大型结构特征值问题的并行EBE－子空间迭代法

本文利用ＥＢＥ策略和预处理共轭梯度法（ＰＣＧ法），将广义特征值问题子空间迭代法中各步的计算都单元化，从而避免了总刚度和总质量矩阵的组集，大大节省了存储量。由此建立的ＥＢＥ－子空间迭代法尤其适宜于并行计算。在银河－２机上的数值算例结果表明，无论是串行，还是并行计算，该方法都能有效提高计算速度。如对模型问题，若网格取４８０，则在串行计算时，ＥＢＥ计算途径较传统的总体计算途径的速度提高倍数达３．２７，而在挂用４个处理机进行并行计算时的ＥＢＥ－子空间迭代法较串行的总体计算途径的速度提高倍数可达１１．４。总之，该方法为一种有效的大型结构动力分析问题的求解方法。

Parallel EBE-Subspace Iteration for Large-Scale Structural Eigenproblems

By the EBE strategy and the preconditioned conjugate gradient method (PCG method),we have developed an EBE-subspace iteration for generalized eigenproblems, in which all computations are performed on the element level. The method not only can save memory space efficiently because of avoiding the formation of the global stiffness and mass matrices,but also is very suitable for parallel computation.The numerical example on YH2 super-computer demonstrated that the above EBE-subspace iteration can speed up the computation largely. For example,when a model problem with 480 elements was run on YH-2 super-computer,the speed of serial EBE-subspace iteration is 3.27 times that of the global computational method,and the proposed parallel EBE-subspace iteration using 4 processors is shown to deliver speed-up as high as 11. 4 with respect to the conventional serial computation methods. In a word,the method is one of the effective solution methods for large-scale structural dynamic analysis.