Solving very large EM problems (109 DoFs or greater) using the MPI-CBFDTD method

We describe a novel FDTD approach, called CBFDTD, which is based on the characteristic basis function method (CBFM) and a serial/parallel approach. The method is useful for solving electromagnetic problems that are difficult to handle via a direct application of the FDTD algorithm because of their large size. Like the CBMOM technique (Parakash, V. and Mittra, R., Microwave and Optical Technology Letters, vol.36, no.2, p.95-100, 2003), CBFDTD is based on dividing a large structure into relatively small sub-regions, and evaluating the characteristic functions that are localized in each of these sub-regions. The excitation of the sub-regions can either be direct sources that yield primary bases, or be derived from the adjacent regions through interfaces that generate secondary bases. We briefly describe the technique and present some results that validate the approach. The advantage of using the CBFDTD approach is that it can handle very large problems - involving 10⁹, or even larger, numbers of unknowns - that are well beyond the scope of direct methods.