集群上的弹性静力问题并行边界元解法及其工程应用

Parallel Boundary Element Method for Elasto-static Problems on Cluster and Its Application

对集群并行环境下的弹性静力问题的并行边界元解法进行了研究和应用.采用结点超行卷帘方案对边界元系统方程组进行存储,实现了计算负载平衡和系统方程的独立并行生成;基于结点超行卷帘分布存储方案,给出了一种求解边界元系统方程组的并行高斯-约当消去方法;采用分子域结点超行卷帘存储,以及分子域并行凝聚和消去的方法处理任意非均匀子域划分的情况;基于微机集群并行计算环境编制了相应的并行程序,进行了数值试验;最后将并行边界元解法在地下洞室开挖效应计算中进行了实际工程应用.计算结果和工程应用表明该方法可以提高边界元分析的计算效率和扩大分析规模.

The parallel Boundary Element Method（BEM）for elasto-static problems on cluster was studied and applied.The node-super-row cycle storage was used to implement the parallel formation of BE equations and load balance.A parallel Gauss-Jordan elimination of BE equations was presented based on node-super-row cycle storage.To solve the arbitrary sub-domain partition problems,the parallel condensation and elimination sub-domain by sub-domain were used based on the node-super-row cycle storage.The programs of these algorithms were developed on PC cluster and the numerical examples were tested.Finally,the parallel BEM was applied to the computation of excavation of the underground cavity.Computing results and engineering application show that the computational efficiency can be improved and larger problem can be analyzed.