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Abstract

In this paper, we describe our vectorized and parallelized adaptive mesh refinement (AMR) N-body code with shared time steps, and report its performance on a Fujitsu VPP5000 vector-parallel supercomputer. Our AMR N-body code puts hierarchical meshes recursively where higher resolution is required and the time step of all particles are the same. The parts which are the most difficult to vectorize are loops that access the mesh data and particle data. We vectorized such parts by changing the loop structure, so that the innermost loop steps through the cells instead of the particles in each cell, in other words, by changing the loop order from the depth-first order to the breadth-first order. Mass assignment is also vectorizable using this loop order exchange and splitting the loop into \(2^{N_{dim}}\) loops, if the cloud-in-cell scheme is adopted. Here, \(N_{dim}\) is the number of dimension. These vectorization schemes which eliminate the unvectorized loops are applicable to parallelization of loops for shared-memory multiprocessors. We also parallelized our code for distributed memory machines. The important part of parallelization is data decomposition. We sorted the hierarchical mesh data by the Morton order, or the recursive N-shaped order, level by level and split and allocated the mesh data to the processors. Particles are allocated to the processor to which the finest refined cells including the particles are also assigned. Our timing analysis using the \(\Lambda\)-dominated cold dark matter simulations shows that our parallel code speeds up almost ideally up to 32 processors, the largest number of processors in our test.

Details

1009240
Title
Vectorization and Parallelization of the Adaptive Mesh Refinement N-body Code
Publication title
arXiv.org; Ithaca
Publication year
2005
Publication date
Jul 14, 2005
Section
Astrophysics
Publisher
Cornell University Library, arXiv.org
Source
arXiv.org
Place of publication
Ithaca
Country of publication
United States
University/institution
Cornell University Library arXiv.org
e-ISSN
2331-8422
Source type
Working Paper
Language of publication
English
Document type
Working Paper
Publication history
 
 
Online publication date
2015-06-24
Milestone dates
2005-07-14 (Submission v1)
Publication history
 
 
   First posting date
24 Jun 2015
ProQuest document ID
2083133968
Document URL
https://www.proquest.com/working-papers/vectorization-parallelization-adaptive-mesh/docview/2083133968/se-2?accountid=208611
Full text outside of ProQuest
Copyright
Notwithstanding the ProQuest Terms and conditions, you may use this content in accordance with the associated terms available at http://arxiv.org/abs/astro-ph/0507339.
Last updated
2019-04-13
Database
ProQuest One Academic