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

A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation

“…PML optimisation at fixed cost has traditionally focused on tuning the absorbing functions σ i , while keeping the thickness of the PML regions, δ PML , fixed and typically comparable to the wavelength or some problemspecific lengthscale; see e.g. [22,28]. Rabinovich et al [26] analysed the effect of variations in δ PML and N PML on the accuracy of the solution, but restricted themselves to PML thicknesses within that range.…”

Hybrid Asynchronous Perfectly Matched Layer for seismic wave propagation in unbounded domains

“…It is called a dual approach because Lagrange multipliers are the new unknowns of the problem, in contrast to the hybrid formulation proposed by Kucukcoban and Kallivokas [18] based on primal Schur approach with the displacement at the interface as unknowns. In the continuous formulation, imposing any kinematic continuity at the interface leads to the same solution.…”

“…From the frequency-domain equations of Basu and Chopra, Kucukcoban and Kallivokas derived an unsplit mixed approach of the PML, by retaining the displacement and stress fields as unknowns in the time domain [17]. Next, in order to couple their PML to a displacement-only field formulation in the physical interior domain, the authors extended their PML to a mixed hybrid approach [18,19].…”

“…The main benefit is a higher versatility and numerical efficiency of the PML which can be implemented using a more appropriate time integrator associated with a larger time step than the one employed in the soil medium imposed by the CFL condition for ensuring the algorithm stability [20]. The proposed PMLs can be viewed as a hybrid and asynchronous PML version because different time integrators can be adopted as in the work of Kucukcoban and Kallivokas [18,19], with the adding desirable properties of dealing with different time scales in the same dynamic simulation. Moreover, the proposed approach enables the number of unknowns to be reduced in comparison to the previous mixed displacement-stress formulation.…”

A framework for assessing the uncertainty in wave energy delivery to targeted subsurface formations

“…We negotiate the semi-infinite extent of the domain of interest by truncating it with a buffer of hybrid perfectly-matched-layers (PMLs) (Kucukcoban and Kallivokas, 2013). The layered elastic domain contains a target inclusion, and tractions applied on the loaded boundary (ground surface) initiate the wave motion.…”