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Matched layers are commonly used in numerical simulations of wave propagationto model (semi-)infinite domains. Attenuation functions describe the damping inlayers, and provide a matching of the wave impedance at the interface betweenthe domain of interest and the absorbing region. Selecting parameters in theattenuation functions is non-trivial. In this work, an optimisation procedurefor automatically calibrating matched layers is presented. The procedure isbased on solving optimisation problems constrained by partial differentialequations with polynomial and piecewise-constant attenuation functions. We showexperimentally that, for finite element time domain simulations,piecewise-constant attenuation function are at least as efficient as quadraticattenuation functions. This observation leads us to introduce consecutivematched layers as an alternative to perfectly matched layers, which can easilybe employed for problems with arbitrary geometries. Moreover, the use ofconsecutive matched layers leads to a reduction in computational cost comparedto perfectly matched layers. Examples are presented for acoustic, elastodynamicand electromagnetic problems. Numerical simulations are performed with thelibraries FEniCS/DOLFIN and dolfin-adjoint, and the computer code to reproduceall numerical examples is made freely available.

Automatic calibration of damping layers in finite element time domain simulations