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Direct and Inverse Methods for Waveguides and Scattering Problems in the Time Domain
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.
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Numerical simulation is an important tool in understanding the electromagnetic field and how it interacts with the environment. Different topics for time-domain finite-difference (FDTD) and finite-element (FETD) methods for Maxwell's equations are treated in this thesis.

Subcell models are of vital importance for the efficient modeling of small objects that are not resolved by the grid. A novel model for thin sheets using shell elements is proposed. This approach has the advantage of taking into account discontinuities in the normal component of the electric field, unlike previous models based on impedance boundary conditions (IBCs). Several results are presented to illustrate the capabilities of the shell element approach.

Waveguides are of fundamental importance in many microwave applications, for example in antenna feeds. The key issues of excitation and truncation of waveguides are addressed. A complex frequency shifted form of the uniaxial perfectly matched layer (UPML) absorbing boundary condition (ABC) in FETD is developed. Prism elements are used to promote automatic grid generation and enhance the performance. Results are presented where reflection errors below -70dB are obtained for different types of waveguides, including inhomogeneous cases. Excitation and analysis via the scattering parameters are achieved using waveguide modes computed by a general frequency-domain mode solver for the vector Helmholtz equation. Huygens surfaces are used in both FDTD and FETD for excitation in waveguide ports.

Inverse problems have received an increased interest due to the availability of powerful computers. An important application is non-destructive evaluation of material. A time-domain, minimization approach is presented where exact gradients are computed using the adjoint problem. The approach is applied to a general form of Maxwell's equations including dispersive media and UPML. Successful reconstruction examples are presented both using synthetic and experimental measurement data. Parameter reduction of complex geometries using simplified models is an interesting topic that leads to an inverse problem. Gradients for subcell parameters are derived and a successful reconstruction example is presented for a combined dielectric sheet and slot geometry.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2005. , p. 47
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 102
Keywords [en]
Maxwell's equations, time-domain, FDTD, finite-element, hybrid, thin sheet, waveguide, PML, inverse scattering, adjoint, gradient-based, minimization
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-6013ISBN: 91-554-6364-9 (print)OAI: oai:DiVA.org:uu-6013DiVA, id: diva2:167116
Public defence
2005-11-04, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2005-10-11 Created: 2005-10-11 Last updated: 2011-10-27Bibliographically approved
List of papers
1. Hybrid time domain solvers for the Maxwell equations in 2D
Open this publication in new window or tab >>Hybrid time domain solvers for the Maxwell equations in 2D
Show others...
2002 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 53, p. 2185-2199Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-44333 (URN)10.1002/nme.380 (DOI)
Projects
GEMS
Available from: 2007-01-26 Created: 2007-01-26 Last updated: 2018-01-11Bibliographically approved
2. Waveguide Truncation Using UPML in the Finite-Element Time-Domain Method
Open this publication in new window or tab >>Waveguide Truncation Using UPML in the Finite-Element Time-Domain Method
2005 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2005-026
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-80256 (URN)
Projects
GEMS
Available from: 2007-02-03 Created: 2007-02-03 Last updated: 2014-09-03Bibliographically approved
3. Solving inverse electromagnetic problems using FDTD and gradient-based minimization
Open this publication in new window or tab >>Solving inverse electromagnetic problems using FDTD and gradient-based minimization
2006 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 68, p. 650-673Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-80802 (URN)10.1002/nme.1731 (DOI)000241713800003 ()
Projects
GEMS
Available from: 2007-01-26 Created: 2007-01-26 Last updated: 2018-01-13Bibliographically approved
4. Thin Sheet Modeling Using Shell Elements in the Finite-Element Time-Domain Method
Open this publication in new window or tab >>Thin Sheet Modeling Using Shell Elements in the Finite-Element Time-Domain Method
2006 (English)In: IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, E-ISSN 1558-2221, Vol. 54, p. 28-34Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-80325 (URN)10.1109/TAP.2005.861554 (DOI)000235016700004 ()
Projects
GEMS
Available from: 2007-01-26 Created: 2007-01-26 Last updated: 2018-01-13Bibliographically approved
5. Modeling of inhomogeneous waveguides using hybrid methods
Open this publication in new window or tab >>Modeling of inhomogeneous waveguides using hybrid methods
2005 (English)Manuscript (preprint) (Other academic)
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-93590 (URN)
Projects
GEMS
Available from: 2005-10-11 Created: 2005-10-11 Last updated: 2018-01-13Bibliographically approved

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