基于EBE方法的三维有限元并行计算

Parallel 3-D finite element analysis using jacobi-conditioned conjugate gradient based on element-by-element policy

在水利工程中,施工过程的模拟、动力的时域分析、开裂计算等,都对大规模并行计算提出了迫切的需求。然而,基于高斯消去的有限元直接解法,通常会占用大量的内存,并花费大量的CPU时间。而水利工程中的问题多为大带宽问题,这些问题更为突出。基于EBE-PCG方法的有限元方法,可以避免形成整体刚度矩阵,进而,显著减少内存的需求。而且,这种方法可以有效地并行实现,为大规模数值计算提供了可能。采用基于EBE策略的Jacobi预处理共轭梯度法,编制了有限元计算程序,并成功应用于溪洛渡、锦屏等工程的大规模数值分析。结果表明,对水利工程中的大带宽问题,该方法是一种很有效的并行计算方法。

In engineering problems, large scale numerical analysis increase the demand for high-speed computing. To meet the demand, parallel computing is proposed to increase the calculational scale and shorten computing time. Direct methods, i.e., those based upon Gaussian elimination, usually require very large amounts of both CPU time and storage. However, iterative procedures based on element-by-element (EBE) preconditioned conjugate gradients (PCG) can avoid the formation and factorization of a global system matrix. Thus it can circumvent the difficulty in the direct methods and is well suited for shared-memory architectures. But on the distributed-memory architectures, the time of inter-processor communication is a key factor to the efficient performance of parallel solver. In this paper, the authors present an EBE-PCG solver which adopt Jacobi- conditioned conjugate gradient algorithm. Two examples on analysis of arch dams in this paper demonstrate that this solver is very applicable for large bandwidth problems.