Efficient numerical simulation for long range wave propagation

Authors:
Kai Huang;George Papanicolaou;Knut Solna;Chrysoula Tsogka;Hongkai Zhao
Affiliations:
Department of Mathematics, University of California at Irvine, Irvine, CA;Department of Mathematics, Stanford University, Stanford, CA;Department of Mathematics, University of California at Irvine, Irvine, CA;Department of Mathematics, University of Chicago, Chicago, IL;Department of Mathematics, University of California at Irvine, Irvine, CA
Venue:
Journal of Computational Physics
Year:
2006

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Abstract

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.