並列タイトル等Evaluation of Finite Element Analysis on the Parallel Simulation Machine Cenju
タイトル（掲載誌）航空宇宙技術研究所特別資料 = Special Publication of National Aerospace Laboratory SP-16
一般注記出版タイプ： NA
This paper describes parallelization of Finite Element Methods (FEM) on the Parallel Simulation Machine Cenju. One of the most time consuming problems in FEM which we decided to investigate is nonlinear dynamic finite element analysis. The main loop of the nonlinear dynamic finite element analysis is the loop based on Newton-Raphson method which is composed of the following two stages, namely: 1. Calculation of the Stiffness Matrix 2. Solution of a set of linear equations. We decided to tackle the above two problems independently. Generation of the Stiffness Matrix consists of: Process 1 Per Element Calculation in which the element stiffness matrix as well as the reactance force is calculated for each element. Process 2 Accumulative Calculation in which the element stiffness matrices are combined to form the global stiffness matrix. It is quite straightforward to parallelize Process 1, just allocate a group of elements to processors and let them calculate the values for the elements. On the other hand, Process 2 is not so easy to parallelize. We tried two strategies to parallelize Process 2. By eliminating the serial bottleneck, we were able to attain a speed-up of 48 on a 64 processor system. For parallelizing solution of linear equations, we tried two approaches. 1. Prallelizing LU-Factorization. 2. Parallelizing Conjugate Gradient Methods. We first evaluated parallelizing LU-Factorization on a comparatively small set of data. However, due to insufficient amount of parallelism, the speed-up was low-2.9 using 7 processors. So, we decided to tackle parallelizing the conjugate gradient method. The conjugate gradient method we chose is Scaled Conjugate Gradient Method (SCG) which was developed by Hayami for vector computers. For a large scale matrix (8,904 by 8,904) we were able to attain a speed-up of 36 on a 64 processor system.
資料番号: NALSP0016014
レポート番号: NAL SP-16
連携機関・データベース国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
提供元機関・データベース宇宙航空研究開発機構 : 宇宙航空研究開発機構リポジトリ