20,715 research outputs found
A COMPARISON OF PRECONDITIONING TECHNIQUES FOR PARALLELIZED PCG SOLVERS FOR THE CELL-CENTERED FINITE-DIFFERENCE PROBLEM
Abstract This paper reports on a parallelization of the preconditioned conjugate gradient algorithm for sparse, symmetric matrices. Parallelization is based in domain partitioning into non-overlapping subdomains; the resulting parallelized algorithm is briefly described. Comparisons are made between three block preconditioners commonly used in the parallelization of the preconditoned conjugate gradient methods: Jacobi, incomplete Choleski, and Gauss Seidel. Basic timing and iteration results for these preconditioners are presented; these results tentatively indicate that the simpler block Jacobi algorithm is as efficient as the more complex block incomplete Cholesky and block Gauss Seidel
NBODY6++GPU: Ready for the gravitational million-body problem
Accurate direct -body simulations help to obtain detailed information
about the dynamical evolution of star clusters. They also enable comparisons
with analytical models and Fokker-Planck or Monte-Carlo methods. NBODY6 is a
well-known direct -body code for star clusters, and NBODY6++ is the extended
version designed for large particle number simulations by supercomputers. We
present NBODY6++GPU, an optimized version of NBODY6++ with hybrid
parallelization methods (MPI, GPU, OpenMP, and AVX/SSE) to accelerate large
direct -body simulations, and in particular to solve the million-body
problem. We discuss the new features of the NBODY6++GPU code, benchmarks, as
well as the first results from a simulation of a realistic globular cluster
initially containing a million particles. For million-body simulations,
NBODY6++GPU is times faster than NBODY6 with 320 CPU cores and 32
NVIDIA K20X GPUs. With this computing cluster specification, the simulations of
million-body globular clusters including primordial binaries require
about an hour per half-mass crossing time.Comment: 13 pages, 9 figures, 3 table
Parallelization Strategies for Density Matrix Renormalization Group Algorithms on Shared-Memory Systems
Shared-memory parallelization (SMP) strategies for density matrix
renormalization group (DMRG) algorithms enable the treatment of complex systems
in solid state physics. We present two different approaches by which
parallelization of the standard DMRG algorithm can be accomplished in an
efficient way. The methods are illustrated with DMRG calculations of the
two-dimensional Hubbard model and the one-dimensional Holstein-Hubbard model on
contemporary SMP architectures. The parallelized code shows good scalability up
to at least eight processors and allows us to solve problems which exceed the
capability of sequential DMRG calculations.Comment: 18 pages, 9 figure
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