A surface integral equation method for dielectrics at low frequencies

This thesis is dedicated to using surface integral equations to solve electro- magnetic problems involved in integrated circuits. Since normally the sizes of the devices in this application are much smaller than the wavelength of the electromagnetic waves, special considerations are needed because of the low frequency breakdown. The augmented technique, a useful remedy for low frequency breakdown of the electric field integral equation is introduced as the background of this thesis. This augmented electric field integral equation provides a simple solu- tion for broadband electromagnetic simulation of perfect electric conductor structures. This thesis presented here exploits the augmented method for lossless and lossy dielectrics. The use of the conventional Rao-Wilton-Glisson (RWG) basis function as basis and testing functions fails because of the testing issue. Instead, the Buffa-Christiansen (BC) basis function is proposed to overcome this diffi- culty. With the combined use of RWG and BC basis functions, a new formu- lation is developed achieving a good convergence and accuracy. For highly lossy medium, however, a new integration scheme and a simple, efficient strategy with a fast algorithm is adopted. After these treatments, the skin depth of current in the conductive medium can be accurately captured down to very low frequency