Lax-Wendroff集中质量有限元法地震波场模拟

A Lax-Wendroff lumped mass finite element method for seismic simulations

为了高精度、高效地震波模拟的需要,本文在空间离散上运用集中质量三角网格有限元法求解弹性波方程,在时间离散上运用Lax-Wendroff方法获得时间四阶精度,提出了模拟弹性波传播的Lax-Wendroff集中质量有限元法(LWFEM)。为了防止人工截断边界而引起的虚假反射,构造了二阶位移形式的PML吸收边界条件。在周期性网格中,构造LWFEM频散分析的一般特征值问题,得到了LWFEM的稳定性条件。在数值实验中通过与中心差分有限元法(CDFEM)、Runge-Kutta有限元法(RKFEM)以及Newmark谱元法(NSEM)等常见方法的对比,证实了LWFEM弹性波模拟的高效、高精度性及对复杂模型的适应性。

Using lumped mass finite element method with triangle mesh to solve elastic wave equations and Lax-Wendroff method to obtain fourth-order temporal accuracy, we develop Lax-Wendroff lumped mass finite element method(LWFEM)for elastic wave simulations.To avoid artificial boundary reflections,the second-order PML absorbing boundary condition(PML ABC)in terms of displacement is constructed.The stability criterion on aperiod grid is analyzed based on constructing generalized eigenvalue problems of the finite element method.In numerical experiments,the accuracy and efficiency are discussed by comparing with conventional methods such as central difference finite element method(CDFEM),Runge-Kutta finite element method(RKFEM)and Newmark spectral element method(NSEM).Numerical results demonstrate the validity of LWFEM in complex models.