Abstract: This talk will present our works on the regularized boundary integral equation method for solving wave scattering problems with bounded obstacles, open-surfaces or a layered-medium. The regularization here lies in two aspects. The first one is the regularization of singular integrals which can reduces the strongly- and hyper-singular integrals to combinations of weakly-singular integrals and surface differential operators. Another regularization is the analytic preconditioning of boundary integral equations, relying on the spectral properties of integral operators, to reduce the iteration number when solving the discretized system. Numerical examples utilizing the fast and highly accurate Chebyshev-based rectangular-polar solver will be presented.

Inviter: 李宏杰