Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

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• 作者：Shaolin Liu^a ; Dinghui Yang^a ; ^{dhyang@math.tsinghua.edu.cn} ; Chao Lang^a ; Wenshuai Wang^b ; Zhide Pan^c
• 关键词：Acoustic wave equation ; Symplectic scheme ; Nearly analytic discrete method ; Perfectly matched layers
• 刊名：Computer Physics Communications
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：213
• 期：Complete
• 页码：52-63
• 全文大小：1192 K
• 卷排序：213

文摘

Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge–Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.