A Fast Huygens Sweeping Method for Green's Function of Helmholtz Equations in High Frequency Regime

Abstract: We present a Eulerian geometrical-optics method, namely fast Huygens sweeping method, for numerical solutions of Helmholtz equations with point sources. The method combines the geometrical optics approximations and Huygens secondary sources principle in a way that geometrical optics provides approximations of locally valid.

Green's functions and Huygens principle integrates locally valid Green's functions to obtain globally valid Green's function and captures the caustics automatically. Factorization approaches are introduced to compute high accurate phase and amplitude to approximate locally valid Green's functions, and a modified fast butterfly algorithm is incorporated to efficiently evaluate the Huygens-Kirchhoff integral. Numerical example will be presented.