The Multilevel Fast Multipole Algorithm (MLFMA) for Solving Large-Scale Computational Electromagnetics Problems

In general, conventional surface formulations are unstable when the contrast of the object is very low. To obtain accurate results, those formulations should be stabilized, as discussed later in this chapter, Section 2.2. On the other hand, the inaccuracy of surface formulations for relatively high contrasts is due to the approximation of the actual geometry in numerical solutions. For example, when planar triangles are used for the discretization, the computational model and the actual geometry of a smooth object are different. If the permittivity or permeability of the object is high, small discrepancies between the model and actual geometry may create large errors. The error is not due to the insufficient discretization of equivalent currents since the discretized model is solved with a desired level of accuracy, e.g., using /10 triangles. The error is due to the geometric difference between the actual object and the computational model.

Figure 2.8 presents the backscattered and forward-scattered RCS of a lossy sphere with a radius of 0.5 located in free space. The relative complex permittivity of the sphere changes from to . Computational results obtained by using CTF, MNMF, and ...