| 1. |
- Botha, Matthys M, et al.
(författare)
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An improved quadrature error estimate for nearly-singular MoM integrals
- 2018
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Ingår i: 2018 IEEE Antennas and Propagation Society International Symposium and USNC/URSI National Radio Science Meeting, APSURSI 2018 - Proceedings. ; , s. 2431-2432
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Konferensbidrag (refereegranskat)abstract
- A well-known numerical integration scheme for weakly near-singular integrands on triangle domains, is the Radial-Angular-RI-Sqrt near-singularity cancellation transformation quadrature scheme. Such integrals feature routinely in the method of moments (MoM), for integral equation based numerical electromagnetic field calculations. Recently, a closed-form quadrature error estimate has been proposed for this scheme. In this paper, the estimate is further improved, such that its range of applicability is extended.
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| 2. |
- Botha, Matthys M, et al.
(författare)
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Analysis and estimation of quadrature errors in weakly singular source integrals of the method of moments
- 2018
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Ingår i: International Journal of Numerical Modelling: Electronic Networks, Devices and Fields. - : Wiley. - 0894-3370 .- 1099-1204. ; 31:1
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Tidskriftsartikel (refereegranskat)abstract
- The method of moments (MoM) is used for the numerical solution of electromagnetic field integral equations. Weakly singular integrals over surfaces in 3 dimensions (3D) are routinely evaluated for the impedance matrix setup and for post-processing. Available numerical integration schemes range from direct application of Gauss-Legendre product-rule quadrature, to singularity and near-singularity cancellation, coordinate transformation schemes. This paper presents a general, explicit, pole-based, a priori procedure to estimate quadrature errors in the numerical evaluation of weakly singular and near-singular, 3D surface integrals in the MoM. It is based on an error theorem for linear Gaussian quadrature, which involves the analytic extension of the integrand into the complex plane. Errors are linked to poles in the complex plane. New closed-form estimates are presented for direct Gaussian product-rule integration, polar-coordinate integration, and the Radial-Angular-R 1 -Sqrt singularity cancellation scheme, for triangle integration domains. This work can serve as a foundation/template for further, 3D MoM-related work to identify appropriate quadrature schemes according to their error characteristics; for automatic selection of optimal schemes and quadrature orders in a computer implementation of the MoM; and for local and global estimation of MoM quadrature errors. This work can be specialized to the MoM for surfaces in 2D.
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| 3. |
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| 4. |
- Botha, Matthys M, et al.
(författare)
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Quadrature error estimation for MoM matrix entries
- 2017
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Ingår i: 19th International Conference on Electromagnetics in Advanced Applications, ICEAA 2017; Verona; Italy; 11 September 2017 through 15 September 2017. - 9781509044511 ; , s. 973-975
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Konferensbidrag (refereegranskat)abstract
- This paper is concerned with the method of moments (MoM) for electric field integral equation (EFIE) based numerical electromagnetic analysis of conducting surface structures. Inner (source) and outer (testing) integrals are encountered, when evaluating matrix entries. The well-known Radial-Angular-R1-Sqrt (RA-R1-Sqrt) weak near singularity cancellation transformation quadrature scheme for the inner integrals and standard Gaussian numerical integration for the outer integrals, are considered. It is shown that the quadrature error in the matrix entries, due to inner integral evaluation, can be accurately estimated under certain circumstances. A closed-form quadrature error estimate for the RA-R1-Sqrt scheme is employed.
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| 5. |
- Dommisse, William R., et al.
(författare)
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Macro Basis Functions for Efficient Analysis of Thick Wires in the MoM
- 2024
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Ingår i: IEEE Transactions on Antennas and Propagation. - 0018-926X .- 1558-2221. ; 72:7, s. 5865-5876
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Tidskriftsartikel (refereegranskat)abstract
- This article presents a macro basis function (MBF) formulation for efficient method of moments (MoM) modelling of conducting wires with appreciable thickness. General surface formulations are prohibitively inefficient for electrically thin wires, while the typical exact-kernel, rooftop-basis, thin-wire MoM becomes wholly inaccurate for electrically thick cylinders. The MBF formulation bridges the gap between thin-wire MoM, and general conducting surface MoM formulations, by introducing circumferential variations and components beyond the standard rooftop basis functions. The MBFs are constructed upon a full-order, divergence-conforming, triangle element MoM discretization. Comprehensive junction and end-cap treatment, and tapered wire support, are natural features of the formulation. As with thin-wire MoM, degrees of freedom (DoFs) are purely proportional to the electrical length of the wire. Results demonstrate that the intermediate range of “thick wires” is analyzed with practically the same accuracy as general surface MoM, with significantly reduced DoFs.
