The Research and Optimization of Parallel Finite Element Algorithm based on MiniFE

TL;DR

This paper analyzes and optimizes the parallel finite element method implementation based on MiniFE, focusing on the SpMV kernel, achieving an average performance increase of 8.31% through storage format and hybrid programming improvements.

Contribution

It introduces specific optimizations for MiniFE's SpMV kernel using BCRS format and hybrid MPI+OpenMP, enhancing parallel FEM performance.

Findings

Optimized MiniFE's SpMV kernel with BCRS format.

Hybrid MPI+OpenMP improves synchronization efficiency.

Performance increased by an average of 8.31%.

Abstract

Finite element method (FEM) is one of the most important numerical methods in modern engineering design and analysis. Since traditional serial FEM is difficult to solve large FE problems efficiently and accurately, high-performance parallel FEM has become one of the essential way to solve practical engineering problems. Based on MiniFE program, which is released by National Energy Research Scientific Computing Center(NERSC), this work analyzes concrete steps, key computing pattern and parallel mechanism of parallel FEM. According to experimental results, this work analyzes the proportion of calculation amount of each module and concludes the main performance bottleneck of the program. Based on that, we optimize the MiniFE program on a server platform. The optimization focuses on the bottleneck of the program - SpMV kernel, and uses an efficient storage format named BCRS. Moreover, an improving plan of hybrid MPI+OpenMP programming is provided. Experimental results show that the optimized program performs better in both SpMV kernel and synchronization. It can increase the performance of the program, on average, by 8.31%. Keywords : finite element, parallel, MiniFE, SpMV, performance optimization