DOWNLOAD POSTER PDFWe present an efficient, robust aggregation based algebraic multigrid preconditioning tech-nique for the solution of large sparse linear systems. These linear systems arise from the dis- cretization elliptic PDEs in various applications. Some of the applications include reservoir simulations, heat equations and incompressible Navier-Stokes equations. Algebraic multigrid methods provide grid independent convergence for these problems, making them one among the best for the solutions of elliptic PDEs in practical applications. The method involves two stages, setup and solve. In the setup stage, hierarchical coarse grids are constructed through aggregation of the fine grid nodes. These aggregations are obtained using a set of maximal independent nodes from the fine grid nodes. The aggregations are combined with a piecewise constant (unsmooth) interpolation from the coarse grid solution to the fine grid solution, ensuring low setup and interpolation cost. The grid independent convergence is achieved by using recursive Krylov iterations (K-cycles) in the solve stage. An efficient combination of K-cycles and standard multigrid V-cycles is used as the preconditioner for the Conjugate Gradient method. We perform the setup on CPU using C++ and STL libraries and solve using the kernels written in a unified threading language OCCA for performance portability of the implementations on traditional CPU and modern many core GPU architectures. We present a comparison of performance of OCCA kernels when cross compiled with OpenCL, CUDA, and OpenMP at runtime on GPUs and CPUs.
