Multi-Wavelength Sized Finite Elements for Three Dimensional Elastic Wave Problems

弹性波传播模型存在于许多工程应用中，包括公路和铁路的交通振动、地震诱发的振动和地基施工等。传统的有限元方法在频域内对这些问题进行数值模拟，要求有限元网格相对于波长足够精细，才能得到准确的结果。当通常采用分段线性有限元时，每个较低波长需要大约10个节点，以确保足够的波型分辨率。然而，在高频(小波长)和/或大范围感兴趣的情况下，有限元网格需要大量的单元，因此该过程变得计算量大且不切实际。所提出的工作的目的是用较少的单元精确地模拟三维弹性波问题，能够包含每个节点间距的多个波长，并且不需要在每个频率上细化网格。由此产生的计算效率的提高将使实际感兴趣的问题能够使用大多数工程设计室提供的计算设施来模拟。

Elastic wave propagation modelling arises in many engineering applications, including traffic vibrations from roads and railways, seismic induced vibrations and foundation construction, etc. The numerical modelling of these problems, in frequency domain by the conventional Finite Element Method (FEM), requires finite element grids sufficiently fine in comparison with the wavelengths, to get accurate results. When typically, the piecewise linear finite element is implemented, around ten nodal points per lower wavelength are needed, to ensure adequate resolution of the wave pattern. However, in the case of high frequency (small wavelength) and/or large domain of interest, the finite element mesh requires a large number of elements, and consequently the procedure becomes computationally expensive and impractical. The aim of the proposed work is to accurately model three-dimensional elastic wave problems with fewer elements, capable of containing many wavelengths per nodal spacing, and without refining the mesh at each frequency. The resulting improvement in computational efficiency will enable problems of practical interest to be simulated using computing facilities available in most engineering design offices.