-Place Sorting with OpenMP

Rok
2016
Publikováno
Scalable Computing: Practice and Experience. 2016, 17(4), 369-391. ISSN 1895-1767.
Typ
Článek
Anotace
A new multi-threaded variant of the quicksort algorithm called AQsort and its C++/OpenMP implementation are presented. AQsort operates in place and was primarily designed for high-performance computing (HPC) runtime environments. It can work with multiple arrays at once; such a functionality is frequently required in HPC and cannot be accomplished with standard C pointer-based or C++ iterator-based approach. An extensive study is provided that evaluates AQsort experimentally and compares its performance with modern multi-threaded implementations of in-place and out-of-place sorting algorithms based on OpenMP, Cilk Plus, and Intel TBB. The measurements were conducted on several leading-edge HPC architectures, namely Cray XE6 nodes with AMD Bulldozer CPUs, Cray XC40 nodes with Intel Hasswell CPUs, IBM BlueGene/Q nodes, and Intel Xeon Phi coprocessors. The obtained results show that AQsort provides good scalability and sorting performance generally comparable to its competitors. In particular cases, the performance of AQsort may be slightly lower, which is the price for its universality and ability to work with substantially larger amounts of data.

Block Iterators for Sparse Matrices

Autoři
Langr, D.; Šimeček, I.; Tomáš Dytrych, T.D.
Rok
2016
Publikováno
Proceedings of the 2016 Federated Conference on Computer Science and Information Systems. New York: Institute of Electrical and Electronics Engineers, 2016. pp. 695-704. ISBN 978-83-60810-90-3.
Typ
Stať ve sborníku
Anotace
Finding an optimal block size for a given sparse matrix forms an important problem for storage formats that partition matrices into uniformly-sized blocks. Finding a solution to this problem can take a significant amount of time, which, effectively, may negate the benefits that such a format brings into sparse-matrix computations. A key for an efficient solution is the ability to quickly iterate, for a particular block size, over matrix nonzero blocks. This work proposes an efficient parallel algorithm for this task and evaluate it experimentally on modern multi-core and many-core high performance computing (HPC) architectures.

Efficacy of the SU(3) scheme for ab initio large-scale calculations beyond the lightest nuclei

Autoři
Dytrych, T.; Maris, P.; Launey, K.D.; Draayer, J.P.; Vary, J.P.; Langr, D.; Saule, E.; Caprio, M.A.; Catalyurek, U.; Sosonkina, M.
Rok
2016
Publikováno
Computer Physics Communications. 2016, 207 202-210. ISSN 0010-4655.
Typ
Článek
Anotace
We report on the computational characteristics of ab initio nuclear structure calculations in a symmetry-adapted no-core shell model (SA-NCSM) framework. We examine the computational complexity of the current implementation of the SA-NCSM approach, dubbed LSU3shell, by analyzing ab initio results for 6Li and 12C in large harmonic oscillator model spaces and SU3-selected subspaces. We demonstrate LSU3shell’s strong-scaling properties achieved with highly-parallel methods for computing the many-body matrix elements. Results compare favorably with complete model space calculations and significant memory savings are achieved in physically important applications. In particular, a well-chosen symmetry-adapted basis affords memory savings in calculations of states with a fixed total angular momentum in large model spaces while exactly preserving translational invariance.

Efficient parallel evaluation of block properties of sparse matrices

Rok
2016
Publikováno
Proceedings of the 2016 Federated Conference on Computer Science and Information Systems. New York: Institute of Electrical and Electronics Engineers, 2016. pp. 709-716. ISBN 978-83-60810-90-3.
Typ
Stať ve sborníku
Anotace
Many storage formats for sparse matrices have been developed. Majority of these formats can be parametrized, so the algorithm for finding optimal parameters is crucial. For overall efficiency, it is important to reduce the execution time of this preprocessing. In this paper, we propose a new algorithm for the determination of the number of nonzero blocks of the given size in a sparse matrix. The proposed algorithm requires relatively a small amount of auxiliary memory. Our approach is based on the Morton reordering and bitwise manipulations. We also present a parallel (multithreaded) version and evaluate its performance and space complexity.

