Towards a combined perfectly matching layer and infinite element formulation for unbounded elastic wave problems

This paper presents a framework for implementing a novel Perfectly
Matching Layer and Infinite Element (PML+IE) combination boundary
condition for unbounded elastic wave problems in the time domain. To
achieve this, traditional hexahedral finite elements are used to model
wave propagation in the inner domain and infinite element test functions
are implemented in the exterior domain. Two alternative
implementations of the PML formulation are studied: the case with
constant stretching in all three dimensions and the case with spatially
dependent stretching along a single direction. The absorbing ability of
the PML+IE formulation is demonstrated by the favourable comparison
with the reflection coefficient for a plane wave incident on the boundary
achieved using a finite element only approach where stress free
boundary conditions are implemented at the domain edge. Values for the
PML stretching function parameters are selected based on the
minimisation of the reflected wave amplitude and it is shown that the
same reduction in reflection amplitude can be achieved using the PML+IE
approach with approximately half of the number of elements required in
the finite element only approach.