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| 6. |
- Du Plessis, Jacques T., et al.
(författare)
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Scattering Analysis of Thick Wires with the MoM using Macro Basis Functions
- 2022
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Ingår i: 2022 International Conference on Electromagnetics in Advanced Applications, ICEAA 2022. ; , s. 340-342
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Konferensbidrag (refereegranskat)abstract
- This work is concerned with the analysis of scattering by conducting wires connected to conducting structures, using the method of moments (MoM). Based on thin-wire assumptions, low numbers of degrees of freedom (DoFs) are required by typical exact-kernel thin-wire MoM solvers, for accurate analysis. However, the thin-wire assumptions break down when the wire diameter becomes appreciably large in terms of the wavelength. An approach based on macro basis functions (MBFs) for wire current representation is outlined, aimed at extending the wire thickness range of accurate analysis, while maintaining a low number of DoFs similar to that of thin-wire formulations. Preliminary results demonstrate the effectiveness of the MBF approach.
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| 7. |
- Ludick, D. J., et al.
(författare)
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Accelerating the CBFM-enhanced jacobi method
- 2017
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Ingår i: 19th International Conference on Electromagnetics in Advanced Applications, ICEAA 2017; Verona; Italy; 11 September 2017 through 15 September 2017. - 9781509044511 ; , s. 346-349
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Konferensbidrag (refereegranskat)abstract
- The Characteristic Basis Function Method (CBFM)-enhanced Jacobi method has been introduced as an improvement to the standard iterative Jacobi method for finite array analysis. This technique is a domain decomposition approach based on the Method of Moments (MoM) formulation. In some cases, e.g. array environments with a low degree of mutual coupling, the runtime benefit of the CBFM-enhanced Jacobi method is not as significant when compared to that of the Jacobi technique. The reason for this is that additional computational overhead is introduced during each iteration, i.e. setting up and solving the CBFM reduced matrix equation. In this work the adaptive cross approximation (ACA) algorithm is used to accelerate this step in the CBFM-enhanced Jacobi method.
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| 8. |
- Ludick, D. J., et al.
(författare)
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Comparison of the iterative jacobi method and the iterative Domain Green'S Function Method for finite array analysis
- 2016
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Ingår i: 10th European Conference on Antennas and Propagation, EuCAP 2016, Davos, Switzerland, 10-15 April 2016. - 2164-3342. - 9788890701863
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Konferensbidrag (refereegranskat)abstract
- The purpose of this work is to compare two iterative techniques that may be used for the analysis of large, disjoint finite antenna arrays, viz. the iterative Jacobi method and the iterative Domain Green's Function Method. These methods are conceptually similar, in that they offer alternative ways to improve non-local current distributions during the iterative process. The error convergence of each method will be studied at the hand of an example.
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| 9. |
- Rylander, Thomas, 1972, et al.
(författare)
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Exact-Kernel Thin-Wire MoM with Geometric Representation by Bezier Curves
- 2022
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Ingår i: IEEE International Symposium on Electromagnetic Compatibility. - 1077-4076 .- 2158-1118. ; 2022-September, s. 389-393
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Konferensbidrag (refereegranskat)abstract
- Electromagnetic field simulation of wire structures is important to high-frequency electromagnetic engineering applications, including antenna design and electromagnetic compatibility studies. This paper exploits the electric field integral equation to solve for the induced current on a curved thin-wire, which is modelled as a perfect electric conductor (PEC). The singular part of the Green's function is integrated by means of the complete elliptic integral of the first kind. The geometry of the curved wire is described by Bezier-curve segments, where this approach is particularly useful for problems where a smooth wire-geometry requires better representation than the current at (typically) low frequencies. The formulation is tested on the scattering from a closed PEC ring shaped as a circle for three different frequencies. As the number of elements is increased, the induced currents tend toward the reference solution provided by FEKO.
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