% Absorption profile for an open boundary.
%
%   s = sponge(x, y, L, w, smax)
%
% All in SI: positions and widths in metres, the result in inverse seconds.
% Zero in the interior, ramping up quadratically over a layer of width w
% inside each edge of the square [-L/2, L/2]^2 and reaching smax at the wall.
% Added to a scene's absorption, this is what makes the finite grid stand in
% for an unbounded medium: a wave that leaves the region of interest is
% attenuated before it reaches the outer boundary, and whatever reflects off
% that boundary is attenuated again on the way back.
%
% The ramp is gradual on purpose. An absorbing layer is itself an impedance
% mismatch, so a sudden one reflects; spreading it over a couple of
% wavelengths keeps that reflection small. It is not a perfectly matched
% layer, and at grazing incidence it does leak.
function s = sponge(x, y, L, w, smax)
  dx = max(0, w - (L/2 - abs(x))) / w;
  dy = max(0, w - (L/2 - abs(y))) / w;
  d = max(dx, dy);
  s = smax * d.^2;
end