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

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*** 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. ***