Cancellations of surface loop basis functions

To capture the fine details of integrated circuits and small antennas, the mesh size is usually much smaller than the wavelength. When the traditional RWG-type bases are used, the electric field integral equation suffers from low-frequency breakdown. This problem can be solved by using the loop-star/tree basis. We have developed a code which uses the loop-tree basis and the low-frequency multi-level fast multipole algorithm to solve a large linear system with small size mesh. The fine details are simulated accurately and efficiently from very low frequencies to very high frequencies. To validate the code, some canonical problems which have closed form solutions are simulated. One of the canonical problems is the scattering from a conducting sphere. We found that the cancellation exists in not only for the excitation on a loop basis function, but also the calculation of the far electric field. We discuss how the cancellation is removed analytically in calculating the far field from a loop basis function. The cancellation also exists in the interaction associated with a loop basis function when it is far away from the other basis function.