• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文学位 >Parallel Algebraic Multigrid for the Pressure Poisson Equation in a finite element Navier-Stokes solver.
【24h】

Parallel Algebraic Multigrid for the Pressure Poisson Equation in a finite element Navier-Stokes solver.

机译：有限元Navier-Stokes求解器中压力Poisson方程的并行代数多重网格。

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The focus of this thesis is on a parallel Algebraic Multigrid (AMG) algorithm and its application within the parallel Navier-Stokes finite element (FEM) solver, PHASTA. Specifically we focus on solving the Pressure Poisson Equation (PPE) arising from the finite element discretization of the incompressible Navier-Stokes equations using parallel AMG as the preconditioner to a Conjugate Gradient (CG) solver.;First a review of recent serial and parallel AMG algorithms is provided to set the stage for a detailed description of our state-of-the-art multilevel serial AMG implementation. Classical Ruge-Stuben AMG is set as the base algorithm. It is then altered in several aspects to better fit for our flow problems. Also, recent smoother advancements like polynomial smoothing are tested and implemented with different options. A recently developed external accelerator for multigrid, the General Global Basis (GGB) method, is studied and implemented. In the serial AMG study, a dramatic reduction (usually above 90% in our test problems) in the number of iteration vectors is observed.;The parallelization of the PPE solver is then studied in great detail. The difficulties for AMG are carefully studied. These difficulties include the matrix-matrix product form of PPE from multiplicand matrices that are locally incomplete, the special parallel data structures designed for a simple Krylov solver, and the mesh-based partitioning scheme. These difficulties make it impractical to construct a parallel AMG cycle that is identical to the serial case. A new AMG algorithm for parallelization that works close to the serial one but is easy to parallelize, is then proposed. This new parallel AMG algorithm separates the smoothing process for different levels of AMG, and makes use of the PPE construction at the finest level to apply a complete smoothing operation only at that level. The implementation of this new algorithm is carefully matched within the framework of the current parallel FEM software. A serial validation of the algorithm is also carried out.;The algorithms are also contrasted to assess efficiency. Techniques like freezing setups for multiple solves are studied to increase the efficiency for long time runs in the numerical examples. For several examples tested, significant reduction in the number of iteration vectors does not degrade as the number of processors is increased. The scaling of the algorithm is tested on IBM Bluegene supercomputer, and the excellent computational time scalability of the original FEM plus CG solve is maintained with each algorithm improvement up to 16k processors.
机译：本文的重点是并行代数多重网格（AMG）算法及其在并行Navier-Stokes有限元（FEM）求解器PHASTA中的应用。具体来说，我们专注于解决由不可压缩Navier-Stokes方程的有限元离散化而产生的压力泊松方程（PPE），该方程使用并行AMG作为共轭梯度（CG）求解器的前置条件。提供了一些算法，为详细描述我们最新的多级串行AMG实现奠定了基础。古典Ruge-Stuben AMG被设置为基本算法。然后在几个方面进行更改，以更好地适应我们的流量问题。而且，最近的更平滑的进步（如多项式平滑）已经通过不同的选项进行了测试和实现。研究并实现了最近开发的用于多网格的外部加速器，即通用全局基础（GGB）方法。在串行AMG研究中，观察到迭代向量的数量显着减少（通常在我们的测试问题中超过90％）。;然后，对PPE求解器的并行化进行了详细的研究。对AMG的困难进行了认真研究。这些困难包括局部不完整的被乘矩阵的PPE矩阵矩阵乘积形式，为简单的Krylov求解器设计的特殊并行数据结构以及基于网格的分区方案。这些困难使得构造与串行情况相同的并行AMG循环不切实际。然后提出了一种新的并行化AMG算法，该算法与串行算法相似，但易于并行化。这种新的并行AMG算法将不同级别的AMG的平滑过程分开，并在最高级使用PPE结构仅在该级别上应用完整的平滑操作。在当前并行FEM软件的框架内，已仔细匹配了此新算法的实现。还对算法进行了串行验证。;还对比了算法以评估效率。在数值示例中，研究了诸如针对多个求解的冻结设置之类的技术，以提高长时间运行的效率。对于测试的几个示例，随着处理器数量的增加，迭代向量数量的显着减少不会降低。该算法的缩放比例在IBM Bluegene超级计算机上进行了测试，并且每次算法最多可改进16k处理器，从而保持了原始FEM和CG解算的出色的计算时间可扩展性。

著录项

  • 作者

    Sun, Chun.;

  • 作者单位

    Rensselaer Polytechnic Institute.;

  • 授予单位 Rensselaer Polytechnic Institute.;
  • 学科 Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 2008
  • 页码 127 p.
  • 总页数 127
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 机械、仪表工业;
  • 关键词

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号