  Matched layers are commonly used in numerical simulations of wave propagation
to model (semi-)infinite domains. Attenuation functions describe the damping in
layers, and provide a matching of the wave impedance at the interface between
the domain of interest and the absorbing region. Selecting parameters in the
attenuation functions is non-trivial. In this work, an optimisation procedure
for automatically calibrating matched layers is presented. The procedure is
based on solving optimisation problems constrained by partial differential
equations with polynomial and piecewise-constant attenuation functions. We show
experimentally that, for finite element time domain simulations,
piecewise-constant attenuation function are at least as efficient as quadratic
attenuation functions. This observation leads us to introduce consecutive
matched layers as an alternative to perfectly matched layers, which can easily
be employed for problems with arbitrary geometries. Moreover, the use of
consecutive matched layers leads to a reduction in computational cost compared
to perfectly matched layers. Examples are presented for acoustic, elastodynamic
and electromagnetic problems. Numerical simulations are performed with the
libraries FEniCS/DOLFIN and dolfin-adjoint, and the computer code to reproduce
all numerical examples is made freely available.
