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Parallel Solution Strategies for Triangular Systems arising from Oil Reservoir Simulations

机译：油藏模拟产生的三角系统并行解决方案策略

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The results so far appear to indicate that promising alternatives to standard backward and forward eliminations in a parallel programming environment do exist. At present a lack of available hardware prohibits the author from proving their worth further here, but at least the timing models themselves reflect how comparatively inefficient orthodox parallel triangular solvers are. Even though not every banded matrix of this type can be expected to reduce to just one sparse factor, solutions based on several sparse factors would still appear to be competetive with the existing elimination process. The 2 colour, or red/black reordering strategy also merits further investigation. This method is particularly appealing because formulating the actual reordering is fairly trivial once the nx,ny,nz parameters of the problem are known. The main disadvantage comes with the effect both reorderings may have on the convergence rate of the problem [4]. Initial investigations have found a three fold increase in the number of iterations when preconditioned TFQMR is applied to a the 2 colour reordered problem. Whether such a degredation in performance is acceptable within the context of the overall solution, or is even advisable regarding the quality of the solution, is yet to be seen. With this in mind, we may find ourselves limited to strategies (5) and (8), which only reorder when solving the triangular factorized systems in the preconditioning stage.
机译：到目前为止的结果似乎表明在并行编程环境中确实存在有希望的标准后向和前向消除方法的替代方案。目前，缺乏可用的硬件阻止了作者在这里进一步证明其价值，但至少时序模型本身反映了相对低效的正统并行三角求解器。即使不是所有这种类型的带状矩阵都可以预期减少到一个稀疏因子，但基于多个稀疏因子的解决方案仍然看起来可以与现有消除方法竞争。 2色或红色/黑色重新排序策略也值得进一步研究。这种方法特别吸引人，因为一旦知道问题的nx，ny，nz参数，制定实际的重新排序就变得很简单。主要缺点在于两种重新排序都可能对问题的收敛速度产生影响[4]。初步研究发现，将预处理的TFQMR应用于2色重排序问题时，迭代次数增加了三倍。在整个解决方案的范围内，这种性能下降是否可以接受，或者就解决方案的质量而言甚至是可取的，还有待观察。考虑到这一点，我们可能会发现自己局限于策略（5）和（8），它们仅在预处理阶段求解三角分解系统时才会重新排序。

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  • 来源
  • 会议地点 Milan(IT);Milan(IT)
  • 作者

    A. Sunderland;

  • 作者单位

    Institute of Advanced Scientific Computation, University of Liverpool, Liverpool, U.K.;

  • 会议组织
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 TQ4;
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