26 research outputs found

    Reducing Communication in the Solution of Linear Systems

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    There is a growing performance gap between computation and communication on modern computers, making it crucial to develop algorithms with lower latency and bandwidth requirements. Because systems of linear equations are important for numerous scientific and engineering applications, I have studied several approaches for reducing communication in those problems. First, I developed optimizations to dense LU with partial pivoting, which downstream applications can adopt with little to no effort. Second, I consider two techniques to completely replace pivoting in dense LU, which can provide significantly higher speedups, albeit without the same numerical guarantees as partial pivoting. One technique uses randomized preprocessing, while the other is a novel combination of block factorization and additive perturbation. Finally, I investigate using mixed precision in GMRES for solving sparse systems, which reduces the volume of data movement, and thus, the pressure on the memory bandwidth

    Properties of the η and η' mesons from lattice QCD

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    In this thesis we compute masses, decay constants and gluonic matrix elements of the flavour-diagonal pseudoscalar mesons η and η' from lattice QCD. To control all relevant systematic errors we employ Nf = 2 + 1 flavour simulations along two distinct quark mass trajectories leading to and including the physical point. The continuum extrapolation is guided by four lattice spacings. The ensembles were generated within the coordinated lattice simulations initiative, and we set their relative scales in this work. We discuss noise reduction techniques for the efficient calculation of the disconnected contributions that are important building blocks of the relevant correlation functions of the η and η' system. The physical states are no flavour eigenstates, and hence sophisticated analysis methods are required to extract them from the data. We develop a matrix generalization of the effective mass method which we employ in conjunction with additional techniques to determine masses and matrix elements. The physical point extrapolation employs next-to-leading order large-Nc chiral perturbation theory, and we determine all relevant low energy constants. For the first time also their renormalization scale dependence is taken into account, and this provides an important check of the range of validity of this effective field theory with implications on many existing phenomenological analyses. Our physical point results for the masses are in agreement with experimental values and read Mη = 554.7(9.2) MeV and Mη' = 930(21) MeV. The determination of the four η and η' decay constants is the first from first principles and we obtain F8 = 115.0(2.8) MeV and θ8 = −25.8(2.3)◦ in the octet channel and F0 = 100.1(3.0) MeV and θ0 = −8.1(1.8)◦ for the singlet in the MS scheme at 2 GeV. These results are in excellent agreement with phenomenological determinations and at a similar level of precision. Finally, we connect these axialvector decay constants with pseudoscalar and gluonic matrix elements to test the axial Ward identities, and predict the anomalous matrix elements to be aη = = 0.0170(10) GeV^3 and aη' = = 0.0381(84) GeV^3 at the physical point and µ = 2 GeV

    Gradient-flow scale setting with Nf=2+1+1N_f=2+1+1 Wilson-clover twisted-mass fermions

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    We present a determination of the gradient flow scales w0 , t0‾‾√ and t0/w0 in isosymmetric QCD, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with Nf=2+1+1 flavours of Wilson-clover twisted-mass quarks including configurations close to the physical point for all dynamical flavours. The simulations are carried out at three values of the lattice spacing and the scale is set through the PDG value of the pion decay constant, yielding w0=0.17383(63) fm, t0‾‾√=0.14436(61) fm and t0/w0=0.11969(62) fm. Finally, fixing the kaon mass to its isosymmetric value, we determine the ratio of the kaon and pion leptonic decay constants to be fK/fπ=1.1995(44)

    Generalized averaged Gaussian quadrature and applications

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    A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

    MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

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    Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

    Lattice Quantum Chromodynamics on Intel Xeon Phi based supercomputers

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    Preface The aim of this master\u2019s thesis project was to expand the QPhiX library for twisted-mass fermions with and without clover term. To this end, I continued work initiated by Mario Schr\uf6ck et al. [63]. In writing this thesis, I was following two main goals. Firstly, I wanted to stress the intricate interplay of the four pillars of High Performance Computing: Algorithms, Hardware, Software and Performance Evaluation. Surely, algorithmic development is utterly important in Scientific Computing, in particular in LQCD, where it even outweighed the improvements made in Hardware architecture in the last decade\u2014cf. the section about computational costs of LQCD. It is strongly influenced by the available hardware\u2014think of the advent of parallel algorithms\u2014but in turn also influenced the design of hardware itself. The IBM BlueGene series is only one of many examples in LQCD. Furthermore, there will be no benefit from the best algorithms, when one cannot implement the ideas into correct, performant, user-friendly, read- and maintainable (sometimes over several decades) software code. But again, truly outstanding HPC software cannot be written without a profound knowledge of its target hardware. Lastly, an HPC software architect and computational scientist has to be able to evaluate and benchmark the performance of a software program, in the often very heterogeneous environment of supercomputers with multiple software and hardware layers. My second goal in writing this thesis was to produce a self-contained introduction into the computational aspects of LQCD and in particular, to the features of QPhiX, so the reader would be able to compile, read and understand the code of one truly amazing pearl of HPC [40]. It is a pleasure to thank S. Cozzini, R. Frezzotti, E. Gregory, B. Jo\uf3, B. Kostrzewa, S. Krieg, T. Luu, G. Martinelli, R. Percacci, S. Simula, M. Ueding, C. Urbach, M. Werner, the Intel company for providing me with a copy of [55], and the J\ufclich Supercomputing Center for granting me access to their KNL test cluster DEE

    Proceedings, MSVSCC 2016

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    Proceedings of the 10th Annual Modeling, Simulation & Visualization Student Capstone Conference held on April 14, 2016 at VMASC in Suffolk, Virginia
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