Evaluation Criteria for Sparse Matrix Storage Formats

Rok
2016
Publikováno
IEEE Transactions on Parallel and Distributed Systems. 2016, 27(2), 428-440. ISSN 1045-9219.
Typ
Článek
Anotace
When authors present new storage formats for sparse matrices, they usually focus mainly on a single evaluation criterion, which is the performance of sparse matrix-vector multiplication (SpMV) in FLOPS. Though such an evaluation is essential, it does not allow to directly compare the presented format with its competitors. Moreover, in case that matrices are within an HPC application constructed in different formats, this criterion alone is not sufficient for the key decision whether or not to convert them into the presented format for the SpMV-based application phase. We establish ten evaluation criteria for sparse matrix storage formats, discuss their advantages and disadvantages, and provide general suggestions for format authors/evaluators to make their work more valuable for the HPC community.

Parallel solver of large systems of linear inequalities using Fourier--Motzkin elimination

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Rok
2016
Publikováno
Computing and Informatics. 2016, 35(6), 1307-1337. ISSN 1335-9150.
Typ
Článek
Anotace
Fourier-Motzkin elimination is a computationally expensive but powerful method to solve a system of linear inequalities. These systems arise e.g. in execution order analysis for loop nests or in integer linear programming. This paper focuses on the analysis, design and implementation of a~parallel solver for distributed memory for large systems of linear inequalities using the Fourier--Motzkin elimination algorithm. We also measure the speedup of parallel solver and prove that this implementation results in good scalability.

Space and execution efficient formats for modern processor architectures

Rok
2016
Publikováno
17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. Los Alamitos: IEEE Computer Society, 2016. pp. 98-105. ISBN 978-1-5090-0461-4.
Typ
Stať ve sborníku
Anotace
Sparse matrix-vector multiplication (shortly SpMV) and transposed SpMV (shortly SpMTV) are the most common routines in the numerical algebra. Sparse storage formats describe a way how sparse matrices are stored in a computer memory. Since the commonly used storage formats (like COO or CSR) are not sufficient for high-performance computations, extensive research has been conducted about maximal computational efficiency of these routines. For modern CPU architectures, the main bottleneck of these routines is the limited memory bandwidth. In this paper, we introduce a new approach for these routines for modern processor architectures using a space efficient hierarchical format, which can significantly reduce the amount of transferred data from memory for almost all types of matrices arising from various application disciplines. This format represents a trade-off between space and execution efficiency. The performance of these routines with this format seems to be very close to the hardware limits.

A new parallel and GPU version of a TREOR-based algorithm for indexing powder diffraction data

Autoři
Šimeček, I.; Zahradnický, T.; Langr, D.; Rohlíček, J.
Rok
2015
Publikováno
Journal of Applied Crystallography. 2015, 48(1), 166-170. ISSN 0021-8898.
Typ
Článek
Anotace
One of the key parts of the crystal structure solution process from powder diffraction data is indexing - the determination of the lattice parameters from experimental data. This paper presents a modification of the TREOR indexing method that makes the algorithm suitable and efficient for execution on graphics processing units. The TREOR algorithm was implemented in its pure form, which can be simply described as a `brute-force' approach. The effectiveness and time consumption of such an algorithm was tested on several data sets including monoclinic and triclinic examples. The results show the potential of using GPUs for indexing powder diffraction data.

Dominant Modes in Light Nuclei - Ab Initio View of Emergent Symmetries

Autoři
Draayer, J.P.; Dytrych, T.; Launey, K.D.; Dreyfuss, A.C.; Langr, D.
Rok
2015
Publikováno
XXXVII Symposium on Nuclear Physics. Bristol: IOP Publishing Ltd, 2015. pp. 1-10. Journal of Physics: Conference Series. ISSN 1742-6588.
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Stať ve sborníku
Anotace
An innovative symmetry-guided concept is discussed with a focus on emergent symmetry patterns in complex nuclei. In particular, the ab initio symmetry-adapted no-core shell model (SA-NCSM), which capitalizes on exact as well as partial symmetries that underpin the structure of nuclei, provides remarkable insight into how simple symmetry patterns emerge in the many-body nuclear dynamics from first principles. This ab initio view is complemented by a fully microscopic no-core symplectic shell-model framework (NCSpM), which, in turn, informs key features of the primary physics responsible for the emergent phenomena of large deformation and alpha-cluster substructures in studies of the challenging Hoyle state in Carbon-12 and enhanced collectivity in intermediate-mass nuclei. Furthermore, by recognizing that deformed configurations often dominate the low-energy regime, the SA-NCSM provides a strategy for determining the nature of bound states of nuclei in terms of a relatively small subspace of the symmetry-reorganized complete model space, which opens new domains of nuclei for ab initio investigations, namely, the intermediate-mass region, including isotopes of Ne, Mg, and Si.

