Inner product computation for sparse iterative solvers on\ud distributed supercomputer

Recent years have witnessed that iterative Krylov methods without re-designing are not suitable for distribute supercomputers because of intensive global communications. It is well accepted that re-engineering Krylov methods for prescribed computer architecture is necessary and important to achieve higher performance and scalability. The paper focuses on simple and practical ways to re-organize Krylov methods and improve their performance for current heterogeneous distributed supercomputers. In construct with most of current software development of Krylov methods which usually focuses on efficient matrix vector multiplications, the paper focuses on the way to compute inner products on supercomputers and explains why inner product computation on current heterogeneous distributed supercomputers is crucial for scalable Krylov methods. Communication complexity analysis shows that how the inner product computation can be the bottleneck of performance of (inner) product-type iterative solvers on distributed supercomputers due to global communications. Principles of reducing such global communications are discussed. The importance of minimizing communications is demonstrated by experiments using up to 900 processors. The experiments were carried on a Dawning 5000A, one of the fastest and earliest heterogeneous supercomputers in the world. Both the analysis and experiments indicates that inner product computation is very likely to be the most challenging kernel for inner product-based iterative solvers to achieve exascale

Minimizing synchronizations in sparse iterative solvers for distributed supercomputers

Eliminating synchronizations is one of the important techniques related to minimizing communications for modern high performance computing. This paper discusses principles of reducing communications due to global synchronizations in sparse iterative solvers on distributed supercomputers. We demonstrates how to minimizing global synchronizations by rescheduling a typical Krylov subspace method. The benefit of minimizing synchronizations is shown in theoretical analysis and is verified by numerical experiments using up to 900 processors. The experiments also show the communication complexity for some structured sparse matrix vector multiplications and global communications in the underlying supercomputers are in the order P1/2.5 and P4/5 respectively, where P is the number of processors and the experiments were carried on a Dawning 5000A

Magnetic quantum phase transition in an anisotropic Kondo lattice

The quantum phase transition between paramagnetic and antiferromagnetic phases of the Kondo lattice model with Ising anisotropy in the intersite exchange is studied within the framework of extended dynamical mean-field theory. Nonperturbative numerical solutions at zero temperature point to a continuous transition for both two- and three-dimensional magnetism. In the former case, the transition is associated with critical local physics, characterized by a vanishing Kondo scale and by an anomalous exponent in the dynamics close in value to that measured in heavy-fermion CeCu_{5.9}Au_{0.1}.Comment: 4 pages, 3 figures. Version published in Phys. Rev. Let

Interplay between Superconductivity and Antiferromagnetism in a Multi-layered System

Based on a microscopic model, we study the interplay between superconductivity and antiferromagnetism in a multi-layered system, where two superconductors are separated by an antiferromagnetic region. Within a self-consistent mean-field theory, this system is solved numerically. We find that the antiferromagnetism in the middle layers profoundly affects the supercurrent flowing across the junction, while the phase difference across the junction influences the development of antiferromagnetism in the middle layers. This study may not only shed new light on the mechanism for high-$T_{c}$ superconductors, but also bring important insights to building Josephson-junction-based quantum devices, such as SQUID and superconducting qubit.Comment: 4+ pages, 5 figures, Accepted for publication in Phys. Rev.

Automated access to well-defined ionic oligosaccharides

Ionic polysaccharides are part of many biological events, but lack structural characterisation due to challenging purifications and complex synthesis. Four monosaccharides bearing modifications not found in nature are used for the automated synthesis of a collection of ionic oligosaccharides. Structural analysis reveals how the charge pattern affects glycan conformation

Interactions between unidirectional quantized vortex rings

We have used the vortex filament method to numerically investigate the interactions between pairs of quantized vortex rings that are initially traveling in the same direction but with their axes offset by a variable impact parameter. The interaction of two circular rings of comparable radii produce outcomes that can be categorized into four regimes, dependent only on the impact parameter; the two rings can either miss each other on the inside or outside, or they can reconnect leading to final states consisting of either one or two deformed rings. The fraction of of energy went into ring deformations and the transverse component of velocity of the rings are analyzed for each regime. We find that rings of very similar radius only reconnect for a very narrow range of the impact parameter, much smaller than would be expected from geometrical cross-section alone. In contrast, when the radii of the rings are very different, the range of impact parameters producing a reconnection is close to the geometrical value. A second type of interaction considered is the collision of circular rings with a highly deformed ring. This type of interaction appears to be a productive mechanism for creating small vortex rings. The simulations are discussed in the context of experiments on colliding vortex rings and quantum turbulence in superfluid helium in the zero temperature limit

Angular Dependence of the Superconducting Transition Temperature in Ferromagnet-Superconductor-Ferromagnet Trilayers

The superconducting transition temperature, $T_c$, of a ferromagnet (F) - superconductor (S) - ferromagnet trilayer depends on the mutual orientation of the magnetic moments of the F layers. This effect has been previously observed in F/S/F systems as a $T_c$ difference between parallel and antiparallel configurations of the F layers. Here we report measurements of $T_c$ in CuNi/Nb/CuNi trilayers as a function of the angle between the magnetic moments of the CuNi ferromagnets. The observed angular dependence of $T_c$ is in qualitative agreement with a F/S proximity theory that accounts for the odd triplet component of the condensate predicted to arise for non-collinear orientation of the magnetic moments of the F layers.Comment: 4 + \epsilon pages including 4 figures. To appear in Phys. Rev. Let