多样本环境下Chebyshev加速算法在单样本有限元中的应用

APPLICATION OF CHEBYSHEV SPEED ALGORITHM IN SINGLE-SAMPLE FINITE ELEMENT METHOD UNDER MULTI-SAMPLE CONDITION

研究在多样本环境下单样本的有限元计算方法,提出了样本的计算冗余度和多样本冗余度压缩计算两个问题.证明了一般分裂迭代法与Neumann法等价.在此基础上,将Chebyshev加速技术引入多样冗余度压缩计算,建立了一种加快单样本计算的方法,算例验证了这种方法的有效性.

The single-sample finite element method under multi-sample condition was studied. The sample computation redundancy and the redundant compressed algorithm were brought forward. The general iteration algorithm was proved equivalent to the Neumann method. On the basis of these results,Chebyshev speed algorithm was brought into the multi-sample FEM to establish a new redundant compressed algorithm, i. e. , Single-Sample Finite Element Method, whose efficiency was shown by numerical examples.