Efficient Converting of Large Sparse Matrices to Quadtree Format

Rok
2015
Publikováno
16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. Los Alamitos: IEEE Computer Society, 2015. pp. 122-129. ISBN 978-1-4799-8448-0.
Typ
Stať ve sborníku
Anotace
Computations with sparse matrices are widespread in scientific projects. Used data format affects strongly the performance and also the space-efficiency. Commonly used storage formats (such as COO or CSR) are not suitable neither for some numerical algebra operations (e.g., The sparse matrix-vector multiplication) due to the required indirect addressing nor for I/O file operations with sparse matrices due to their high space complexities. In our previous papers, we prove that the idea of using the quad tree for these purposes is viable. In this paper, we present a completely new algorithm based on bottom-up approach for the converting matrices from common storage formats to the quad tree format. We derive the asymptotic complexity of our new algorithm, design the parallel variant of the classical and the new algorithm, and discuss their performance.

Electron-scattering form factors for 6Li in the ab initio symmetry-guided framework

Autoři
Dytrych, T.; Hayes, A.C.; Launey, K.D.; Draayer, J.P.; Maris, P.; Vary, J.P.; Langr, D.; Oberhuber, T.
Rok
2015
Publikováno
PHYSICAL REVIEW C. 2015, 91(2), ISSN 2469-9985.
Typ
Článek
Anotace
We present an ab initio symmetry-adapted no-core shell-model description for 6Li. We study the structure of the ground state of 6Li and the impact of the symmetry-guided space selection on the charge density components for this state in momentum space, including the effect of higher shells. We accomplish this by investigating the electron scattering charge form factor for momentum transfers up to q ~ 4 fm^-1. We demonstrate that this symmetry-adapted framework can achieve significantly reduced dimensions for equivalent large shell-model spaces while retaining the accuracy of the form factor for any momentum transfer. These new results confirm the previous outcomes for selected spectroscopy observables in light nuclei, such as binding energies, excitation energies, electromagnetic moments, E2 and M1 reduced transition probabilities, as well as point-nucleon matter rms radii.

Emergence of Simple Patterns in Complex Atomic Nuclei from First Principles

Autoři
Dytrych, T.; Launey, K.D.; Draayer, J.P.; Maris, P.; Vary, J.P.; Langr, D.; Oberhuber, T.
Rok
2015
Publikováno
Proceedings of the 38th Symposium on Nuclear Physics. London: IOP Publishing, 2015. pp. 1-11. Journal of Physics: Conference Series. ISSN 1742-6588.
Typ
Stať ve sborníku
Anotace
We study the structure of low-lying states in 6Li, 6He, 8Be, 8B, 12C, and 16O, using ab initio symmetry-adapted no-core shell model. The results of our study demonstrate that collective modes in light nuclei emerge from first principles. We investigate the impact of the symmetry-adapted model space on spectroscopic properties and, in the case of the ground state of 6Li, on elastic electron scattering charge form factor. The results confirm that only a small symmetry-adapted subspace of the complete model space is needed to accurately reproduce complete-space observables and the form factor momentum dependence.

HPC-enabled Nuclear Structure Studies - Description and Applications of the Symmetry-adapted No-Core Shell Model

Autoři
Draayer, J.P.; Dytrych, T.; Launey, K.D.; Dreyfuss, A.C.; Langr, D.
Rok
2015
Publikováno
11th International Spring Seminar on Nuclear Physics: Shell Model and Nuclear Structure. London: IOP Publishing, 2015. pp. 1-7. Journal of Physics: Conference Series. ISSN 1742-6588.
Typ
Stať ve sborníku
Anotace
By exploiting symmetries that enable the accounting of vital collective correlations in nuclei, we achieve significantly reduced dimensions for equivalent ultra-large model spaces, and hence resolve the scale explosion problem in nuclear structure calculations, i.e, the explosive growth in computational resource demands with increasing number of particles and size of the spaces in which they reside. As a result, we provide - with the help of High Performance Computing (HPC) resources - first solutions for selected benchmark calculations with remarkable findings of large-deformation and low-spin dominance in low-lying nuclear states. In the framework of a complementary symmetry-adapted study, one is able, facilitated by symmetry-preserving pieces of the inter-nucleon interaction, to accommodate unprecedented shell-model spaces critical to capture the physics governing the Hoyle state in 12C, thereby addressing a 60-year-old puzzle on the emergence of cluster substructures within a no-core shell model framework. All of these findings underline the key role of symmetries in nuclear structure studies

