We show that an integral equation formulation of the measured equation of invariance (IE-MEI) fulfills a duality and the duality is useful to solve the scattering problems to a 2-D object in TM and TE waves incident simultaneously. The duality of the IE-MEL is derived naturally from the formulation of the IE-MEI. Fromt he formulation, we have found that the application range of the IE-MEI method is very wide: it can treat scattering problems to perfect electric conductor (PEC), lossy mateials, and lossless materials as well. The excitation source can be at near or far from the scatterer. In the IE_MEL method, there exists efficient computational algorithm using sparse matrices. We show the validity of the algorithm by numerical examples of a circular and a square PEC cylinders illuminated by a TM and a TE plane waves.
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