A Preconditioner for Surface Integral Equation Formulations of Dielectric Problems

Discretizations of surface integral equation (SIE) formulations of dielectric problems yield 2 x 2 partitioned linear systems. Due to the different scales between electric and magnetic fields along with equivalent currents, different parts of the partitioned impedance matrices show very difference in amplitude which lead to the imbalance between the partitions. The imbalance usually results in very high condition numbers which make the matrices highly ill-conditioned, then a series of problems will come up such as slow convergence of iterative solvers or descending of accuracy. The preconditioner with a complexity of O(N) presented in this paper could balance the elements and improve the condition numbers of the matrices without modifying the underlying SIE formulations.