An integrated-field-equations method complying with the interface conditions for the electromagnetic field in strongly heterogeneous media

We present a novel computational method for the modeling of electromagnetic fields in strongly heterogeneous media. The underlying principle is that, on a geometrically discretized configuration, local field representations are used that maintain their (physically required) continuity properties even across interfaces at which the electromagnetic constitutive parameters show large jump discontinuities. The method is inspired by the method of domain-integrated field equations (see de Hoop, A.T. and Lager, I.E., IEEE Trans. on Magnetics, vol.34, p.3355-8, 1998) developed for static field problems. We consider the frequency-domain wavefield problem and, as alternative to domain-integration, we use the integrated form of the Maxwell equations (also known as Ampere´s circuital law and Faraday´s law). The compatibility relations are satisfied implicitly. The method is fully described for 3D problems and we test some 2D configurations. We show that good results are obtained for a simple homogeneous configuration as well as for a four-media configuration with large contrasts. Applying the integrated Maxwell equations to the boundaries of the element gives better results than applying domain-integration in combination with the compatibility relation. A disadvantage of the method is the large number of expansion coefficients needed and a future step towards downsizing the system of equations is suggested.