A symmetric hybrid formulation for transient wave simulations in PML-truncated heterogeneous media

作者：Kucukcoban S; Kallivokas L F^*

来源：Wave Motion, 2013, 50(1): 57-79.

DOI：10.1016/j.wavemoti.2012.06.004

• Unsplit-field perfectly matched layers
• Hybrid formulation
• Mixed finite elements
• Transient wave propagation
• Semi-infinite domains

The numerical simulation of wave motion in arbitrarily heterogeneous semi-infinite media requires the truncation of the semi-infinite extent of the domain to yield a finite computational domain. In the presence of heterogeneity, the domain truncation is best accomplished via the introduction of perfectly-matched-layers (PMLs) at the truncation surface.
By and large, most PML formulations treat in an identical manner both the interior domain and the PML buffer zone. By construction, the complex-coordinate-stretched equations used to introduce the PML, also serve to describe the interior domain, where they reduce to the original, unstretched, system of governing equations. Such a unified treatment, however, results in increased computational cost.
In this development, we discuss a hybrid formulation that leads to a mixed form within the PML, coupled with a standard displacement-only form for the interior domain, both of which are second-order in time. We discuss the formulation and the numerical implementation using finite elements in the context of a standard Galerkin scheme that yields fully symmetric discrete forms, and results in optimal computational cost. We show that existing displacement-based codes for interior domains can be easily modified to accommodate PMLs as a means of domain truncation.
We report on numerical results demonstrating the stability, efficacy, and cost-effectiveness of the hybrid formulation.

• 出版日期2013-1