SBP-SAT方法及其在波动领域的应用

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摘要基于分部求和（summation by parts）方法和同时逼近项（simultaneous approximation terms）技术建立的有限差分方法，具有更高的精度和稳定性。同时在介质几何不连续、参数突变条件具有较大的优势。国内对SBP-SAT方法的相关研究目前较少，论文对该方法的研究背景，方法发展过程进行了介绍并基于SBP-SAT方法和弹性波动理论，结合初边值条件，推导出曲线网格条件下的弹性波动SBP-SAT离散方程。最后，通过数值模拟实现地震波传播过程，介绍该方法在地震数值模拟领域中的应用价值和前景。

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	杨在林1
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	孙铖1
	蒋关希曦1
	杨勇1
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关键词 ： SBP算子, 有限差分法, 边界条件, SAT, 高阶方法, 能量法, 稳定性

Abstract：Summation by parts with simultaneous approximation terms have a set of properties that leading to provable time stability and higher order spatial discretization of partial differential equations. The finite difference methods based on this theory can establish the scheme that have incomparable advantages for simulating geometric discontinuity or complex media. At present, there are few researches on SBP-SAT methods in China. Therefore, this paper provides the history of SBP-SAT methods and its application to the numerical solution of partial differential equations. Then, the discrete equations of elastic wave under the curvilinear coordinates are derived. At last, combining initial value conditions and boundary conditions, a simple simulation for imitating seismic wave propagation is functioning. The potential and the application value are present.

Key words： summation by parts operators finite difference methods boundary conditions simultaneous approximation terms higher order methods energy method stability

收稿日期: 2019-02-25 出版日期: 2020-06-15

引用本文:

杨在林1,2，孙铖1，蒋关希曦1，杨勇1,2. SBP-SAT方法及其在波动领域的应用[J]. 振动与冲击, 2020, 39(12): 150-157.
YANG Zailin1, 2,SUN Cheng1,JIANG Guanxixi1,YANG Yong1,2. A SBP-SAT method for the numerical solution and its application in the wave motion. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(12): 150-157.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I12/150

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