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Time-Domain Sensitivity Analysis for Conductivity Distribution in Maxwell's Equations
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.ORCID-id: 0000-0002-1318-7519
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.ORCID-id: 0000-0003-0473-3263
2015 (Engelska)Rapport (Övrigt vetenskapligt)
Abstract [en]

We present expressions for the derivatives of the outgoing signal in coaxial cables with respect to the conductivity distribution in a specific domain. The derived expressions can be used with gradient-based optimization methods to design metallic electromagnetic devices, such as antennas and waveguides. We use the adjoint-field method to derive the expressions and the derivation is based on the 3D time-domain Maxwell's equations. We present two derivative expressions; one expression is derived in the continuous case and the second is derived based on the FDTD discretization of Maxwell's equations, including the uniaxial perfectly match layer (UPML) to simulate the radiation boundary condition. The derivatives are validated through a numerical example, where derivatives computed by the adjoint-field method are compared against derivatives computed with finite differences. Up to 7 digits precision matching is obtained.

Ort, förlag, år, upplaga, sidor
Umeå: Umeå University , 2015. , s. 20
Serie
UMINF 15.06
Nyckelord [en]
Maxwell's equations, antennas, waveguide, finite-difference time-domain (FDTD), gradient-based optimization, adjoint-field problem, sensitivity analysis.
Nationell ämneskategori
Datavetenskap (datalogi)
Forskningsämne
datalogi
Identifikatorer
URN: urn:nbn:se:umu:diva-79483OAI: oai:DiVA.org:umu-79483DiVA, id: diva2:642030
Anmärkning

Originally published in licentiate thesis "Metallic Antenna Design Based on Topology Optimization Techniques",  under the title

"Sensitivity Analysis for Conductive Material Distribution Using the Time-Domain Maxwell’s Equations"

Tillgänglig från: 2013-08-20 Skapad: 2013-08-20 Senast uppdaterad: 2018-06-08Bibliografiskt granskad
Ingår i avhandling
1. Metallic antenna design based on topology optimization techniques
Öppna denna publikation i ny flik eller fönster >>Metallic antenna design based on topology optimization techniques
2013 (Engelska)Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
Ort, förlag, år, upplaga, sidor
Umeå: Department of Computing Science, Umeå University, 2013. s. 15
Serie
UMINF, ISSN 0348-0542 ; 13.08
Nationell ämneskategori
Data- och informationsvetenskap
Identifikatorer
urn:nbn:se:umu:diva-76691 (URN)978-91-7459-649-6 (ISBN)
Presentation
2013-05-03, Mit-huset, MC313, Umeå universitet, Umeå, 10:15
Tillgänglig från: 2013-07-10 Skapad: 2013-07-10 Senast uppdaterad: 2018-06-08Bibliografiskt granskad
2. Topology optimization of antennas and waveguide transitions
Öppna denna publikation i ny flik eller fönster >>Topology optimization of antennas and waveguide transitions
2015 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

This thesis introduces a topology optimization approach to design, from scratch, efficient microwave devices, such as antennas and waveguide transitions. The design of these devices is formulated as a general optimization problem that aims to build the whole layout of the device in order to extremize a chosen objective function. The objective function quantifies some required performance and is evaluated using numerical solutions to the 3D~Maxwell's equations by the finite-difference time-domain (FDTD) method. The design variables are the local conductivity at each Yee~edge in a given design domain, and a gradient-based optimization method is used to solve the optimization problem. In all design problems, objective function gradients are computed based on solutions to adjoint-field problems, which are also FDTD discretization of Maxwell's equations but solved with different source excitations. For any number of design variables, the computation of the objective function gradient requires one solution to the original field problem and one solution to the associated adjoint-field problem. The optimization problem is solved iteratively using the globally convergent Method of Moving Asymptotes (GCMMA).

By the proposed approach, various design problems, including tens of thousands of design variables, are formulated and solved in a few hundred iterations. Examples of solved design problems are the design of wideband antennas, dual-band microstrip antennas, wideband directive antennas, and wideband coaxial-to-waveguide transitions. The fact that the proposed approach allows a fine-grained control over the whole layout of such devices results in novel devices with favourable performance. The optimization results are successfully verified with a commercial software package. Moreover, some devices are fabricated and their performance is successfully validated by experiments.

Ort, förlag, år, upplaga, sidor
Umeå: Umeå University, 2015. s. 29
Serie
UMINF, ISSN 0348-0542 ; 15:07
Nyckelord
Maxwell's equations, topology optimization, antennas, waveguide transition, finite-difference time-domain, gradient-based optimization, adjoint-field problem, microwave devices.
Nationell ämneskategori
Datavetenskap (datalogi)
Forskningsämne
administrativ databehandling
Identifikatorer
urn:nbn:se:umu:diva-102505 (URN)978-91-7601-255-0 (ISBN)
Disputation
2015-05-26, Naturvetarhuset, N450, Umeå universitet, Umeå, 10:15 (Engelska)
Opponent
Handledare
Tillgänglig från: 2015-05-05 Skapad: 2015-04-27 Senast uppdaterad: 2018-06-07Bibliografiskt granskad

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