SBIR PHASE I: A Global Multi-Grid GMRES Scheme for an Adaptive Cartesian/Prism Flow Solver on Distributed Memory Machines

*9560782王这个小型企业创新研究第一阶段项目建议在分布式内存并行机上为新开发的自适应笛卡尔/棱柱网格流解算器开发和演示一个并行算法。一种全局广义最小残差算法(GMRES)将与显式多重网格预处理器相结合来驱动流动到稳态。在最粗网格上采用递归特征向量二分法(RSB)，在最细网格上采用分治型局部网格偏移(LCM)的混合区域分解方法，以平衡最细网格上的负载。该策略确保了最粗网格的原始结构不会因区域分解而被破坏。为数据通信提供了域间每个多网格级别的一个单元深度的重叠。消息传递将通过并行虚拟机(PVM)包提供。此外，还提出了一种新的通信和计算重叠(CCO)机制，以实现处理器之间的数据同步和零等待时间。由于GMRES算法和显式多网格预处理器都可以有效地并行化，因此整个方法有望在分布式存储并行机上获得很好的性能，无论是同构的还是异质的。网格自动生成和负载平衡方法大大降低了并行计算机网格生成和域分解的开销。可并行化的GMRES多网格求解算法非常适合于分布式存储机器，有望进一步加快流到稳态的收敛速度。如果这一概念在第一阶段得到成功验证，它将在以后的阶段扩展到3D。主要的商业目标是开发一种专门为分布式存储机器设计的计算流体动力学(CFD)代码，这些机器被许多人视为用于大型科学和工程模拟的最具成本效益的计算机体系结构。***

*** 9560782 Wang This Small Business Innovation Research Phase I project proposes to develop and demonstrate a parallel algorithm for a newly developed adaptive Cartesian/prism grid flow solver on distributed memory parallel machines. A global Generalized Minimal RESidual algorithm (GMRES) will be utilized in combination with an explicit multi-grid pre-conditioner to drive flow to steady state. A hybrid domain decomposition method, i.e., a recursive eigenvector bisection (RSB) method on the coarsest grid and a divide and conquer type local cell migration method (LCM) on the finest grid, will be implemented to balance load on the finest grid. The strategy ensures that the original structure of the coarsest grid is not destroyed with domain decomposition. Overlap of one cell deep at each multi-grid level between domains is provided for data communication. Message passing will be provided through a parallel virtual machine (PVM) package. In addition, a novel communication and computation overlap (CCO) procedure is proposed to achieve data synchronization and zero wait time by processors. Since both the GMRES algorithm and the explicit multi-grid pre-conditioner can be effectively parallelized, the overall approach is expected to perform very well on distributed memory parallel machines, both homogeneous and heterogeneous. The automatic grid generation and load balancing approaches drastically reduce the overhead cost associated with grid generation and domain decomposition for parallel computers. The parallelizable GMRES multi-grid solution algorithm is ideally suited for distributed memory machines and is expected to further speed up convergence of flow to steady state. If the concept is successfully proven in Phase I, it will be extended to 3D in later phases. The key commercial objective is to develop a computational fluid dynamics (CFD) code that is specially designed for distributed memory machines, which are viewed by many as the most cost-effective computer archit ecture for large scientific and engineering simulations. ***