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Accurate techniques for 2D electromagnetic scattering
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.ORCID iD: 0000-0002-5522-0110
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of three parts. The first part is an introduction and referencessome recent work on 2D electromagnetic scattering problems at high frequencies. It alsopresents the basic integral equation types for impenetrable objects. A brief discussionof the standard elements of the method of moments is followed by summaries of thepapers.Paper I presents an accurate implementation of the method of moments for a perfectlyconducting cylinder. A scaling for the rapid variation of the solution improves accuracy.At high frequencies, the method of moments leads to a large dense system of equations.Sparsity in this system is obtained by modifying the integration path in the integralequation. The modified path reduces the accuracy in the deep shadow.In paper II, a hybrid method is used to handle the standing waves that are prominentin the shadow for the TE case. The shadow region is treated separately, in a hybridscheme based on a priori knowledge about the solution. An accurate method to combinesolutions in this hybrid scheme is presented.

Place, publisher, year, edition, pages
Växjö: Linnaeus University , 2014. , 12 p.
Keyword [en]
Integral equations, method of moments, sparsity, scaling, shadow boundary, B-S
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:lnu:diva-31523OAI: oai:DiVA.org:lnu-31523DiVA: diva2:689034
Presentation
2014-01-14, Växjö, 10:15 (English)
Opponent
Supervisors
Available from: 2014-04-28 Created: 2014-01-19 Last updated: 2016-12-20Bibliographically approved
List of papers
1. Scaling and sparsity in an accurate implementation of the method of moments in 2-D
Open this publication in new window or tab >>Scaling and sparsity in an accurate implementation of the method of moments in 2-D
2014 (English)In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 49, no 8, 643-652 p.Article in journal (Refereed) Published
Abstract [en]

The integral equations of electromagnetic scattering are often solved numericallyby means of the method of moments. At high frequencies, this method typically leads to a large linear system with a dense matrix. Higher order basis functions is a means to improve the accuracy. B-splines are used here for a two-dimensional testbed study that avoids the complexity of 3D implementation.

For smooth convex scatterers one may use \emph{a priori} knowledge about the oscillatory behaviour of the solution to reformulate the integral equation.This fast scale of variation is included in the kernel of the integral equation. An extension of this idea deals with the variation in the shadow, particularly for circular geometry, and is an improvement that is presented in this study. Generally, the TE-case is less studied at high frequencies and our numerical results therefore relate to this harder problem.

A sparse matrix can be obtained by modification of the integration path in the integral equation. The decay of the modified kernel makes this possible for high frequencies but the modified path reduces the accuracy in the deep shadow. This study investigates these modified paths for the case where the shadow region is not omitted from the formulation.

Place, publisher, year, edition, pages
John Wiley & Sons, 2014
Keyword
method of moments; sparsity
National Category
Telecommunications
Research subject
Technology (byts ev till Engineering)
Identifiers
urn:nbn:se:lnu:diva-34025 (URN)10.1002/2013RS005357 (DOI)000342824800006 ()2-s2.0-84906072291 (Scopus ID)
Available from: 2014-04-28 Created: 2014-04-28 Last updated: 2017-12-05Bibliographically approved
2. Accurate hybrid techniques for the method of moments in 2D
Open this publication in new window or tab >>Accurate hybrid techniques for the method of moments in 2D
2016 (English)In: AEU - International Journal of Electronics and Communications, ISSN 1434-8411, E-ISSN 1618-0399, Vol. 70, no 5, 539-543 p.Article in journal (Refereed) Published
Abstract [en]

The integral equations of electromagnetic scattering can be solved numerically by means of the method of moments. This normally leads to a linear system with a dense matrix. Higher order basis functions such as B-splines is a means to improve the accuracy.

For smooth convex scatterers and high frequencies the oscillatory behaviour of the solution can be used to reformulate the integral equation. A sparse matrix can be obtained by modification of the integration path used in the integral equation.This is quite straightforward for the two-dimensional TM case, since the currentdecays rapidly in the shadow in that setting.

In order to increase sparsity and handle the standing waves that are prominent for the TE case, the shadow region can be treated separately, in a hybrid scheme based on \emph{a priory} knowledge about the solution. An accurate method to combine solutions in this hybrid scheme is presented.

Place, publisher, year, edition, pages
Elsevier, 2016
National Category
Telecommunications
Research subject
Physics, Electrotechnology
Identifiers
urn:nbn:se:lnu:diva-34024 (URN)10.1016/j.aeue.2015.12.021 (DOI)000373865600003 ()2-s2.0-84977878040 (Scopus ID)
Note

Available from: 2014-04-28 Created: 2014-04-28 Last updated: 2017-12-05Bibliographically approved

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