Architecting the finite element method pipeline for the GPU

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:257

Article

Whitaker, Ross T.¹ 

[1] Univ Utah, Sch Comp, Salt Lake City, UT 84112 USA

关键词: Finite element method (FEM);    Graphical processing units (GPUs);    Algebraic multigrid (AMG);   

DOI  :  10.1016/j.cam.2013.09.001

来源: Elsevier

【 摘 要 】

The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (CPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the CPU. First we propose an efficient CPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the CPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multigrid (AMC) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of CPU. Comparison of our on-CPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 x speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51x versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other CPU-based, sparse, linear solvers. Published by Elsevier B.V.

【 授权许可】

Free