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Scattering field formulation used in DGFEM 
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Apr2913, 05:35 AM

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Hello!
Reading up on simulations of electromagnetic scattering with DGFEM and trying some myself, I got stuck. In some of papers I have read, a scattering field formulation is used, in which the total field is linearly decomposed in incident field and scattering field: [itex] E^{T}=E^{S}+E^{I}[/itex] And, the 2D equations for the scattering field in a lossless, isotropic medium are: [itex] \epsilon_{r} \frac{\partial E^{S}}{\partial t} = \nabla \times H^{S}  (\epsilon_{r}  \epsilon_{r}^{I}) \frac{\partial E^{i}}{\partial t} [/itex] [itex] \mu_{r} \frac{\partial H^{S}}{\partial t} = \nabla \times E^{S}  (\mu_{r}  \mu_{r}^{I}) \frac{\partial H^{i}}{\partial t} [/itex] My problem is in the interpretation of the "scattering field" and "incident field" in this context. In every use I see of this formulation [itex]\epsilon_{r}[/itex] is space dependent, while [itex]\epsilon_{r}^{I}[/itex] is a constant  specifically, the incident medium's permittivity (same for the permeability). How can this work for multisubstrate cases, where, if I am thinking correctly, the medium considered incident should change? (I am quite confused with the affair in general, so any clarifications are quite welcome) 


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