3,343 research outputs found
Progress in Lattice Field Theory Algorithms
I present a summary of recent algorithmic developments for lattice field
theories. In particular I give a pedagogical introduction to the new
Multicanonical algorithm, and discuss the relation between the Hybrid
Overrelaxation and Hybrid Monte Carlo algorithms. I also attempt to clarify the
role of the dynamical critical exponent z and its connection with
`computational cost.' [Includes four PostScript figures]Comment: 27 page
Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs
We design and implement a parallel algebraic multigrid method for isotropic
graph Laplacian problems on multicore Graphical Processing Units (GPUs). The
proposed AMG method is based on the aggregation framework. The setup phase of
the algorithm uses a parallel maximal independent set algorithm in forming
aggregates and the resulting coarse level hierarchy is then used in a K-cycle
iteration solve phase with a -Jacobi smoother. Numerical tests of a
parallel implementation of the method for graphics processors are presented to
demonstrate its effectiveness.Comment: 18 pages, 3 figure
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Preparing sparse solvers for exascale computing.
Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'
Afivo: a framework for quadtree/octree AMR with shared-memory parallelization and geometric multigrid methods
Afivo is a framework for simulations with adaptive mesh refinement (AMR) on
quadtree (2D) and octree (3D) grids. The framework comes with a geometric
multigrid solver, shared-memory (OpenMP) parallelism and it supports output in
Silo and VTK file formats. Afivo can be used to efficiently simulate AMR
problems with up to about unknowns on desktops, workstations or single
compute nodes. For larger problems, existing distributed-memory frameworks are
better suited. The framework has no built-in functionality for specific physics
applications, so users have to implement their own numerical methods. The
included multigrid solver can be used to efficiently solve elliptic partial
differential equations such as Poisson's equation. Afivo's design was kept
simple, which in combination with the shared-memory parallelism facilitates
modification and experimentation with AMR algorithms. The framework was already
used to perform 3D simulations of streamer discharges, which required tens of
millions of cells
Simple parallel and distributed algorithms for spectral graph sparsification
We describe a simple algorithm for spectral graph sparsification, based on
iterative computations of weighted spanners and uniform sampling. Leveraging
the algorithms of Baswana and Sen for computing spanners, we obtain the first
distributed spectral sparsification algorithm. We also obtain a parallel
algorithm with improved work and time guarantees. Combining this algorithm with
the parallel framework of Peng and Spielman for solving symmetric diagonally
dominant linear systems, we get a parallel solver which is much closer to being
practical and significantly more efficient in terms of the total work.Comment: replaces "A simple parallel and distributed algorithm for spectral
sparsification". Minor change
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