高阶有限元在分析地震波传播中的有效性
Efficiency of Higher Order Finite Elements for the Analysis of Seismic Wave Propagation
摘要：
分析线性阻尼介质中波的传播问题，必须同时考虑波的传播特性和衰减过程。为了通过有限差分或有限元法进行精确的数值研究，必须考虑一个称为波的数值色散的特定问题。数值频散可能会增加传播过程中的数值误差，因为波速（相位和群）取决于数值模型的特征。本文对线性本构关系的有限单元法波传播数值模拟进行了分析和讨论。本文通过研究高阶15节点有限元对数值色散的精度的一维计算来分析数值色散。关于波衰减的数值分析，经典瑞利假设的流变学解释已在该杂志中提出。
英文摘要：
The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one must consider a specific problem known as the numerical dispersion of waves. Numerical dispersion may increase the numerical error during the propagation process as the wave velocity (phase and group) depends on the features of the numerical model. In this paper, the numerical modelling of wave propagation by the finite element method is thus analyzed and dis-cussed for linear constitutive laws. Numerical dispersion is analyzed herein through 1D computations investigating the accuracy of higher order 15-node finite elements towards numerical dispersion. Concerning the numerical analy-sis of wave attenuation, a rheological interpretation of the classical Rayleigh assumption has for instance been previously proposed in this journal.
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