弹性波二维散射快速多极子间接边界元法求解

求解方程的稠密矩阵特征极大削弱了传统边界元法在求解大规模实际工程问题中的优势。为此,结合快速多极子展开技术,发展一种新的高精度快速间接边界元方法,用于求解大尺度或高频弹性波二维散射问题。以全空间孔洞周围SH波散射为例,给出了具体求解步骤。算例分析表明该方法具有很高的计算精度和求解效率,同时能够大幅度降低计算存储量,可在目前主流计算机上实现上百万自由度弹性波散射问题的快速求解。最后以半空间中凹陷场地对SH波的高频散射为例,讨论了凹陷周围高频波散射的基本特征,可为峡谷地形中大型工程抗震设计提供部分理论依据。

FMM-IBEM SOLUTION TO TWO-DIMENSINAL SCATTERING OF ELASTIC WAVES

Dense matrix equations greatly weaken the advantages of traditional boundary element methods for solving large scale practical engineering problems. Therefore, combined with the fast multipole expansion technique, a new rapid indirect boundary element method is developed for solving large scale or high frequency elastic wave scattering problems. Taking the scattering of an SH wave around a cavity as an example, the detailed solution process of FMM-IBEM is presented. It is verified that this method greatly improves computing speed and reduces storage requirements, meaning that elastic wave scattering problems with millions of DOF’s can be solved effectively and accurately on an ordinary personal computer. Finally, a high frequency scattering problem involving an SH wave scattered by a canyon in elastic half space is solved, and some important characteristics of the high frequency wave scattering are discussed based on the numerical results, which can provide a theoretical basis for seismic design of large engineering projects located in canyons.