Solution of two-part scattering problems via the cross-flux

In simulating electromagnetic scattering problems, one often encounters "two-part" problems, in which each part may be more appropriately solved by a different method. There is also the case where both parts of the problem can be solved using the same method, but one may wish to change one part while keeping the other unchanged. The problem then arises as to how the fields can be combined meaningfully. We explore the use of the cross flux theory, first developed by G.A. Deschamps (see "Electromagnetic Theory and Antennas, Part 1", Pergamon Press, 1963), for combining the simulated scattered fields from two bodies into a meaningful approximation of the fields obtained from simulation of the entire two-body system. Approximations to the original cross flux formulation are presented that allow the Deschamps\´ formulation to be expressed as a series of higher order terms. This allows control over the accuracy of a problem solved using the cross flux. The approximations of Deschamps\´ formulation were tested on several 2D canonical problems using the method of moments (MoM). The results show that inclusion of the higher order terms does, in the limit, approach the exact solution.