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基于辛格式的谱元法及其在横向各向同性介质波场模拟中的应用

汪文帅1,2, 李小凡3   

  1. 1. 宁夏大学数学计算机学院, 银川 750021;
    2. 中国科学院地质与地球物理研究所, 北京 100029;
    3. 中国科学院地质与地球物理研究所, 北京 100029
  • 收稿日期:2011-12-01 出版日期:2013-03-15 发布日期:2013-03-12
  • 基金资助:

    国家自然科学基金 (41174047, 40874024, 41204041)和国家重点基础研究发展计划"973"计划(2007CB209603).

汪文帅, 李小凡. 基于辛格式的谱元法及其在横向各向同性介质波场模拟中的应用[J]. 数值计算与计算机应用, 2013, 34(1): 20-30.

Wang Wenshuai, Li Xiaofan. THE SEM BASED ON SYMPLECTICAL SCHEMES AND ITS APPLICATION IN MODELING THE WAVE PROPAGATION IN TRANSVERSELY ISOTROPIC MEDIA[J]. Journal of Numerical Methods and Computer Applications, 2013, 34(1): 20-30.

THE SEM BASED ON SYMPLECTICAL SCHEMES AND ITS APPLICATION IN MODELING THE WAVE PROPAGATION IN TRANSVERSELY ISOTROPIC MEDIA

Wang Wenshuai1,2, Li Xiaofan3   

  1. 1. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China;
    2. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China;
    3. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
  • Received:2011-12-01 Online:2013-03-15 Published:2013-03-12
基于分部的Runge-Kutta离散形式, 给出了一种新的三阶辛积分算法, 数值试验表明,长时程计算时该算法具有好的控制误差累积的能力; 与有限差分法进行空间域离散相结合, 通过数值试验进一步说明算法的有效性. 注意到位移波动方程通过谱元离散后的微分方程组, 完全符合新推导的三阶辛算法离散所需形式, 因此将该三阶辛算法与谱元法结合具有很好的优势, 并通过对横向各向同性介质弹性波场的模拟, 结果显示不但成功模拟了波的传播特性, 而且相对于传统算法, 优势明显.
A new three-stage third-order solution (NTSTO) to symplectical schemes is obtained based on partitioned Runge-Kutta form, several numerical results show that, the scheme is excellent in suppressing residual increase. Combining finite difference(FD) in spatial discretization with the new symplectical scheme in temporal discretization, the further numerical experiments are provided and the results also show that the method is effective. The form is completely consistent with the requirements of the symplectical scheme in time domain when the elastic wave equations are discretized using spectral element methods(SEM) in space domain. So it is natural to solve the elastic wave equations using the symplectical scheme combined with the spectral element methods (NTSTO-SEM). Finally, the algorithm is employed to simulate wave propagation in transversely isotropic media, the results show that the performance is good and superior to classical algorithms, such as Newmark method combined with SEM (Newmark-SEM) and Runge-Kutta method of third-order combined with SEM (RK3-SEM).

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