Efficient numerical simulation for long range wave propagation

We develop an efficient algorithm for simulating wave propagation over long distances with both weak and strong scatterers. In domains with weak heterogeneities the wave field is decomposed into forward propagating and back scattered modes using two coupled parabolic equations. In the region near strong scatterers, the Helmholtz equation is used to capture the strong scattering events. The key idea in our method is to combine these two regimes using a combined domain decomposition and wave decomposition method. A transparent interface condition is derived to couple these two regions together. Numerical examples show that the simulated field is close to the field obtained using the full Helmholtz equation in the whole domain.