Shape optimization for the Helmholtz equation

Seifrt F, Leugering G, Rohan E (2008)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2008


Publisher: Gesellschaft für Angewandte Mathematik und Mechanik (GAMM)

Book Volume: 8

Pages Range: 10705-10706

Volume: 8

Issue: 1

Journal Issue: 1


DOI: 10.1002/pamm.200810705

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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.

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Seifrt, F., Leugering, G., & Rohan, E. (2008). Shape optimization for the Helmholtz equation. Proceedings in Applied Mathematics and Mechanics, 8(1), 10705-10706.


Seifrt, František, Günter Leugering, and Eduard Rohan. "Shape optimization for the Helmholtz equation." Proceedings in Applied Mathematics and Mechanics 8.1 (2008): 10705-10706.

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