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Numerical techniques for mixed high-low frequency EM-problems
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
2002 (English)Conference paper (Refereed)
Abstract [en]

Our poster present numerical methods to be used for wave propagation problems where both relatively short and long wavelengths, λ , are present. Short and long wavelengths is referred to the characteristic sizes of the scales in the boundary conditions (BC) and material properties (MP). We propose that, depending on properties of the BC, one of three different Boundary Element Methods (BEM) are hybridised with a wave front, as opposed to a ray, implementation of Geometrical Theory of Diffraction (GTD). We will only consider the scattering problem in the presentation. Sometimes the electromagnetic engineer needs to know how a small size feature, e.g. a small perturbation of the BC, affects scattering parameters. We indicate the original Scatterer by an upper case S and the small scatterer, i.e. the perturbation, with lower case s . If the perturbation together with the Scatterer is small, BEM will serve as an excellent tool for numerical computations. However, when the complexity of the problem overcome the computer resources, other methods must be used. We propose that either of the three following boundary element methods are hybridised with GTD. If the perturbation only consist in an addition of a geometrical detail, i.e. the Scatterer’s BC and MP is unaffected by the perturbation, the perturbation can be discretized with local boundary elements and the impact on scattering parameters can be taken into account with GTD. If a boundary element is close to the scatterer, hence does not illuminate the scatterer with a ray field, we propose to use a linear combination of the image solution and the GTD to model the illumination. From an implementation point of view the interaction between the perturbation and the scattering is preferably done out-of-core and iteratively thereby leaving the GTD-solver and the BEM-solver separated. If the perturbation actually consist of a modifications of the Scatterer we propose that, at least in the two dimensional case, edge diffraction is applied to the artificial edges that indicate the points separating the perturbed and unperturbed parts of the Scatterer. No iteration needs to be done in this case since we assume that all scattered waves are outgoing. The third BEM is to be used when the perturbation actually changes the scatterer and the shape of the Scatterer close to the perturbation is crucial and needs to be rigorously taken into account. We then need to have mixed local and global boundary elements in the BEM-domain to model the interaction properly. We discuss how to formulate the boundary integral problem for a small change in a infinite electric perfect conducting ground plane. To take into account features that are far away from the perturbation can, as mentioned above, GTD be used. GTD has its origin in the method of characteristics. The characteristics are typically found with two types of methods in CEM-software.By using analytical or numerical methods applied to a variational problem with constraints. The method will fail in caustics since we then have infinite many solutions.By using the so-called shooting method. The shooting method succeed in caustics but may produce bad resolution for certain problems. We propose that our implementation of GTD, which we call the Wave Front method (WF-method), is used instead of the two methods presented above since we then will avoid the problems with efficiency and accuracy. It can be used in a CAD-setting and also be applied to smooth surface diffraction and inhomogeneousan isotropic materials. We will present numerical results from the presented methods in future publications.

Place, publisher, year, edition, pages
2002. 18-22 p.
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-90290OAI: diva2:504830
Proceedings of RVK02

QC 20140124

Available from: 2012-02-21 Created: 2012-02-21 Last updated: 2014-01-24Bibliographically approved

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Engquist, Björn
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Numerical Analysis, NA (closed 2012-06-30)
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