Fast field calculation by a multilevel fast multipole algorithm for large complex radiators and scatterers

Field calculation is an important. post-processing step for integral equation (IE) based electromagnetics solvers. However, the cost. of field calculation is often ignored because it takes a relatively small portion of simulation time compared with those for impedance matrix setup and iterative solution. For some applications where the field must be calculated repeatedly for large observation planes, a fast field formulation can significantly reduce the cost. The improvement is obvious when the scatterers and radiators are electrically large and the number of observation points is close to the number of current basis functions. We present a fast field calculation that is fundamentally different from current techniques. Instead of using the physics of specific structures and FFT, a multilevel fast multipole algorithm (MLFMA) is applied to reduce the number of interactions between observation points and current bases for arbitrary structures. Moreover, the fast far field calculation by MLFMA does not require prior knowledge of the near field as in a NF-FF transformation. Once the radiation pattern of the root box in MLFMA has been set up, the far field in any observation angle can be extracted at very little cost. We briefly review the fast field formulation and apply it to vehicle antenna simulation.