PIE-MLFMA Implementation for Solving Complex Subwavelength Electromagnetic Problems

We present stable solutions of low-frequency electromagnetic problems involving small objects and their dense discretizations with respect to wavelength. Recently developed potential integral equations (PIEs), which are based on the boundary conditions for the magnetic vector potential and the electric scalar potential, are used to formulate complex problems. A multilevel fast multipole algorithm (MLFMA) based on scaled plane waves for stable computations of short-distance interactions is further employed to achieve fast iterative solutions. The accuracy and stability of the developed PIE-MLFMA implementation are demonstrated on complex subwavelength structures.