Efficient AMG on Heterogeneous Systems

Abstract

In many numerical simulation codes the backbone of the application covers the solution of linear systems of equations. Often, being created via a discretization of differential equations, the corresponding matrices are very sparse. One popular way to solve these sparse linear systems are multigrid methods - in particular AMG - because of their numerical scalability. As the memory bandwidth is usually the bottleneck of linear solvers for sparse systems they especially benefit from high throughput architectures like GPUs. We will show that this is true even for a rather complex hierarchical method like AMG. The presented benchmarks are all based on the new open source library LAMA and compare the run times on different GPUs to those of an efficient OpenMP parallel CPU implementation. As the memory access pattern is especially crucial for GPUs we have a focus on the performance of different sparse matrix formats.