三维混合有限元--谱边界积分法模拟复杂无界域地震
A three-dimensional hybrid finite element -- spectral boundary integral method for modeling earthquakes in complex unbounded domains
摘要：
本文提出了一种结合有限元法和谱边界积分法的三维混合方法来模拟无界区域的非线性问题。有限元法的灵活性被用来模拟复杂的、非均匀的和非线性的部分--例如具有近断层塑性的沿断层的动态破裂--而SBIM的高精度和计算效率被用来模拟完美地截断所有入射波的外部半空间。精确的截断使我们能够大大减少域的空间离散相比，传统的有限元方法，导致相当大的节省计算成本和内存需求。通过在计算定义的边界处交换牵引和位移边界条件，实现了FEM和SBIM的耦合。该方法适合在大规模并行计算机上实现。我们通过一个基准问题来验证所开发的方法。三个更复杂的例子，低速断层带，低速断故障夹杂物，和多个故障的相互作用，分别证明了混合计划在解决非常大的规模的问题的能力。最后，我们讨论了混合方法在物理和工程问题中的潜在应用。
英文摘要：
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.
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