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Numerical modeling of 3D time-harmonic scattering problems with regularized difference potentials
We propose a method for the numerical computation of the 3D time-harmonic scattering about objects of complex shape. Our approach relies on the method of difference potentials combined with the lacunae-based integration of the Helmholtz equation. The former allows to handle curvilinear boundaries of scattering shapes on regular Cartesian grids with no loss of accuracy. The lacunae-based integration is a simple alternative to standard methods for solving the Helmholtz equation that guarantees a perfect treatment of outgoing waves on a finite computational domain. Attention is paid to the regularization of the resulting equations. It naturally exploits the patched representation of
the scattering shape and can be performed prior to major computation at low cost. The numerical simulations corroborate the basic concepts presented in the paper.