Nested Kernel-Independent Method for Electromagnetic Scattering From Composite Objects

This letter presents a fast solver for volume surface integral equations (VSIEs) of composite perfect electric conductors (PEC) and high contrast dielectric objects by a nested kernel-independent method. The kernel-dependent approximations are effective only when groups are far away from each other in terms of wavelength. However, this will restrict the octree from being divided into finer levels for high dielectric contrast regions. We adopt an inverse source process for low-rank compression of PEC and dielectrics impedance matrix, which is kernel-independent, thus avoiding the aforementioned problems. The far-field couplings between both volume and surface unknowns are approximately represented by a smaller number of equivalent sources distributed on the equivalent surface. Therefore, VSIEs are only constructed at the finest level, while at other levels SIEs are applied. Our method has the computational complexity of O(N) at low and intermediate frequencies. Numerical results verify the accuracy and the high efficiency of the proposed method.