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Exterior Electromagnetic Shaping using Wavelet BEM

Eppler, Karsten; Harbrecht, Helmut

Inst. Mathematik

The present paper is concerned with exterior electromagnetic shaping in two dimensions. We model the conductors by regular densities which leads to a finite value for the objective and makes a line-search realizable. In order to compute the pressure on the surface we optimize an Augmented Lagrangian by a Newton method using a second order approach for the Lagrange multiplier. Since the underlying state function satisfies an exterior boundary value problem, we compute its first and second order derivatives by boundary integral equations which are solved numerically by a fast wavelet Galerkin scheme. Numerical results demonstrate that we arrive at a fast and robust algorithm for the solution of the considered class of problems.