Integral Equation Methods for Multiple Scattering

The phenomenon of multiple scattering is ubiquitous. It is of great significance in numerous scientific and engineering applications to characterize, simulate, and effectively apply the properties of multiple scattering from the perspectives of both mathematical theory and computational methods. The integral equation method has been one of the most important numerical schemes for solving wave scattering problems. In recent years, significant progress has been made in the research of numerical methods for multiple scattering problems, yet many key scientific issues remain to be resolved. This article presents some recent advances and open problems in the integral equation methods for several typical frequency-domain multiple scattering problems involving multiple obstacles, periodic structures, layered media, and multi-physical fields, as well as the time-domain multiple scattering problems.