Advanced Optimizations of An Implicit Navier-Stokes Solver on GPGPU based on a Fine-grained BILU solver

摘要

General-purpose graphics processing units (GPGPU) is a promising technology for massively parallel high-performance computation. Their heterogeneous nature requires careful designs of parallel algorithms and data management, which imposes a great hurdle for general scientific computation. With the emergence of more sophisticated programming tools, the utilization of GPGPU in CFD applications has been growing rapidly. One of the more challenging subjects is the adoption of implicit CFD solvers on GPGPU, which has been proven particularly difficult due to the strong data-dependency of efficient iterative linear solvers or preconditioners. Our study of an implicit Navier-Stokes solver on GPGPU leads to the development of highly efficient GPGPU algorithms for block-incomplete LU (BILU) factorization and triangle solve using fine-grained parallelization techniques. The fine-grained BILU (FGBILU) scheme based on wavefront ordering offers concurrent computation at O(n~2N~2) scale (n is the number of unknowns in PDE and N is the linear dimension of the computation domain), while preserving mathematical efficiency and robustness of the original sequential global BILU.