20130607
Shielding sheets are commonly used in the protection of electronic devices. With their large aspect ratios they become a serious issue for the direct application of the finite element method, as many small cells are required to resolve the sheets, as well as the direct application of the boundary element method (BEM) due to the occuring almost singular integrals. Impedance transmission conditions (ITCs), posed on the sheet midline Γ, allow for finite element formulations in the exterior of the sheet midline or boundary element formulations on this midline only. We introduce the ideas behind the commonly used ITCs for the timeharmonic eddy current problem in two dimensions. We show how by an asymptotic analysis that all the classical models (except PEC) are robust with respect to the skin depth or frequency, but all of order 0.
By asymptotic expansions we derive two families of impedance boundary conditions ITC1N and ITC2N where N denotes the order. The family ITC1N is derived for a conductivity or frequency scaled like 1/d and for ITC2N it is scaled like 1/d^{2}. We find ITC10 the natural limit for d → 0. For ITC11 and ITC12 are of higher order for low frequencies. The ITC21 are of order 1 independent of the frequency and outform all the classical conditions.
In the second part of the talk we will propose boundary integral equations (BIE) and boundary element methods of the classical and recent impedance transmissions conditions.
Category: CE SeminarTechnische Universität Darmstadt
Graduate School CE
Dolivostraße 15
D64293 Darmstadt

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