Algorithm 947: Paraperm: Parallel Generation of Random Permutations with MPI

Autoři
Langr, D.; Tvrdík, P.; Dytrych, T.D.; Draayer, J.P.
Rok
2014
Publikováno
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE. 2014, 41(1), 1-26. ISSN 0098-3500.
Typ
Článek
Anotace
An algorithm for parallel generation of a random permutation of a large set of distinct integers is presented. This algorithm is designed for massively parallel systems with distributed memory architectures and the MPI-based runtime environments. Scalability of the algorithm is analyzed according to the memory and communication requirements. An implementation of the algorithm in a form of a software library based on the C++ programming language and the MPI application programming interface is further provided. Finally, performed experiments are described and their results discussed. The biggest of these experiments resulted in a generation of a random permutation of 2^41 integers in slightly more than four minutes using 131072 CPU cores.

Parallel Data Acquisition for Visualization of Very Large Sparse Matrices

Autoři
Rok
2014
Publikováno
15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. Los Alamitos: IEEE Computer Society, 2014. pp. 336-343. ISBN 978-1-4799-3035-7.
Typ
Stať ve sborníku
Anotace
The problem of visualization of very large sparse matrices emerging on massively parallel computer systems is identified and a new method along with an accompanying algorithm for parallel acquisition of visualization data for such matrices are presented. The proposed method is based on downsampling a matrix into blocks for which the desired visualization data are saved into a file. This file is then supposed to be downloaded and processed into a final image on a personal computer. Experimental results for the evaluation of the performance and scalability of the proposed algorithm are further provided and discussed.

Space Efficient Formats for Structure of Sparse Matrices Based on Tree Structures

Rok
2014
Publikováno
15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. Los Alamitos: IEEE Computer Society, 2014. pp. 344-351. ISBN 978-1-4799-3035-7.
Typ
Stať ve sborníku
Anotace
Very large sparse matrices are often processed on massively parallel computer systems with distributed memory architectures consisting of tens or hundreds of thousands of processor cores. The problem occurs when we want or need to load/store these matrices from/to a distributed file system. This paper deals with the design of new formats for storing very large sparse matrices suitable for parallel I/O systems. The first one is based on arithmetic coding and the second one is based on binary tree format. We compare the space complexity of common storage formats and our new formats and prove that the latter are considerably more space efficient.

The study of impact of matrix-processor mapping on the parallel sparse matrix-vector multiplication

Autoři
Šimeček, I.; Langr, D.; Srnec, E.
Rok
2014
Publikováno
15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. Los Alamitos: IEEE Computer Society, 2014. pp. 321-328. ISBN 978-1-4799-3035-7.
Typ
Stať ve sborníku
Anotace
Sparse matrix-vector multiplication (shortly spMV) is one of the most common subroutines in the numerical linear algebra. The parallelization of this task looks easy and straightforward, but it is not optimal in general case. This paper discuss some matrix-processor mappings and their impact on parallel spMV execution on massively parallel systems. We try to balance the performance and the overhead of the required transformation. We also present algorithms for redistribution. We propose four quality measures and derive lower and upper bound for different mappings. Our $spMV$ algorithms are scalable for almost all matrices arising from various technical areas.

Tree-based Space Efficient Formats for Storing the Structure of Sparse Matrices

Rok
2014
Publikováno
Scalable Computing: Practice and Experience. 2014, 15(1), 1-20. ISSN 1895-1767.
Typ
Článek
Anotace
Sparse storage formats describe a way how sparse matrices are stored in a computer memory. Extensive research has been conducted about these formats in the context of performance optimization of the sparse matrix-vector multiplication algorithms, but memory efficient formats for storing sparse matrices are still under development, since the commonly used storage formats (like COO or CSR) are not sufficient. In this paper, we propose and evaluate new storage formats for sparse matrices that minimize the space complexity of information about matrix structure. The first one is based on arithmetic coding and the second one is based on binary tree format. We compare the space complexity of common storage formats and our new formats and prove that the latter are considerably more space efficient.

