Parallel Finite Element Computation on Personal Computer Cluster

• Main Authors: Huang Chien Chang, 黃建彰
• Other Authors: 何旭彬
• Format: Others
• Language: zh-TW
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/73443419702644156041

碩士 === 國立成功大學 === 機械工程學系 === 88 === Abstract Finite Element Method is a numerical method of seeking the approximate solution by discretizing the structure or continuum into a finite degree of freedom system and then solving the set of equations : Ku = f. When the mechanical problems are more and more complicated, a huge amount of computations will take a lot of computer time. To save the computation time, we parallelize two iterative methods : Jacobi-Conjugate Gradient Method (J-CG) and SSOR-Conjugate Gradient Method (SSOR-CG) to solve the set of equations on a personal computer cluster which is composed by two dual-CPU personal computers. We analyze the results and evaluate the efficiency of iterative methods with parallel computing on personal computer cluster. We proceed our evaluation by parallelizing the most time-consuming precedures of the two methods : sparse matrix-vector multiplication and the solve of the set of equations of upper/lower triangular sparse matrix. The result shows that : choosing J-CG to solve a finite element problem , we can get a speed ratio of 1.8 and 3.0 for using 2 and 4 CPUs；choosing SSOR method with initially changing the structure of stiffness matrix, we successfully parallelize the sequential procedures and get a speed ratio of 1.9 and 3.0 for using 2 and 4 CPUs. Overall, the computing speed is raised with the increase of the number of CPU, also the effect of parallelization can be better in the problems with more nodes. This result in this reseach can be the foundation of parallel finite element computation on personal computer cluster with larger size.