2013-06-07

Highly accurate impedance boundary conditions for thin conducting sheets

Dr. Kersten Schmidt, TU Berlin

17 Jun 2013, 10:30–12:00; Location: S2|17-103

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 mid-line Γ, allow for finite element formulations in the exterior of the sheet mid-line or boundary element formulations on this mid-line only. We introduce the ideas behind the commonly used ITCs for the time-harmonic 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 ITC-1-N and ITC-2-N where N denotes the order. The family ITC-1-N is derived for a conductivity or frequency scaled like 1/d and for ITC-2-N it is scaled like 1/d2. We find ITC-1-0 the natural limit for d → 0. For ITC-1-1 and ITC-1-2 are of higher order for low frequencies. The ITC-2-1 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 Seminar

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Technische Universität Darmstadt

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