A scalable Schur-complement fluids solver for heterogeneous compute platforms

摘要

We present a scalable parallel solver for the pressure Poisson equationrnin fluids simulation which can accommodate complex irregularrndomains in the order of a billion degrees of freedom, using a singlernserver or workstation fitted with GPU or Many-Core accelerators.rnThe design of our numerical technique is attuned to the subtletiesrnof heterogeneous computing, and allows us to benefit fromrnthe high memory and compute bandwidth of GPU accelerators evenrnfor problems that are too large to fit entirely on GPU memory. Thisrnis achieved via algebraic formulations that adequately increase therndensity of the GPU-hosted computation as to hide the overhead ofrnoffloading from the CPU, in exchange for accelerated convergence.rnOur solver follows the principles of Domain Decomposition techniques,rnand is based on the Schur complement method for ellipticrnpartial differential equations. A large uniform grid is partitioned inrnnon-overlapping subdomains, and bandwidth-optimized (GPU orrnMany-Core) accelerator cards are used to efficiently and concurrentlyrnsolve independent Poisson problems on each resulting subdomain.rnOur novel contributions are centered on the careful steps necessaryrnto assemble an accurate global solver from these constituentrnblocks, while avoiding excessive communication or dense linear algebra.rnWe ultimately produce a highly effective Conjugate Gradientsrnpreconditioner, and demonstrate scalable and accurate performancernon high-resolution simulations of water and smoke flow.