Optimizing OpenFOAM GPU Solvers

The paper presents preliminary research on improving performance of CFD simulations in OpenFOAM via offloading parts of computations (specifically, solution of linear systems) to a graphics accelerator (GPU). We present a short review of OpenFOAM package and describe porting conjugate gradient method to the GPU architecture using CUDA programming model. Porting the basic algorithm is straightforward, however care should be taken to avoid unnecessary copying over PCI-Express bus. Efficient preconditioning on the GPU is then discussed. We use approximate inverse preconditioning, which can be implemented with good parallelism on the GPU. To amortize the cost of preparing the preconditioner, we allow reuse of preconditioners on the GPU and compute them on the CPU in a helper thread asynchronously. We mention several optimization opportunities: reordering the preconditioner to upper-left triangular form so that CUDA blocks multiplying by denser parts of preconditiner factors are scheduled first; using single-precision storage for the preconditioner to save memory bandwidth; reordering the mesh with nested dissection method from Metis library and using mixed-precision iteration for the conjugate gradient method. Preliminary performance testing results show performance improvement starting from 64000-cell meshes and reaching 2x for a 1-million cell mesh for a non-parallel run. As future work we mention support for parallel runs with MPI, research of other solvers such as multigrid, BiCGStab and IDR, and choosing drop tolerance automatically for the AINV preconditioner.