Proposal of extended boundary integral equation method for rupture dynamics interacting with medium interfaces

在这里，我们提出了一个扩展的BIEM（XBIEM），适用于由均匀子区域组成的非均匀有界介质。在XBIEM的公式中，子区域的界面被视为扩展边界，并在其上额外推导出边界积分方程。这最初被称为在频域中分析地震波传播的多区域方法，在这里被用于在时域中与介质界面相互作用的破裂动力学。所有的边界积分方程都是通过在扩展边界上施加边界条件来完全耦合的，然后在时空离散后进行数值求解。本文给出了反平面非平面问题的离散应力核的显式表达式和数值实现方法，并在两个典型的平面断层问题中进行了验证。

Here we propose an extended BIEM (XBIEM) that is applicable in an inhomogeneous bounded medium consisting of homogeneous sub-regions. In the formulation of the XBIEM, the interfaces of the sub-regions are regarded as extended boundaries upon which boundary integral equations are additionally derived. This has been originally known as a multiregional approach in the analysis of seismic wave propagation in the frequency domain and it is employed here for rupture dynamics interacting with medium interfaces in time domain. All of the boundary integral equations are fully coupled by imposing boundary conditions on the extended boundaries and then numerically solved after spatiotemporal discretization. This paper gives the explicit expressions of discretized stress kernels for anti-plane nonplanar problems and the numerical method for the implementation of the XBIEM, which are validated in two representative planar fault problems.