有限元法与伪谱法混合求解弹性波动方程

在地震波场数值模拟中,有限差分法、有限元法和伪谱法都是常用的基本方法,但它们各有不同的适应性和优缺点,如有限差分法、有限元法都存在减弱网格频散和提高计算效率的矛盾,而伪谱法的网格频散小且计算效率高.有限差分法和伪谱法在处理地表结构复杂或地表剧烈起伏以及地下结构复杂的情况时存在较大的难度,而有限元法可较为理想地拟合起伏地表和任意弯曲界面,且可方便地处理自由边界条件和界面边界条件.尝试将有限元法和伪谱法相结合,形成地震波场数值模拟的一种混合方法,利用二者的优点,克服二者的缺点,达到既减弱网格频散又提高计算精度和效率的目的.并采用所谓的‘过度区域‘技术解决两种不同算法的衔接问题.模拟实例表明,给出的混合模拟方法不失为弹性波场数值模拟的一种有效方法.

Hybrid method combining finite difference and pseudospectral method for solving the elastic wave equation

Many different methods proposed for modeling waves have their own range of validity and limitation.For example.Finite different(FD) techniques have been widely used in wave modeling.One advantage of FD techniques is their ability to model wave propagation in media with fairly general spatial variation of elastic properties. However ,particularly for models with sharp discontinuities,FD schemes are by no means free from accuracy problem. Finite element(FE) method has been shown to be an efficient alternative tool for modeling wave propagation in complex structures. Pseudo-spectral method(PS) has advantages of higher accuracy and lower dispersion than FD method and FE method,but ,there exists difficulties in dealing with free surface boundary condition as FD method. Here we develop a hybid method which couples the FE method with PS method to model near boundary wave field and inner wave field respectively, to use the advantages of the two methods and to increase the numerical accuracy and computation efficiency. The problems concerning connection of the two methods are solved by introducing the transition region between near boundary and inner region.Numerical examples have demonstrated the validity and the advantages of the hybid method given here.