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Parallel Implementation of Discretization Methods for Nonstructured Meshes on Distributed Shared Memory Architectures

分布式共享内存架构上非结构化网格离散化方法的并行实现

基本信息

批准号：
13480080
负责人：
OYANAGI Yoshio
金额：
$ 9.79万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13480080/
关键词：
partial differential equations unstructured meshes algebraic multigrid method conjugate gradient methods preconditioning parallel processing distributed shared memory fast Fourier transform コモディティアーキテクチャ

项目摘要

This research has achieved the following results on the two main targets of the project :1. Algebraic Multigrid Preconditioner for Finite Element MethodsMGCG, the geometric multigrid preconditioned conjugate gradient method, which has been proposed and implemented by our group in 1992, is one of the most effective and scalable solvers for convection diffusion equations, but it has a drawback of slow convergence on anisotropic problems. This study proposed AMGCG, the algebraic multigrid preconditioned conjugate gradient method based on smoothed aggregation, which cancels the effect of geometric anisotropy, and implemented on a SPARC workstation cluster with 256 CPUs. Experiments up to 250^3 mesh points showed that the method achieves more than three times as fast convergence as ICCG, the conjugate gradient method with incomplete Cholesky factorization, for the largest size. Furthermore, using parallel direct solver on the coarsest grid, the method shows constant convergence time even on isotropic problems.2. High Performance Computing on Distributed Shared MemoryDistributed shared memory architecture is one of the key technologies to make high performance computing on commodity shared memory machines scalable. We have built Linux environments on two Intel Processor based distributed shared memory computers, NEC's AzusA and IBM's xSeries 440. Our implementation of low level basic linear algebra routines and fast Fourier transform codes shows that we can achieve good scalability on such commodity DSM architectures, but careful tuning of the operation system is also required to get lair memory bandwidth.

本研究在项目的两个主要目标上取得了以下成果：1。几何多网格预条件共轭梯度法（几何多网格预条件共轭梯度法）是我们于1992年提出并实现的对流扩散方程最有效且可扩展的求解方法之一，但它在各向异性问题上存在收敛速度慢的缺点。提出了一种消除几何各向异性影响的基于平滑聚集的代数多网格预条件共轭梯度方法AMGCG，并在256个cpu的SPARC工作站集群上实现。250^3个网格点的实验表明，该方法的收敛速度是ICCG（不完全Cholesky分解的共轭梯度方法）的3倍以上。此外，在最粗糙网格上使用并行直接求解器，该方法即使在各向同性问题上也具有恒定的收敛时间。分布式共享内存上的高性能计算分布式共享内存架构是实现商用共享内存机器上高性能计算可扩展性的关键技术之一。我们在两台基于英特尔处理器的分布式共享内存计算机上构建了Linux环境，这两台计算机是NEC的AzusA和IBM的xSeries 440。我们对低级基本线性代数例程和快速傅立叶变换代码的实现表明，我们可以在这种商品DSM架构上实现良好的可扩展性，但也需要对操作系统进行仔细的调优，以获得较低的内存带宽。