8,695 research outputs found
A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries
We present a new multigrid scheme for solving the Poisson equation with
Dirichlet boundary conditions on a Cartesian grid with irregular domain
boundaries. This scheme was developed in the context of the Adaptive Mesh
Refinement (AMR) schemes based on a graded-octree data structure. The Poisson
equation is solved on a level-by-level basis, using a "one-way interface"
scheme in which boundary conditions are interpolated from the previous coarser
level solution. Such a scheme is particularly well suited for self-gravitating
astrophysical flows requiring an adaptive time stepping strategy. By
constructing a multigrid hierarchy covering the active cells of each AMR level,
we have designed a memory-efficient algorithm that can benefit fully from the
multigrid acceleration. We present a simple method for capturing the boundary
conditions across the multigrid hierarchy, based on a second-order accurate
reconstruction of the boundaries of the multigrid levels. In case of very
complex boundaries, small scale features become smaller than the discretization
cell size of coarse multigrid levels and convergence problems arise. We propose
a simple solution to address these issues. Using our scheme, the convergence
rate usually depends on the grid size for complex grids, but good linear
convergence is maintained. The proposed method was successfully implemented on
distributed memory architectures in the RAMSES code, for which we present and
discuss convergence and accuracy properties as well as timing performances.Comment: 33 pages, 15 figures, accepted for publication in Journal of
Computational Physic
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Large-scale lattice Boltzmann simulations of complex fluids: advances through the advent of computational grids
During the last two years the RealityGrid project has allowed us to be one of
the few scientific groups involved in the development of computational grids.
Since smoothly working production grids are not yet available, we have been
able to substantially influence the direction of software development and grid
deployment within the project. In this paper we review our results from large
scale three-dimensional lattice Boltzmann simulations performed over the last
two years. We describe how the proactive use of computational steering and
advanced job migration and visualization techniques enabled us to do our
scientific work more efficiently. The projects reported on in this paper are
studies of complex fluid flows under shear or in porous media, as well as
large-scale parameter searches, and studies of the self-organisation of liquid
cubic mesophases.
Movies are available at
http://www.ica1.uni-stuttgart.de/~jens/pub/05/05-PhilTransReview.htmlComment: 18 pages, 9 figures, 4 movies available, accepted for publication in
Phil. Trans. R. Soc. London Series
Distributed-Memory Breadth-First Search on Massive Graphs
This chapter studies the problem of traversing large graphs using the
breadth-first search order on distributed-memory supercomputers. We consider
both the traditional level-synchronous top-down algorithm as well as the
recently discovered direction optimizing algorithm. We analyze the performance
and scalability trade-offs in using different local data structures such as CSR
and DCSC, enabling in-node multithreading, and graph decompositions such as 1D
and 2D decomposition.Comment: arXiv admin note: text overlap with arXiv:1104.451
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