Improving the scalability of a symmetric iterative eigensolver for multi‐core platforms

Aktulga, Hasan Metin; Yang, Chao; Ng, Esmond G.; Maris, Pieter; Vary, James P.

doi:10.1002/cpe.3129

Cited by 93 publications

(129 citation statements)

References 17 publications

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“…Odd values of N max then correspond to states with "unnatural" parity. These calculations are performed with the code MFDn [14][15][16], a hybrid MPI/OpenMP configuration interaction code for ab initio nuclear structure calculations. The paper is organized as follows.…”

Section: Ab Initio No Core Full Configuration Approachmentioning

confidence: 99%

Ab initiono-core solutions for⁶Li

Shin

Kim

Maris

et al. 2017

J. Phys. G: Nucl. Part. Phys.

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We solve for properties of 6 Li in the ab initio No-Core Full Configuration approach and we separately solve for its ground state and J π = 2 + 2 resonance with the Gamow Shell Model in the Berggren basis. We employ both the JISP16 and chiral NNLOopt realistic nucleon-nucleon interactions and investigate the ground state energy, excitation energies, point proton root-meansquare radius and a suite of electroweak observables. We also extend and test methods to extrapolate the ground state energy, point proton root-mean-square radius, and electric quadrupole moment. We attain improved estimates of these observables in the No-Core Full Configuration approach by using basis spaces up through Nmax = 18 that enable more definitive comparisons with experiment. Using the Density Matrix Renormalization Group approach with the JISP16 interaction, we find that we can significantly improve the convergence of the Gamow Shell Model treatment of the 6 Li ground state and J π = 2 + 2 resonance by adopting a natural orbital single-particle basis.

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Section: Ab Initio No Core Full Configuration Approachmentioning

confidence: 99%

Ab initiono-core solutions for⁶Li

Shin

Kim

Maris

et al. 2017

J. Phys. G: Nucl. Part. Phys.

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“…It gives a good description of most narrow states in light nuclei up to about A = 12 [15,16] without additional three-nucleon forces. For our calculations we use the code MFDn [4,5,6,7] which has been demonstrated to scale to over 200,000 cores, and we consider basis spaces with dimensions up to 3.3 billion basis states, and nearly 4 trillion nonzero matrix elements.…”

Section: Recent Results For Be Isotopes With Jisp16mentioning

confidence: 99%

“…Improved algorithms to construct this matrix and to determine its lowest eigenstates, as well as efficient use of increasing computational resources are critical for these successes [3,4,5,6,7,8].…”

Section: No-core Configuration Interaction Approachmentioning

confidence: 99%

Ab initio calculations for Be-isotopes with JISP16

Maris

2013

J. Phys.: Conf. Ser.

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Abstract. We present recent results from no-core configuration interaction calculations for 8 Be,10 Be, and 12 Be using the phenomenological two-body interaction JISP16. We calculate the binding energies of the ground state and the excitation energies of the low-lying positiveparity states. We discuss the contributions from the proton and neutron intrinsic spin and orbital motion to the total spin for several states, and use this to identify states which may be dominated by α-cluster configurations. In addition, we also calculate other observables such as dipole and quadrupole moments, as well as transition rates for select E2 transitions. No-Core Configuration Interaction approachConfiguration Interaction (CI) methods have been used in recent years to make increasingly accurate large scale ab initio calculations in nuclear structure, see e.g. Refs. [1, 2] and references therein. In this method, the many-body Schrödinger equationbecomes a large sparse matrix problem with eigenvalues E i . Improved algorithms to construct this matrix and to determine its lowest eigenstates, as well as efficient use of increasing computational resources are critical for these successes [3,4,5,6,7,8].In the No-Core CI (NCCI) approach [1, 2, 9] the wavefunction Ψ of a nucleus consisting of A nucleons (protons and neutrons) is expanded in an A-body basis of Slater determinants Φ k of single-particle wavefunctions φ nljm ( r)and A the antisymmetrization operation. Conventionally, one uses a harmonic oscillator (HO) basis for the singleparticle wavefunctions, but it is straightforward to extend this approach to a more general single-particle basis [10]. The single-particle wavefunctions are labelled by the quantum numbers n, l, j, and m, where n and l are the radial and orbital HO quantum numbers, with N i = 2n i + l i the number of HO quanta; j is the total single-particle spin, and m its projection along the z-axis. The many-body basis states Φ k have well-defined total spin-projection, which is simply the sum of m i of the single-particle states, M = m i (hence the name M -scheme), but they do not have a well-defined total spin J. Some of the benefits of this scheme is that it is straightforward to implement, and that in two runs (one for positive and one for negative parity), we get the complete low-lying spectrum, including the ground state, even if the spin of the ground state is not known a priori.

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“…Sparse matrix vector and and sparse matrix transpose vector products are key kernels in the iterative eigensolver. The sparse matrix is stored in a compressed sparse block coordinate (CSB COO) [1,2] format which allows efficient linear algebra operations on the large sparse matrix. The sparse matrix elements and corresponding indices account for 64 GB of the memory and the input/output vectors account for up to 16 GB depending on the specific problem.…”

Section: Mfdnmentioning

confidence: 99%