Research Initiation Award: Overcoming the Multi-Frequency and Non-Uniqueness Problems of the Boundary Element Method in Elastodynamics

针对弹性动力学中边界元方法的多频性和不唯一性问题，提出了几种新的公式。对于多频率问题，提出了两种改进的边界元技术，使全频谱分析成为可能和实用。第一种方法是在频域内插中和边界元系数矩阵；第二种方法是在空间域内插格林函数。这两种技术都适用于超级计算机上的向量化和并行化。对于非唯一性问题，提出了两种“增强型主元”方法，以保证外部波传播问题边界元解的唯一性和精度。基于建议公式的矢量化和并行化代码也将被制作。应用领域包括结构振动、弹性波传播和土-结构相互作用。

Several new formulations are proposed to overcome the multi- frequency and non-uniqueness problems of the boundary element method in elastodynamics. For the multi-frequency problem, two improved boundary element techniques are proposed to make the analysis for an entire frequency spectrum possible and practical. The first technique is to interpolate the "neutralized" boundary element coefficient matrices in the frequency domain; the second technique is to interpolate the Green function in the spatial domain. Both techniques are suitable for vectorization and parallelization on supercomputers. For the non-uniqueness problem, two "enhanced CHIEF" methods are proposed to ensure the uniqueness and accuracy of the boundary element solution for an exterior wave propagation problem. Vectorized and parallelized codes based on the proposed formulations will also be made. Application areas include structural vibration, elastic wave propagation and earth- structure interaction.