Collective Modes in Light Nuclei from First Principles

Autoři
Dytrych, T.; Launey, K.D.; Draayer, J.P.; Maris, P.; Vary, J.P.; Saule, E.; Catalyurek, U.; Sosonkina, M.; Langr, D.; Caprio, M.A.
Rok
2013
Publikováno
Physical Review Letters. 2013, 111(25), 2525010-1-252501-5. ISSN 0031-9007.
Typ
Článek
Anotace
Results for ab initio no-core shell model calculations in a symmetry-adapted SU(3)-based coupling scheme demonstrate that collective modes in light nuclei emerge from first principles. The low-lying states of Li6, Be8, and He6 are shown to exhibit orderly patterns that favor spatial configurations with strong quadrupole deformation and complementary low intrinsic spin values, a picture that is consistent with the nuclear symplectic model. The results also suggest a pragmatic path forward to accommodate deformation-driven collective features in ab initio analyses when they dominate the nuclear landscape.

Storing sparse matrices to files in the adaptive-blocking hierarchical storage format

Rok
2013
Publikováno
Proceedings of the 2013 Federated Conference on Computer Science and Information Systems. Los Alamitos: IEEE Computer Society, 2013. pp. 479-486. ISSN 2325-0348. ISBN 978-1-4673-4471-5.
Typ
Stať ve sborníku
Anotace
When there is a need to store a sparse matrix into a file system, is it worth to convert it first into some space-efficient storage format? This paper tries to answer such question for the adaptive-blocking hierarchical storage format (ABHSF), provided that the matrix is present in memory either in the coordinate (COO) or in the compressed sparse row (CSR) storage format. The conversion algorithms from COO and CSR to ABHSF are introduced and the results of performed experiments are then presented and discussed.

Symmetry-adapted ab initio no-core shell model calculations for 12C

Autoři
Launey, K.D.; Dreyfuss, A.C.; Dytrych, T.; Draayer, J.P.; Langr, D.; Maris, P.; Vary, J.P.; Bahri, C.
Rok
2013
Publikováno
10th International Conference on Clustering Aspects of Nuclear Structure and Dynamics (CLUSTER12). Bristol: IOP Publishing Ltd, 2013. pp. 1-7. Journal of Physics: Conference Series. ISSN 1742-6588.
Typ
Stať ve sborníku
Anotace
Symmetry-adapted no-core shell-model calculations reveal dominant symmetry patterns in the structure of light nuclei, independent of whether the system Hamiltonian is phenomenological in nature or derived from realistic interactions. We show results of large-scale nuclear structure computations based on the ab initio symmetry-adapted no-core shell model that use only a fraction of the model space. In addition, the symmetry patterns unveiled in these results are employed to explore ultra-large model spaces for 12C. The outcome suggests a possible path forward for realizing collective theories that target correlated highly-deformed and alpha-cluster structures in terms of microscopic degrees of freedom that build forward from the nucleon-nucleon interaction itself.

Symmetry-Adapted No-Core Shell Model for Light Nuclei

Autoři
Launey, K.D.; Dytrych, T.; Draayer, J.P.; Tobin, G.K.; Ferriss, M.C.; Langr, D.; Dreyfuss, A.C.; Maris, P.; Vary, J.P.; Bahri, C.
Rok
2013
Publikováno
Fission and Properties of Neutron-Rich Nuclei. Singapore: World Scientific, 2013. pp. 29-38. ISBN 978-981-4525-42-8.
Typ
Stať ve sborníku
Anotace
We present results for p-shell nuclei based on the ab initio symmetry-adapted no-core shell model that utilizes an SU(3) coupling scheme. Details given for 12C are reflective of similar results found for 6Li, 8B, 8Be, and 16O, all of which exhibit a strong preference for large quadrupole deformations and a narrow set of intrinsic spin values. The outcome suggests that a small subspace of symmetry-adapted configurations can very closely approximate the exact solutions. The symmetry patterns unveiled in these results are, in turn, employed to explore ultra-large model spaces for 12C, in particular to study the elusive Hoyle state, as well as for 8Be and sd-shell nuclei including Ne and Mg.

