We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex, heterogeneous, and nonlinear part -- such as the dynamic rupture along a fault with near fault plasticity -- and the high accuracy and computational efficiency of SBIM is used to simulate the exterior half spaces perfectly truncating all incident waves. The exact truncation allows us to greatly reduce the domain of spatial discretization compared to a traditional FEM approach, leading to considerable savings in computational cost and memory requirements. The coupling of FEM and SBIM is achieved by the exchange of traction and displacement boundary conditions at the computationally defined boundary. The method is suited to implementation on massively parallel computers. We validate the developed method by means of a benchmark problem. Three more complex examples with a low velocity fault zone, low velocity off-fault inclusion, and interaction of multiple faults, respectively, demonstrate the capability of the hybrid scheme in solving problems of very large sizes. Finally, we discuss potential applications of the hybrid method for problems in geophysics and engineering.

中文翻译：

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一种三维混合有限元-谱边界积分方法，用于复杂无界域中的地震建模

我们提出了一种3D混合方法，该方法结合了有限元方法（FEM）和光谱边界积分方法（SBIM）来建模无界域中的非线性问题。FEM的灵活性用于建模复杂，异质和非线性的零件-例如具有近似断层塑性的沿断层的动态破裂-SBIM的高精度和计算效率可完美地模拟外部半空间截断所有入射波。与传统的FEM方法相比，精确的截断使我们能够大大减少空间离散化的范围，从而大大节省了计算成本和内存需求。通过在计算定义的边界处交换牵引力和位移边界条件来实现FEM和SBIM的耦合。该方法适合在大规模并行计算机上实现。我们通过基准问题验证了开发的方法。具有低速断层带，低速断层包含和多个断层相互作用的三个更复杂的例子分别证明了混合方案解决非常大尺寸问题的能力。最后，我们讨论了混合方法在地球物理学和工程学中的潜在应用。