Hmm. While the basic shape and behaviour of the waveforms looks good, there are certainly some discrepancies between what we've computed and the reference solution. Now our goal is to see if we can get the signals to match perfectly within the time which they overlap.
The most obvious issue with the signals above is that they differ greatly at later times. There's quite an obvious issue here: the reference solution was computed assuming an infinite domain, but the domain we defined is finite in extent. In fact this is the main issue: we need to add absorbing boundaries.
To preserve the stability of the wavefield solution in the presence of complex or anisotropic media, Salvus employs a two-stage approach to absorbing boundaries. First, we apply absorbing boundary conditions at the edge of the mesh as outlined here
. These conditions provide good absorbing characteristics for wave impacting the boundary at close to normal incidence, and are sufficient for most cases. If a more substantial absorbing profile is desired, one can also pad the simulated domain with a damping layer. This approach follows that given in this
paper. Adding damping layers are advantageous in that they can almost completely cancel any boundary reflections, but do require one to enlarge the computational domain and therefore increase the cost of the resultant simulations. We have found that damping layers provide a good quality / performance tradeoff when 3.5 or more wavelengths are present in the absorbing layer.
In previous versions of Salvus absorbing boundary attachment was unfortunately a manual and tedious process. Fortunately, we now provide an interface to automatically extend the domain in a more user-friendly manner. To activate this feature, we first need to set a few parameters to tell the simulation that we do indeed want a layer of extended absorbing boundaries.