Utilizing Symmetry Coupling Schemes in Ab Initio Nuclear Structure Calculations

Autoři
Dytrych, T.; Draayer, J.P.; Launey, K.D.; Maris, P.; Vary, J.P.; Langr, D.
Rok
2013
Publikováno
Nuclear Theory in the Supercomputing Era. Khabarovsk: Pacific Natiohal University, 2013. pp. 62-72. ISBN 978-5-7389-1384-6.
Typ
Stať ve sborníku
Anotace
We report on ab initio no-core shell model calculations in a symmetry-adapted SU(3)-based coupling scheme that demonstrate that collective modes in p-shell nuclei emerge from first principles. The low-lying states of 6Li, 6He, 8Be, 8B, 12C, and 16O, are shown to exhibit orderly patterns that favor spatial configurations with strong quadrupole deformation and complementary low intrinsic spin values, a picture that is consistent with the nuclear symplectic model. The results also suggest a pragmatic path forward to accommodate deformation-driven collective features in ab initio analyses when they dominate the nuclear landscape.

Ab initio No-core Shell Model Calculations in a SU(3)-based Coupling Scheme

Autoři
Dytrych, T.; Launey, K.D.; Draayer, J.P.; Langr, D.
Rok
2012
Publikováno
Journal of Physics: Conference Series. 2012, 387(1), 012016-012021. ISSN 1742-6588.
Typ
Článek
Anotace
We use powerful algorithms of computational group theory to perform ab initio configuration-interaction calculations in a SU(3)-based symmetry-adapted many-particle basis. We demonstrate that eigenfunctions for the low-lying states of 6Li, 8Be, 12C, and 16O exhibit a strong dominance of low proton, neutron, and total intrinsic spins that carry the same spatial deformation as the leading symplectic Sp(3,R) irreducible representations. Our findings imply that only a small fraction of the complete model space is needed to model nuclear collective dynamics, deformation, and ff-particle clustering even if one uses modern realistic interactions that do not preserve SU(3) symmetry. This in turn points to the importance of using a symmetry-adapted framework, one based on a LS coupling scheme with the associated spatial configurations organized according to deformation.

Adaptive-Blocking Hierarchical Storage Format for Sparse Matrices

Autoři
Langr, D.; Šimeček, I.; Tvrdík, P.; Dytrych, T.; Draayer, J.P.
Rok
2012
Publikováno
Federated Conference on Computer Science and Information Systems (FedCSIS 2012). New York: IEEE, 2012. pp. 545-551. ISBN 978-1-4673-0708-6.
Typ
Stať ve sborníku
Anotace
Hierarchical storage formats (HSFs) can significantly reduce the space complexity of sparse matrices. They vary in storage schemes that they use for blocks and for block matrices. However, the current HSFs prescribe a fixed storage scheme for all blocks, which is not always space-optimal.We show that, generally, different storage schemes are space-optimal for different blocks. We further propose a new HSF that is based on this approach and compare its space complexity with current HSFs for benchmark matrices arising from different application areas.

Fake Run-Time Selection of Template Arguments in C++

Autoři
Langr, D.; Tvrdík, P.; Dytrych, T.; Draayer, J.P.
Rok
2012
Publikováno
Objects, Models, Components, Patterns. Berlin: Springer, 2012. pp. 140-154. ISSN 0302-9743. ISBN 978-3-642-30560-3.
Typ
Stať ve sborníku
Anotace
C++ does not support run-time resolution of template type arguments. To circumvent this restriction, we can instantiate a template for all possible combinations of type arguments at compile time and then select the proper instance at run time by evaluation of some provided conditions. However, for templates with multiple type parameters such a solution may easily result in a branching code bloat. We present a template metaprogramming algorithm called for_id that allows the user to select the proper template instance at run time with theoretical minimum sustained complexity of the branching code.

Heterogeneous cluster for acceleration of linear algebra computations

Rok
2012
Publikováno
Proceedings of International Conference on Applied Mathematics (Aplimat 2012). Bratislava: Slovenská technická univerzita, Strojnícka fakulta, 2012. pp. 299-306. ISBN 978-80-89313-58-7.
Typ
Stať ve sborníku
Anotace
Plenty of numerical algebra libraries have been developed in recent years. These libraries are tuned for the given CPU and its memory architecture, fully utilize its memory hierarchy and inner pipelines and achieve impressive computation power. There is also a new trend in the high-performance computing: GPU computing. This paper deals with a new concept of the heterogeneous grid for acceleration of the numerical linear algebra computing. We design this grid with respect to maximal ratio between cost and computational power. It allows a parallelization of scientific codes with minimal programming effort. We also optimize grid concept to be less sensitive to network parameters.

