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Dispersion analysis of triangle-based spectral element methods for elastic wave propagation

机译:弹性波传播的基于三角频谱元素方法的色散分析

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We study the numerical dispersion/dissipation of Triangle-based Spectral Element Methods (TSEM) of order N ≥ 1 when coupled with the Leap-Frog (LF) finite difference scheme to simulate the elastic wave propagation over a structured triangulation of the 2D physical domain. The analysis relies on the discrete eigenvalue problem resulting from the approximation of the dispersion relation. First, we present semi-discrete dispersion graphs by varying the approximation polynomial degree and the number of discrete points per wavelength. The fully-discrete ones are then obtained by varying also the time step. Numerical results for the TSEM, resp. TSEM-LF, are compared with those of the classical Quadrangle-based Spectral Element Method (QSEM), resp. QSEM-LF.
机译:当结合Leap-Frog(LF)有限差分方案来模拟弹性波在2D物理域的结构化三角剖分上的传播时,我们研究了N≥1阶的基于三角形的光谱元素方法(TSEM)的数值分散/耗散。该分析依赖于色散关系近似所产生的离散特征值问题。首先,我们通过改变近似多项式的度数和每个波长的离散点数来表示半离散色散图。然后通过改变时间步长也可以获得完全离散的信号。 TSEM的数值结果,分别。将TSEM-LF与经典的基于四边形的光谱元素方法(QSEM)进行了比较。 QSEM-LF。

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