Optimization of devices for wave transmission

Martin Berggren

Umeå University

The talk will overview our work on optimization of devices for acoustic (or electromechanical) wave propagation. The devices typically operate in the interface between a source, for instance a transducer of a wave guide, and surrounding space. Numerical optimization techniques are attractive to use in the design of interfacial devices, since the properties of transmission and distribution often are quite sensitive to geometric changes. We employ two different strategies to define the admissible designs. The first strategy (boundary shape optimization) uses explicit boundary displacements with respect to a reference domain, and body-fitted deforming meshes are employed in the computations. In the second strategy (the material distribution approach to topology optimization), the coefficients in the governing equations are directly manipulated by the optimization algorithm, and the computations uses a fixed, typically uniform mesh. Both approaches have their pros and cons. For instance, the first approach yields higher accuracy, but the second offer more general admissible designs. These methods will be illustrated by numerical results from the design of loudspeaker horns, acoustical lenses and “labyrinths”, and from the design of nontraditional brass instrument bells. Some very recent results of optimizing the layout of a microstrip patch antenna will also be presented.

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