Mat-1.3656 Seminar on
numerical analysis and computational science
Monday, March 15, 2010, room
U322 at 14.15, Eirola & Stenberg
Martin Berggren, Umeå Universitet
Computational Techniques for the Design of Acoustical Horns, Lenses, and Labyrinths
We consider the problem of designing interfacial devices between a
source of sound waves, for instance a waveguide or a transducer, and
surrounding space. Such devices can be found in brass instruments and
in loudspeaker systems designed for large halls or for outdoor use. In
the simplest case, these devices are formed like horns, but more
complicated shapes may also be beneficial. Numerical optimization
techniques are attractive to use in the design of such devices, since
the properties of sound transmission and distribution are sensitive to
geometric changes, provided that the device is large enough with
respect to the wavelength. 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 used in the
computations. In the second strategy (the material distribution
approach), the coefficients in the governing Helmholtz equations are
directly manipulated by the optimization algorithm, and the
computations uses a fixed 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.