New algorithm to enable 400+ TFlop/s sustained performance in simulations of disorder effects in high-T&lt;inf&gt;c&lt;/inf&gt; superconductors

Alvarez, Fernando; Summers,; Maxwell,; Eisenbach,; Meredith,; Larkin,; Lévesque,; Maier, Stefan A.; Kent, Paul; D'Azevedo,; Schulthess,

doi:10.1109/sc.2008.5218119

Cited by 7 publications

(11 citation statements)

References 17 publications

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“…BLOCK CHECKERBOARD METHOD FOR 2D AND 3D LATTICES In this paper, we consider the parallelization of the checkerboard method for 2-dimensional meshes and 3-dimensional cubics, since those two types of lattices are of great interests to current researches [4], [18], [19]. The kinetic matrix of a 2-dimensional mesh is highly sparse because only 4 non-zeros per row/column.…”

Section: Block Checkerboard Methodsmentioning

confidence: 99%

“…Determinant Quantum Monte Carlo (DQMC) is a numerical method that simulates the dynamic of electrons of solid materials [1], [2], [3], [4], [5]. The simulated system is characterized by the Hubbard model, H = H k +H v +H μ , where H k , H v and H μ are the Hamiltonian for kinetic energy, potential energy, and chemical potential respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Recent studies on complex materials, which require larger model size and finer discretization, have brought new challenges to the DQMC computation [4], [6]. The time complexity of the DQMC algorithm is O((m 1 + m 2 )N 3 L), where m 1 and m 2 are the numbers of iterations for the thermalization stage and the measurement stage, N is the number of particles in the simulated lattice (called sites), and L is the number of discretized time slices.…”

Section: Introductionmentioning

confidence: 99%

“…Second, for a large N , a longer thermalization stage is required before measurements, which increase the number of un-parallelizable m 1 iterations. In [4], a parallel matrix-matrix multiplication is implemented on multi-core to reduce the cost. Various matrixmatrix multiplication algorithms on GPU [9], [10] are also proposed.…”

Section: Introductionmentioning

confidence: 99%

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Parallelizing the Hamiltonian Computation in DQMC Simulations: Checkerboard Method for Sparse Matrix Exponentials on Multicore and GPU

Lee

Chen

Kao

2012

2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops &Amp; PhD Forum

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Determinant Quantum Monte Carlo (DQMC) simulation is one of few numerical methods that can explore the micro properties of fermions, which has many technically important applications in chemistry and material science. Conventionally, its parallelization relies on parallel Monte Carlo method, whose speedup is limited by the thermalization process and the underlying matrix computation. To achieve better performance, finegrained parallelization on its numerical kernel is essential to utilize the massive parallel processing units, which are multicores and/or GPUs interconnected by high performance network.In this paper, we address the parallelization on one of the matrix kernel in the DQMC simulations: the multiplication of matrix exponentials. The matrix is derived from the kinetic Hamiltonian, which is highly sparse. We approximate its exponential by the checkerboard method, which decomposes the matrix exponential into a product of a sequence of block sparse matrices. We analyze the block sparse matrices of two common used lattice geometry: 2D torus and 3D cubic, and parallelize the computational kernel of multiplying them to a general matrix. The parallel algorithm is designed for multicore CPU and GPU. The results of experiments showed on a quad core processor, 3 times speedup can be observed in average, and on GPU, 145 times speedup is achievable.

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Section: Block Checkerboard Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parallelizing the Hamiltonian Computation in DQMC Simulations: Checkerboard Method for Sparse Matrix Exponentials on Multicore and GPU

Lee

Chen

Kao

2012

2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops &Amp; PhD Forum

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“…It is almost parallel by definition, and delayed update optimizations [10] are irrelevant to the code since rank-one updates, i.e. single spin flips, are not required.…”

Section: Qmc Methodsmentioning

confidence: 99%

Material-Specific Investigations of Correlated Electron Systems

Kampf

Kollar

Kuneš

et al. 2010

High Performance Computing in Science and Engineering, Garching/Munich 2009

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We present the results of numerical studies for selected materials with strongly correlated electrons using a combination of the local-density approximation and dynamical mean-field theory (DMFT). For the solution of the DMFT equations a continuous-time quantum Monte-Carlo algorithm was employed. All simulations were performed on the supercomputer HLRB II at the Leibniz Rechenzentrum in Munich. Specifically we have analyzed the pressure induced metal-insulator transitions in Fe 2 O 3 and NiS 2 , the charge susceptibility of the fluctuating-valence elemental metal Yb, and the spectral properties of a covalent band-insulator model which includes local electronic correlations.

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PSINS: An Open Source Event Tracer and Execution Simulator for MPI Applications

Tikir

Laurenzano

Carrington

et al. 2009

Lecture Notes in Computer Science

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As the size of today's supercomputers grow exponentially in numbers of processors, the applications that run on these systems scale to larger processor counts. The majority of these applications commonly use MPI; a trace of these MPI communication events is an important input to the tools that visualize, simulate for performance modeling, or enable tuning of parallel applications. We introduce an efficient, accurate and flexible trace-driven performance modeling and prediction tool, PMaC's Open Source Interconnect and Network Simulator (PSINS), for MPI applications. A principal feature of PSINS is its usability for applications that scale up to large processor counts. PSINS generates compact and tractable event traces for fast and efficient simulations while producing accurate performance predictions. PSINS was incorporated into PMaC's automated performance prediction framework and used to model three applications from the High Performance Computing Modernization Office's (HPCMO) Technology-Insertion 2009 (TI-09) application suite.

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New algorithm to enable 400+ TFlop/s sustained performance in simulations of disorder effects in high-T<inf>c</inf> superconductors

Cited by 7 publications

References 17 publications

Parallelizing the Hamiltonian Computation in DQMC Simulations: Checkerboard Method for Sparse Matrix Exponentials on Multicore and GPU

Parallelizing the Hamiltonian Computation in DQMC Simulations: Checkerboard Method for Sparse Matrix Exponentials on Multicore and GPU

Material-Specific Investigations of Correlated Electron Systems

PSINS: An Open Source Event Tracer and Execution Simulator for MPI Applications

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