High locality and increased intra-node parallelism for solving finite element models on GPUs by novel element-by-element implementation

Abstract

The utilization of Graphical Processing Units (GPUs) for the element-by-element (EbE) finite element method (FEM) is demonstrated. EbE FEM is a long known technique, by which a conjugate gradient (CG) type iterative solution scheme can be entirely decomposed into computations on the element level, i.e., without assembling the global system matrix. In our implementation, NVIDIA's parallel computing solution, the Compute Unified Device Architecture (CUDA), is used to perform the required element-wise computations in parallel. Since element matrices need not be stored, the memory requirement can be kept extremely low. It is shown that this low-storage but computation-intensive technique is better suited for GPUs than those requiring the massive manipulation of large data sets. This study of the proposed parallel model illustrates a highly improved locality and minimization of data movement, which could also significantly reduce energy consumption in other heterogeneous HPC architectures.