23 Mai 2014
11:00  - 12:00

Seminar in Numerical Analysis: Kersten Schmidt (TU Berlin)

Numerical analysis of boundary element methods for impedance transmission conditions

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 boundary element method (BEM) due to the occuring almost singular integrals.

With impedance transmission conditions (ITCs) we can propose boundary element formulations on the sheet mid-line (or mid-surface) only. In the beginning of the talk we give a motivation of meaningful impedance transmission conditions, which relate jumps and mean values of the Dirichlet and Neumann traces on the mid-line. This relation may
involve surface differential operators, as for boundary conditions of Wentzell's type, and depend on frequency, conductivity, sheet thickness and sheet geometry e.g. curvature). These parameters may take small or large values and may lead to singularly perturbed
boundary integral equations.

We will introduce related boundary element methods in two and three dimensions and analyse well-posedness and discretisation error depending on the model parameters. Numerical experiments confirm the convergence order of the discretisation error of the proposed BEM and that the discretisation error behaves for smooth enough sheets equivalent to the exact solution when varying the model parameters. The results obtained for the eddy current model, for which a Poisson equation has to be solved outside the mid-line, can be transfered to the Helmholtz equation and to transmission conditions
arising from other models.

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