【摘要】 谱元法基于弹性力学方程弱形式基础之上,在有限单元上进行谱展开,从而使该方法具备了有限元适应任意复杂介质模型的韧性和伪谱法的精度,该方法又被称为高阶有限元方法或伪谱法的域分解,同时为地震波传播的数值模拟提供一种方法。本文阐述了基于Legendre多项式的谱元法的理论和推导过程,相对于Chebychev谱元法,Legendre谱元法可以形成对角的全局质量矩阵,这样可以形成显式的时间差分算法,提高运算效率。最后,进行了复杂介质的各向同性地震波数值模拟,结果表明这是数值模拟地震波传播的有效方法。更多还原

【Abstract】 The spectral element method is based on a weak elastic mechanism equation and combines the geometrical flexibility of the finite element method with the accuracy of the pseudospectral method.Hence the method is called the high-order FEM or the domain decomposition of pseudospectral method.It is a new tool for numerical modeeling of elastic wave propagation.Here,the theory and the deducing process of the SEM based on the Legendre polynomials are shown.The Legendre SEM can get diagonal mass matrix relative to the Chebychev SEM,which leads to a very simple explicit time difference scheme with high efficiency.A few of numerical tests are simulated and approved that the SEM is a effective method for modelling of seismic wave propagation.更多还原