地震波动方程的局部间断有限元方法数值模拟

Numerical simulation of seismic wave equation by local discontinuous Galerkin method

近年来,随着地震波数值模拟对计算精度和效率的要求越来越高,间断有限元方法开始受到越来越多的关注.本文中,针对具有吸收边界条件的二维地震声波波动方程,作者提出了一种基于局部间断有限元方法的数值模拟算法.该算法在空间上使用局部间断有限元方法进行离散,在时间上采用了显式蛙跳格式.在这种时空离散的组合方式下,每个时间步上,此算法在空间剖分的每个单元上的求解计算是相互独立的,因而具有极高的并行性.通过数值算例,我们将该算法与连续有限元方法进行了比较.结果表明,本算法不仅具有对起伏构造的良好适应性,而且在计算效率和计算精度等方面,都具有优越性.

In recent years, along with the growing demands for accuracy and efficiency in numerical simulation of seismic wave-field, discontinuous finite element methods begin to attract more and more attentions. In this paper, a numerical simulating algorithm based on local discontinuous Galerkin method is proposed for the 2-D seismic acoustic wave equation, which is imposed on by an absorbing boundary condition. In this algorithm, local discontinuous Galerkin method is applied to spatial discretization, while explicit Leap-Frog method is used for temporal discretization. With this combined pattern, computational process on every spatial element is independent of each other, which causes the algorithm to be highly parallelizable. Numerical experiments, in which this algorithm is compared with continuous finite element method, indicate that this algorithm not only obtains preferable simulation effect when dealing with rugged topography, but also has advantages over continuous finite element method in computational efficiency and accuracy.