A spectral formulation of the boundary integral equation method for antiplane problems is presented. The boundary integral equation method relates the displacement discontinuity and the shear stress at an interface between two half-planes. It involves evaluating a space-time convolution of the shear stress or the displacement discontinuity at the interface. In the spectral formulation, the convolution with respect to the spatial coordinate is performed in the spectral domain. The leads to greater numerical efficiency. Prior work on the spectral formulation of the boundary integral equation method has performed the elastodynamic convolution of the displacement discontinuity at the interface. In the present work, the convolution is performed of the shear stress at the interface. The formulation is validated by numerically calculating the response of the interface to harmonic and to impulsive disturbances, and comparing with known analytical solutions. To illustrate use of the method, dynamic rupture propagation with a slip-weakening friction law is simulated.

中文翻译：

---

反平面问题的边界积分方程方法的谱表示

给出了反平面问题边界积分方程方法的谱表示。边界积分方程法将位移不连续性和两个半平面之间的界面处的剪应力相关联。它涉及评估剪切应力的时空卷积或界面处的位移不连续性。在频谱公式中，相对于空间坐标的卷积在频谱域中执行。导致更高的数值效率。边界积分方程方法的频谱公式化的先前工作已经完成了界面处位移不连续性的弹性动力学卷积。在目前的工作中，对界面处的切应力进行卷积。通过数值计算界面对谐波和脉冲干扰的响应并与已知的分析解决方案进行比较，可以验证该公式。为了说明该方法的使用，模拟了具有弱滑动摩擦定律的动态破裂传播。