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

Impacts of reduced inequalities on quality education: Examining the relationship between regional sustainability and higher education

Although the United Nations’ Sustainable Development Goals (SDGs) advocate, through SDG 4 and SDG 10, equitable quality education and the reduction of inequalities within and between countries, respectively, few studies have examined how inequalities in regional sustainability influence higher education. Therefore, this study aims to examine the relationship between regional sustainability and higher education in China using fixed-effects panel modelling. A systematic force framework showing how regional sustainability drives higher education was constructed from economic, social, and environmental perspectives, and the endogeneity in the process of how regional sustainability affects higher education was explored by introducing one-year lagged values as instrumental variables. Our results show that regional sustainability has a significant impact on higher educational attainment in China, with differing effects in the eastern, central, and western regions, respectively. In central China, economic sustainability plays a significant positive role in higher educational attainment; in the western region, economic and social sustainability have stronger positive effects, while environmental sustainability has significantly negative effects. In terms of policy implications, our findings can be used to support regional development policies to promote regional higher education

Initialization-similarity clustering algorithm

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