Performance Analysis of Different Iterative Solvers Parallelized On GPU Architecture

Abstract

Most Computational Fluid Dynamics (CFD) applications solve the Naiver-Stokes equations using various discretization methods like Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), etc. The most compute-intensive process in CFD algorithms is the pressure Poisson solver. Solving the pressure Poisson equation requires the solution of a set of linear simultaneous equations. As the problem size/complexity increases, so does the effort and time invested in solving the equations. This study presents fast and robust iterative solvers and the acceleration of the same using the Graphics Processing Unit (GPU) architecture. Serial versions of the codes are implemented in the C language and the parallelization on GPU is achieved using Compute Unified Device Architecture (CUDA). For this study, a two-dimensional heat conduction problem is considered. FDM is used for discretization. Iterative solvers Conjugate Gradient and Multi Grid methods have been implemented in serial and parallel. The performance enhancement with single GPU and CPU system over a single CPU in terms of computing time is reported. It is seen that multigrid algorithms are superior in convergence and nearly 13 times speed-up has been obtained through GPU acceleration using CUDA, for a grid size of 2048 X 2048. The tests have been done on a cluster with Intel(R) Xeon(R) CPU E5-2670 CPU and NVIDIA K10 GPU.