Parallel AMG Solver for Three Dimensional Unstructured Grids Using Gpus

Consider a set of points P in three dimensional euclidean space. Each point in P represents a\ud variable and its value is dependent on the value of its neighborhood scaled by predefined constants.\ud The problem is to solve all the variables which reduces to solving a large set of sparse linear equations.\ud This kind of representation arises naturally while solving flow equations in Computational\ud Fluid Dynamics (CFD). Graphics Processing Units (GPUs), over the years have evolved from being\ud graphics accelerator to scalable co-processor. We implement an algebraic multigrid solver for three\ud dimensional unstructured grids using GPUs. Such a solver has extensive applications in Computational\ud Fluid Dynamics. Using a combination of vertex coloring, optimized memory representations,\ud multi-grid and improved coarsening techniques, we obtain considerable speedup in our parallel implementation.\ud For our implementation, we used Nvidia’s CUDA programming model. Our solver\ud is used to accelerate solutions to various problems like heat transfer, Navier-Stokes etc. Our solver\ud achieves 2157 and 29 times speed up for steady state and unsteady state head transfer problem respectively\ud on a grid of size 2.3 million, compared to serial non-multigrid implementation. Our solver\ud provides significant acceleration for solving pressure Poisson equations, which is the most time consuming\ud part while solving Navier-Stokes equations. In our experimental study, we solve pressure\ud Poisson equations for flow over lid driven cavity, laminar flow past square cylinder and plain jet\ud problems. Our implementation achieves 915 times speed up for the lid driven cavity problem on\ud a grid of size 2.6 million and a speed up of 1020 times for the laminar flow past square cylinder\ud problem on a grid of size 1.7 million, compared to serial non-multigrid implementations. For plain\ud jet problem, our solver achieves a speed up of 47 times, compared to serial non-multigrid implementation\ud on a grid of size 2.7 million. We also implement multi GPU AMG solver which achieves a\ud speed up of 1.5 times, compared to single GPU solver for heat transfer problem