Heterogeneous cluster for acceleration of linear algebra computations

Rok
2012
Publikováno
Aplimat - Journal of Applied Mathematics (CD ROM). 2012, 5(2), 225-232. ISSN 1337-6365.
Typ
Článek
Anotace
Plenty of numerical algebra libraries have been developed in recent years. These libraries are tuned for the given CPU and its memory architecture, fully utilize its memory hierarchy and inner pipelines and achieve impressive computation power. There is also a new trend in the high-performance computing: GPU computing. This paper deals with a new concept of the heterogeneous grid for acceleration of the numerical linear algebra computing. We design this grid with respect to maximal ratio between cost and computational power. It allows a parallelization of scientific codes with minimal programming effort. We also optimize grid concept to be less sensitive to network parameters.

Minimal Quadtree Format for Compression of Sparse Matrices Storage

Rok
2012
Publikováno
Proceedings of 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2012). Los Alamitos: IEEE Computer Society, 2012. pp. 359-364. SYNASC'12. ISBN 978-0-7695-4934-7.
Typ
Stať ve sborníku
Anotace
Computations with sparse matrices are widespread in scientific projects. Commonly used storage formats (such as COO or CSR) are not suitable for I/O file operations with sparse matrices due to their high space complexities. Memory-efficient formats are still under development. In this paper, we present a new storage format called the Minimal quadtree (MQ) as well as algorithms for converting matrices from common storage formats to the MQ format. We compare the space complexity of common storage formats and of the MQ format and prove that the idea of using the quadtree as the data structure for sparse matrices is viable.

Space-efficient sparse matrix storage formats for massively parallel systems

Rok
2012
Publikováno
HPCC 2012: IEEE 14th International Conference on High Performance Computing and Communications. Los Alamitos: IEEE Computer Society, 2012. pp. 54-60. ISBN 978-0-7695-4749-7.
Typ
Stať ve sborníku
Anotace
In this paper, we propose and evaluate new storage formats for sparse matrices that minimize the space complexity of information about matrix structure. The motivation of our work are applications with very large sparse matrices that due to their size must be processed on massively parallel computer systems consisting of tens or hundreds of thousands of processor cores and that must be stored in a distributed file system using parallel I/O. The parallel I/O is typically the main performance bottleneck and reading or writing such matrices from/to distributed file system can take significant amount of time. We try to reduce this time by reducing the amount of data to be processed.

Space-efficient sparse matrix storage formats with 8-bit indices

Rok
2012
Publikováno
Seminar on Numerical Analysis. Liberec: Technical University of Liberec, 2012. pp. 161-164. ISBN 978-80-7372-821-2.
Typ
Stať ve sborníku
Anotace
The paper is aimed at space-efficient storage formats for very large sparse matrices (VLSMs). By VLSMs, we mean matrices that because of their size must be stored and processed by massively parallel computer systems with distributed memory architectures consisting of tens or hundreds of thousands of processor cores.

Symmetry-Adapted Ab Initio Open Core Shell Model Theory

Autoři
Draayer, J.P.; Dytrych, T.; Launey, K.D.; Langr, D.; Dreyfuss, A.C.; Bahri, C.
Rok
2012
Publikováno
Journal of Physics: Conference Series. 2012, 387(1), 012017-012021. ISSN 1742-6588.
Typ
Článek
Anotace
By using only a fraction of the model space, we gain further insight - within a symmetry-guided no-core shell model framework - into the many-body nuclear dynamics that gives rise to important single-particle configurations together with correlated highly-deformed and alpha-cluster structures. We show results of the novel ab initio symmetry-adapted no-core shell model for large-scale nuclear structure computations. In addition, we use the symmetry patterns unveiled in these results to explore ultra-large model spaces.

Symmetry-Adapted Ab Initio Shell Model for Nuclear Structure Calculations

Autoři
Draayer, J.P.; Dytrych, T.; Launey, K.D.; Langr, D.
Rok
2012
Publikováno
Journal of Physics: Conference Series. 2012, 366(1), 012014-012018. ISSN 1742-6588.
Typ
Článek
Anotace
An innovative concept, the symmetry-adapted ab initio shell model, that capitalizes on partial as well as exact symmetries that underpin the structure of nuclei, is discussed. This framework is expected to inform the leading features of nuclear structure and reaction data for light and medium mass nuclei, which are currently inaccessible by theory and experiment and for which predictions of modern phenomenological models often diverge. We use powerful computational and group-theoretical algorithms to perform ab initio CI (configuration-interaction) calculations in a model space spanned by SU(3) symmetry-adapted many-body configurations with the JISP16 nucleon-nucleon interaction. We demonstrate that the results for the ground states of light nuclei up through A = 16 exhibit a strong dominance of low-spin and high-deformation configurations together with an evident symplectic structure. This, in turn, points to the importance of using a symmetry-adapted framework, one based on an LS coupling scheme with the associated spatial configurations organized according to deformation.

