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Topology Optimization for Wave Propagation Problems
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.
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. , p. 28
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: urn:nbn:se:uu:diva-98382ISBN: 978-91-554-7438-6 (print)OAI: oai:DiVA.org:uu-98382DiVA, id: diva2:174299
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
List of papers
1. Topology optimization of an acoustic horn
Open this publication in new window or tab >>Topology optimization of an acoustic horn
2006 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 196, p. 420-436Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-83132 (URN)10.1016/j.cma.2006.05.005 (DOI)000242035000031 ()
Projects
Design Optimization
Available from: 2007-01-31 Created: 2007-01-31 Last updated: 2018-01-13Bibliographically approved
2. Topology optimization of wave transducers
Open this publication in new window or tab >>Topology optimization of wave transducers
2006 (English)In: Topological Design Optimization of Structures, Machines and Materials: Status and Perspectives, Dordrecht, The Netherlands: Springer, 2006, p. 301-310Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Dordrecht, The Netherlands: Springer, 2006
Series
Solid Mechanics and its Applications ; 137
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-80778 (URN)10.1007/1-4020-4752-5_30 (DOI)000237578800030 ()1-4020-4729-0 (ISBN)
Projects
Design Optimization
Available from: 2007-01-31 Created: 2007-01-31 Last updated: 2018-01-13Bibliographically approved
3. On the far-field properties of an acoustic horn
Open this publication in new window or tab >>On the far-field properties of an acoustic horn
2006 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2006-042
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-82158 (URN)
Projects
Design Optimization
Available from: 2008-02-19 Created: 2008-02-19 Last updated: 2011-11-18Bibliographically approved
4. Shape and topology optimization of an acoustic horn-lens combination
Open this publication in new window or tab >>Shape and topology optimization of an acoustic horn-lens combination
2010 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 234, p. 1781-1787Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-98374 (URN)10.1016/j.cam.2009.08.028 (DOI)000278570900022 ()
Projects
Design Optimization
Available from: 2009-02-20 Created: 2009-02-20 Last updated: 2018-01-13Bibliographically approved
5. Microwave tomography using topology optimization techniques
Open this publication in new window or tab >>Microwave tomography using topology optimization techniques
2008 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 30, p. 1613-1633Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-16104 (URN)10.1137/070679879 (DOI)000255500500024 ()
Projects
Design Optimization
Available from: 2008-04-22 Created: 2008-04-22 Last updated: 2018-01-12Bibliographically approved
6. High contrast microwave tomography using topology optimization techniques
Open this publication in new window or tab >>High contrast microwave tomography using topology optimization techniques
2010 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 234, p. 1773-1780Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-98380 (URN)10.1016/j.cam.2009.08.027 (DOI)000278570900021 ()
Projects
Design Optimization
Available from: 2009-02-20 Created: 2009-02-20 Last updated: 2018-01-13Bibliographically approved
7. Microwave tomographic imaging as a sequence of topology optimization problems
Open this publication in new window or tab >>Microwave tomographic imaging as a sequence of topology optimization problems
2010 (English)In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 11, p. 597-610Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-87936 (URN)10.1007/s11081-008-9075-x (DOI)000284851600006 ()
Projects
Design Optimization
Available from: 2009-01-15 Created: 2009-01-15 Last updated: 2018-01-13Bibliographically approved
8. Megapixel topology optimization on a graphics processing unit
Open this publication in new window or tab >>Megapixel topology optimization on a graphics processing unit
2009 (English)In: SIAM Review, ISSN 0036-1445, E-ISSN 1095-7200, Vol. 51, p. 707-721Article in journal (Refereed) Published
National Category
Computer Sciences Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-98381 (URN)10.1137/070699822 (DOI)000271983500004 ()
Projects
Design Optimization
Available from: 2009-02-20 Created: 2009-02-20 Last updated: 2018-01-13Bibliographically approved

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