Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation

On the use of perfectly matched layers in the presence of long or backward propagating guided elastic waves

“…References pertaining to PML for time-harmonic elastic wave propagation problems are, for instance, [22,23,8,24]. Here, only the most straighforward kind of PML, that is, with constant coefficients, is considered, but the whole reasoning still applies if these coefficients are complex-valued functions of the space variables satisfying the conditions stated below.…”

Model Reduction for RF MEMS Simulation

“…That is, the bulk of the chip can be modeled as a semi-infinite medium. We model this semi-infinite domain using a perfectly matched layer (PML), which absorbs waves at any angle of incidence [4]. Bérenger invented the perfectly matched layer for problems in electromagnetics [5], but it was almost immediately re-interpreted as a complex-valued change of coordinates which can be applied to any linear wave equation [14,13].…”

“…Bérenger invented the perfectly matched layer for problems in electromagnetics [5], but it was almost immediately re-interpreted as a complex-valued change of coordinates which can be applied to any linear wave equation [14,13]. The weak form of the PML equations for time-harmonic linear elasticity [4] is…”

“…To make the attenuation through the PML frequency-independent, the coordinate transformations in [4] are frequency-dependent. Using a frequency-dependent transformation, the transfer function is given by…”

Perfectly Matched Layer (Pml) for Transient Wave Propagation in a Moving Frame of Reference

“…Later PML was formulated for the elastic wave equation in e.g. [5,6,7]. However, in this approach the solution for the displacements is dependent on computation of the strains in each time step.…”