Symmetry-adapted no-core shell model applications for light nuclei with QCD-inspired interactions

Autoři
Draayer, J.P.; Dytrych, T.; Launey, K.D.; Langr, D.
Rok
2012
Publikováno
Progress in Particle and Nuclear Physics. 2012, 67(2), 516-520. ISSN 0146-6410.
Typ
Článek
Anotace
We use powerful computational and group-theoretical algorithms to perform ab initio CI (configuration-interaction) calculations in a model space spanned by SU(3) symmetry-adapted many-body configurations with the JISP16 nucleon-nucleon interaction. We demonstrate that the results for the ground states of light nuclei up through A=16 exhibit a strong dominance of low-spin and high-deformation configurations together with an evident symplectic structure. We also find states among the lowest-lying 0+ eigenstates of 12C and 16O that are clearly dominated by α-clustering correlations. Our findings imply that only a small fraction of the full model space is needed to model nuclear collective dynamics, including deformations and α-particle clustering, even if one uses modern realistic interactions that do not preserve SU(3) symmetry. This, in turn, points to the importance of using a symmetry-adapted CI framework, one based on an LS coupling scheme with the associated spatial configurations organized according to deformation.

Symmetry-Guided Ab Initio Approach to Light and Medium-Mass Nuclei

Autoři
Dytrych, T.; Draayer, J.P.; Launey, K.D.; Caprio, M.A.; Langr, D.
Rok
2012
Publikováno
Journal of Physics: Conference Series. 2012, 403(1), 012015-012021. ISSN 1742-6588.
Typ
Článek
Anotace
We use algorithms of computational group theory to perform ab initio configuration-interaction calculations in a SU(3)-based coupling scheme for p-shell nuclei. Details given for 6Li are reflective of similar results found for 8B, 8Be, 12C and 16O, all of which exhibit a strong preference for large quadrupole deformations and a narrow set of intrinsic spin quantum numbers. Our results suggest that a small subspace of symmetry-adapted configurations can very closely approximate the exact solutions while allowing for exact factorization of the center-of-mass degrees of freedom. This, in turns, promises to allows us to extend the reach of the ab initio framework for structure and reaction studies towards sd-shell nuclei and beyond.

Ab Initio No-core Shell Model Calculations in SU(3)-scheme Basis

Autoři
Dytrych, T.; Draayer, J.P.; Launey, K.D.; Langr, D.
Rok
2011
Publikováno
Nuclear Theory. 2011, 2011(30), 81-89. ISSN 1313-2822.
Typ
Článek
Anotace
The predictive power of ab initio approaches to nuclear structure depends critically on the choice of a realistic nuclear potential, and on the ability of a finite model space to describe multifaceted properties of atomic nuclei emerging from the underlying nuclear forces. We use powerful algorithms of the computational group theory to perform ab initio configuration-interaction calculations in the model space spanned by SU(3) symmetry-adapted manybody configurations. We demonstrate that the results for the ground states of 6Li, 7Li, 12C, and 16O exhibit a strong dominance of low proton, neutron, and total intrinsic spins, and carry the same spatial deformations as the leading symplectic Sp(3,R) irreducible representations. We also...

Symmetry-adapted Ab Initio Theory for Many-body Correlations in Nuclei

Autoři
Draayer, J.P.; Dytrych, T.; Launey, K.D.; Langr, D.
Rok
2011
Publikováno
Journal of Physics: Conference Series. 2011, 321(1), 012040-012045. ISSN 1742-6588.
Typ
Článek
Anotace
We demonstrate that no-core shell-model results for low-lying states of light and medium mass nuclei, whether they are dilute or dense systems, reveal a strong dominance of low-spin and high-deformation configurations. This result is independent of whether the system Hamiltonian is phenomenological in nature or derived from a realistic interaction. It implies that only a small fraction of the complete model space is required for a description of such states, and this in turn points to the importance of using a symmetry-adapted, no-core shell-model framework for describing such nuclei, one based on an LS coupling scheme with the associated spatial configurations organized according to deformation.