Shape optimization for the Helmholtz equation |
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| Authors: | František Seifrt Günter Leugering Eduard Rohan |
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| Affiliation: | 1. Department of Mathematics, Friedrich–Alexander–Universität Erlangen–Nürnberg, Martensstr. 3, 910 58 Erlangen, Germany;2. Department of Mechanics, University of West Bohemia in Plzeň, Univerzitní 22, 306 14 Plzeň, Czech Republic |
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| Abstract: | The aim of our work is to develop optimal dielectric composite structures with specific qualities. The task is to design interfaces of given material components such that the originated structure attains certain optical properties. Propagation of the electromagnetic waves in the composite is described by the Helmholtz equation. Success of the structure is enumerated by the objective function which is to be minimized. Interfaces of the given materials are parametrized by the cubic B–spline curves. The design variables are afterwards the positions of B–spline control points. For objective function evaluation one forward computation of the Helmholtz equation is needed. To get the sensitivity of the objective function we solve the backward (adjoint) equation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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