Order-corrected symplectic finite element method for elastic wave modelling

Abstract

The advantage of the finite element method (FEM) lies in its flexibility in addressing rugged interfaces in complex geological models. However, the efficiency of the FEM is relatively low for large-scale seismic wave modelling. Here, we introduce an order-corrected symplectic FEM (OCSFEM) with structure-preserving properties and parsimonious memory requirements for the elastic wave equation. In this method, the storage of the large sparse stiffness matrix is changed to the storage of the element Jacobian matrix. An efficient order-corrected symplectic method with third-order temporal accuracy is combined with a triangle-based FEM to construct the OCSFEM. The structure-preserving characteristics and high efficiency of the OCSFEM facilitate the high-fidelity modelling of large-scale and long-term wave phenomena. Complex and large-scale numerical examples show that the OCSFEM exhibits low numerical dispersion and high stability compared with conventional methods, such as the second-order symplectic FEM.

KEYWORDS:

• Finite element method
• order-corrected symplectic method
• elastic wave equation
• numerical dispersion
• stability condition

Acknowledgements

We greatly appreciate the critical suggestions from three anonymous reviewers, which greatly improved the quality of the paper. This research was mainly supported by the research grant from the National Institute of Natural Hazards, Ministry of Emergency Management of China (Grant No. 2DJ2019-18). B. Su was also supported by the National Natural Science Foundation of China (Grant Nos. 41604034 and 41804051), China Postdoctoral Science Foundation (Grant No. 2018M641433) and Doctoral Fund of SWUST (Grant No. 19zx7142).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was mainly supported by the research grant from the National Institute of Natural Hazards, Ministry of Emergency Management of China [grant number ZDJ2019-18]. B. Su was also supported by the National Natural Science Foundation of China [grant numbers 41604034 and 41804051], China Postdoctoral Science Foundation [grant number 2018M641433] and Doctoral Fund of SWUST [grant number 19zx7142].