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Shape and topology optimization of an acoustic horn-lens combination
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
2010 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 234, 1781-1787 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2010. Vol. 234, 1781-1787 p.
National Category
Computational Mathematics Computer Science
Identifiers
URN: urn:nbn:se:uu:diva-98374DOI: 10.1016/j.cam.2009.08.028ISI: 000278570900022OAI: oai:DiVA.org:uu-98374DiVA: diva2:174285
Projects
Design Optimization
Available from: 2009-02-20 Created: 2009-02-20 Last updated: 2017-12-13Bibliographically approved
In thesis
1. Topology Optimization for Wave Propagation Problems
Open this publication in new window or tab >>Topology Optimization for Wave Propagation Problems
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis considers topology optimization methods for wave propagation problems. These methods make no a priori assumptions on topological properties such as the number of bodies involved in the design. The performed studies address problems from two different areas, acoustic wave propagation and microwave tomography. The final study discusses implementation aspects concerning the efficient solution of large scale material distribution problems.

Acoustic horns may be viewed as impedance transformers between the feeding waveguide and the surrounding air. Modifying the shape of an acoustic horn changes the quality of the impedance match as well as the angular distribution of the radiated waves in the far field (the directivity). This thesis presents strategies to optimize acoustic devices with respect to efficiency and directivity simultaneously. The resulting devices exhibit desired far field properties and high efficiency throughout wide frequency ranges.

In microwave tomography, microwaves illuminate an object, and measurements of the scattered electrical field are used to depict the object's conductive and dielectric properties. Microwave tomography has unique features for medical applications. However, the reconstruction problem is difficult due to strongly diffracting waves in combination with large dielectric contrasts. This thesis demonstrates a new method to perform the reconstruction using techniques originally developed for topology optimization of linearly elastic structures. Numerical experiments illustrate the method and produce good estimates of dielectric properties corresponding to biological objects.

Material distribution problems are typically cast as large (for high resolutions) nonlinear programming problems over coefficients in partial differential equations. Here, the computational power of a modern graphics processing unit (GPU) efficiently solves a pixel based material distribution problem with over 4 million unknowns using a gradient based optimality criteria method.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2009. 28 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 612
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-98382 (URN)978-91-554-7438-6 (ISBN)
Public defence
2009-04-03, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2009-03-12 Created: 2009-02-20 Last updated: 2011-10-27Bibliographically approved
2. Shape Optimization for Acoustic Wave Propagation Problems
Open this publication in new window or tab >>Shape Optimization for Acoustic Wave Propagation Problems
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Boundary shape optimization is a technique to search for an optimal shape by modifying the boundary of a device with a pre-specified topology. We consider boundary shape optimization of acoustic horns in loudspeakers and brass wind instruments. A horn is an interfacial device, situated between a source, such as a waveguide or a transducer, and surrounding space. Horns are used to control both the transmission properties from the source and the spatial power distribution in the far-field (directivity patterns).

Transmission and directivity properties of a horn are sensitive to the shape of the horn flare. By changing the horn flare we design transmission efficient horns. However, it is difficult to achieve both controllability of directivity patterns and high transmission efficiency by using only changes in the horn flare. Therefore we use simultaneous shape and so-called topology optimization to design a horn/acoustic-lens combination to achieve high transmission efficiency and even directivity. We also design transmission efficient interfacial devices without imposing an upper constraint on the mouth diameter. The results demonstrate that there appears to be a natural limit on the optimal mouth diameter.

We optimize brasswind instruments with respect to its intonation properties. The instrument is modeled using a hybrid method between a one-dimensional transmission line analogy for the slowly flaring part of the instrument, and a finite element model for the rapidly flaring part.

An experimental study is carried out to verify the transmission properties of optimized horn. We produce a prototype of an optimized horn and then measure the input impedance of the horn. The measured values agree reasonably well with the predicted optimal values.

The finite element method and the boundary element method are used as discretization methods in the thesis. Gradient-based optimization methods are used for optimization, in which the gradients are supplied by the adjoint methods.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2010. 42 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 709
Keyword
shape optimization, design optimization, acoustic wave propagation, Helmholtz equation, Boundary Element Method, Finite Element Method, inverse problems, adjoint method, gradient-based optimization
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-112549 (URN)978-91-554-7707-3 (ISBN)
Public defence
2010-02-26, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppala, 10:15 (English)
Opponent
Supervisors
Available from: 2010-02-03 Created: 2010-01-14 Last updated: 2011-10-26Bibliographically approved

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Wadbro, EddieUdawalpola, Rajitha

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