CR-1998-208435 ICASE Report No . 98-24 Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD
CR-1998-208435 ICASE Report No . 98-24 Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD
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发表时间：
1998
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通讯作者：
W. Gropp;D. Keyes;L. C. McInnes
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作者：
W. Gropp;D. Keyes;L. C. McInnes
隐式求解方法在具有不同时间和空间尺度的偏微分方程建模的应用中非常重要。由于此类应用需要高分辨率和合理的周转时间，因此“常规”并行化至关重要。提出了伪瞬态无矩阵 Newton-KrylovSchwarz (ΨNKS) 算法框架作为答案。我们证明，对于 M6 机翼的三维跨音速欧拉流这一经典问题，ΨNKS 可以通过自适应伪瞬态延拓和牛顿法同时实现全局、渐近快速收敛。 • 通过延迟同步和 Krylov 线性求解器中有利的通信到计算缩放，实现隐式方法的合理并行性； • 通过关注分布式内存和高速缓存局部性，特别是通过 Schwarz 预处理器，实现高每处理器性能。 ΨNKS 方法的两个令人沮丧的特征是它们对基础 PDE 离散化编码的敏感性以及必须选择大量参数来控制收敛。因此，我们根据我们的经验以及对 ΨNKS 各种算法组件的文献的阅读，提炼出了一些建议，并且我们描述了这里使用的求解器的免费可用的、基于 MPI 的便携式并行软件实现。
Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, “routine” parallelization is essential. The pseudo-transient matrix-free Newton-KrylovSchwarz (ΨNKS) algorithmic framework is presented as an answer. We show that, for the classical problem of three-dimensional transonic Euler flow about an M6 wing, ΨNKS can simultaneously deliver • globalized, asymptotically rapid convergence through adaptive pseudo-transient continuation and Newton’s method; • reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and • high per-processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of ΨNKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. We therefore distill several recommendations from our experience and from our reading of the literature on various algorithmic components of ΨNKS, and we describe a freely available, MPI-based portable parallel software implementation of the solver employed here.