弹性波传播模拟的Chebyshev谱元法

A Chebyshev spectral element method for elastic wave modeling

通过在每一个单元中采用谱展开近似,Chebyshev谱元法兼具了有限元处理边界及复杂结构的灵活性和谱方法的快速收敛特性,为弹性波传播的数值模拟提供了一种有效工具。从加权余量原理出发,详细阐述了Chebyshev谱元法用于弹性波传播模拟的基本理论及相应数学公式.给出了使用Chebyshev正交多项式展开得到的,存在等参变换时有关单元质量矩阵和单元刚度矩阵的精确积分公式。同时应用逐元技术极大地减少了内存和计算需求.最后,两个数值算例被用于验证这种谱元方法的高精度和强适应性。

The Chebyshev spectral element method which uses spectral expansion in each element, combines the ad- vantages of spectral method with those of finite element method. It provides an efficient tool in simulating elastic wave equation in complex medium. Based on wemk form of elastodynamic equation, the mathematical formulations for spectra] element method are presented by using Chebyshev orthogonal function. And the analytical integrate results in elastic problem with general mapping are presented using Chebyshev approach. The element by element method is introduced to reduce the memory and computation cost requiring. At last, some numerical examples are simulated to demonstrate the spectral accuracy and the efficiency in dealing with complex problem obtained by the Chebyshev spectral element method.