A Parallel Algebraic Multigrid Solver on Graphics Processing Units

Abstract

Abstract. The paper presents a multi-GPU implementation of the preconditioned conjugate gradient algorithm with an algebraic multigrid preconditioner (PCG-AMG) for an elliptic model problem on a 3D unstructured grid. An efficient parallel sparse matrix-vector multiplication scheme underlying the PCG-AMG algorithm is presented for the manycore GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster and a multi-GPU configuration with eight GPUs is about 100 times faster than a typical server CPU core.

A Brief History of the Parallel Dawn in Karl-Marx-Stadt/Chemnitz

“…The discretization is based on unstructured tetrahedrons. We use therein our own parallel algebraic multigrid (AMG) solver that solves the large systems of equations in parallel [30].…”

A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

“…These devices can actually be utilized in a much wider range of applications than just 3D graphics. Because of this, several compute-intensive software programs seek to take advantage of the GPUs in their operation, and GPUs are already widely used in scientific computing as well (see, e.g., [56,87,86,97,98]). …”

Accelerating algebraic multigrid solvers on NVIDIA GPUs

“…Chen et al designed another hybrid matrix format HEC and SpMV algorithm [26], Krylov solvers [27,28] and classical AMG solver [29]. Haase et al developed a parallel AMG solver using a GPU cluster [30]. Bell et al from NVIDIA investigated fine-grained parallelism of AMG solvers using a single GPU [31].…”

“…For the classical AMG solver, two coarsening strategies, the Ruge-Stüben method and the CLJP method, are implemented. Several interpolation operators are investigated, including standard interpolation, direct interpolation, multi-pass interpolation and an interpolation operator introduced by [30]. The smoothers are unified by a simple formula, and a group of general purpose smoothers are implemented on the GPUs, including the Jacobi, damped Jacobi, weighted Jacobi, block Jacobi, Gauss-Seidel, block-Jacobi-Gauss-Seidel, and polynomial smoothers.…”