Matrix singular value decomposition for pole-free solutions of homogeneous matrix equations as applied to numerical modeling methods

Labay, Vladimir A.; Børnemann, Jens

doi:10.1109/75.122406

Cited by 62 publications

(24 citation statements)

References 8 publications

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“…Although much attention has been devoted previously to the zero-searching procedure [7,10,13,17,19,32], the relevance of this task in many electromagnetic problems still requires the development of new strategies to enhance the efficiency of the overall procedure. To this end, we propose a systematic integral method to find all the real/complex roots of any analytic function within a given region (in the present context, the term analytic means free of both poles and branch points) and without any previous knowledge of the approximate location of the roots (although, if this information were available, it could be used advantageously).…”

Section: A Root Searching Methodsmentioning

confidence: 99%

Systematic and efficient root finder for computing the modal spectrum of planar layered waveguides

Rodríguez-Berral

Mesa

Medina

2003

Int J RF and Microwave Comp Aid Eng

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An efficient and systematic strategy to find the propagation constants of real, complex, and leaky modes of covered and uncovered planar multilayered isotropic/uniaxial waveguides is presented. This strategy first builds up a pole-free characteristic function and then makes use of a root-searching scheme based on an integral nature method to search for its zeros. For uncovered waveguides, the branch points of the characteristic function can be removed by introducing the upper half-space vertical wavenumber as the working variable. Examples of the efficiency, reliability, and robustness of the presented technique are given for both covered and uncovered waveguides, which sets up this technique as a very convenient CAD tool. The method is also applied to study a new and interesting problem: the evolution of the modes of a grounded dielectric waveguide when increasing the permittivity of the upper semi-infinite medium.

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Section: A Root Searching Methodsmentioning

confidence: 99%

Systematic and efficient root finder for computing the modal spectrum of planar layered waveguides

Rodríguez-Berral

Mesa

Medina

2003

Int J RF and Microwave Comp Aid Eng

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“…But the actual implementation of searching is a difficult task because of the fact that det([A(γ)]) is a rapidly changing function with γ, containing not only poles and zeros in close neighborhood but also extremely steep gradients. A method to circumvent this problem is presented in [27] where the singular-value decomposition of the matrix…”

Section: Numerical Resultsmentioning

confidence: 99%

Application of Mode Matching Method to Analysis of Axisymmetric Coaxial Discontinuity Structures Used in Permeability and/or Permittivity Measurement

Huang¹,

Zhang²

2007

PIER

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Abstract-This paper presents a mode matching method to analyze axisymmetric coaxial discontinuity structures, commonly used in the permeability and/or permittivity measurement. By performing the mode matching procedures at all discontinuity interfaces, a set of general simultaneous equations are derived, which can be easily solved. The s parameters and field distribution in the structures are readily obtained from the solution to the simultaneous equations. As a preliminary preparation for the mode matching method, the propagation constants of all the sections in the structure have to be solved. A one-dimensional frequency domain finite difference method is presented in this paper to efficiently solve the propagation constants for the multi-layered axisymmetric structures. Numerical examples show that the results obtained from the method in this paper are in good agreement with those from other methods in the published literature papers, and the method presented here has much higher efficiency.

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“…There are three ways to find the solution of singularity: we can set the determinant, the smallest eigenvalue, or the smallest singular value to zero. All of these are equivalent in terms of the results, but the SVD technique is more stable and faster (Labay & Bornemann, 1992;Mohebbi et al, 2006). Hence, highly stable SVD was used to find the eigenvalues of the matrix A.…”

Section: Theory and Formulationmentioning

confidence: 99%

“…The MM technique, along with an entire domain orthogonal set that was used in this case, led to results that were in good agreement with other methods and experiments. A combination of the MM technique and the generalized scattering matrix (GSM) was reported in Labay and Bornemann (1992) for analysis of infinitely thin microstrip and other printed planar structures. Generally, this hybrid method is a powerful tool for analyzing many composite waveguide structures that are commonly found in practical applications (Itoh, 1989).…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Mode-Matching Point-Matching Technique for Calculation of Dispersion Curve of Strip Gratings

et al. 2008

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The rigorous mode-matching technique combined with point matching is used in this article to find the dispersion curve of the traveling wave in a 1-D strip grating backed by a grounded homogeneous dielectric substrate. The strips are assumed to be infinitely thin. Unlike regular mode matching, a simple sub-domain orthogonal set is used in order to convert the algebraic equations obtained from boundary conditions into a matrix format. There is a good agreement between the results obtained using the proposed method and what was reported in the previous literature.

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Matrix singular value decomposition for pole-free solutions of homogeneous matrix equations as applied to numerical modeling methods

Cited by 62 publications

References 8 publications

Systematic and efficient root finder for computing the modal spectrum of planar layered waveguides

Systematic and efficient root finder for computing the modal spectrum of planar layered waveguides

Application of Mode Matching Method to Analysis of Axisymmetric Coaxial Discontinuity Structures Used in Permeability and/or Permittivity Measurement

A Hybrid Mode-Matching Point-Matching Technique for Calculation of Dispersion Curve of Strip Gratings

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