One can obtain a very important speedup by using the option of mesh decimation. Decimation consists in replacing D points of the mesh by the analytical solution of the wave equation with source. This is done starting from the first point on the left of the cavity toward the last one on the right side. This transformation is done by replacing the traveling wave equations by coupled Delay Algebraic Equations (DAE), see  for details.
The discretization for the two sections is (N1,N2) = (513, 17). One can see on the left the time trace for the output intensity on the right facet of the absorber section. From top to bottom, the decimation factors are: (D1, D2) = (1, 1) (no decimation),
(D1, D2) = (16, 2),
(D1, D2) = (32, 4) and (D1, D2) = (32, 8), respectively.