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Universitat Politècnica de Catalunya

1. Tamayo Palau, José María. Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations.

Degree: Departament de Teoria del Senyal i Comunicacions, 2011, Universitat Politècnica de Catalunya

URL: http://hdl.handle.net/10803/6952

The Method of Moments (MoM) has been widely used during the last decades for the discretization and the solution of integral equation formulations appearing in several electromagnetic antenna and scattering problems. The most utilized of these formulations are the Electric Field Integral Equation (EFIE), the Magnetic Field Integral Equation (MFIE) and the Combined Field Integral Equation (CFIE), which is a linear combination of the other two. The MFIE and CFIE formulations are only valid for closed objects and need to deal with the integration of singular kernels with singularities of higher order than the EFIE. The lack of efficient and accurate techniques for the computation of these singular integrals has led to inaccuracies in the results. Consequently, their use has been mainly restricted to academic purposes, even having a much better convergence rate when solved iteratively, due to their excellent conditioning number. In general, the main drawback of the MoM is the costly construction, storage and solution considering the unavoidable dense linear system, which grows with the electrical size of the object to analyze. Consequently, a wide range of fast methods have been developed for its compression and solution. Most of them, though, are absolutely dependent on the kernel of the integral equation, claiming for a complete re-formulation, if possible, for each new kernel. This thesis dissertation presents new approaches to accelerate or increase the accuracy of integral equations discretized by the Method of Moments (MoM) in computational electromagnetics. Firstly, a novel fast iterative solver, the Multilevel Adaptive Cross Approximation (MLACA), has been developed for accelerating the solution of the MoM linear system. In the quest for a general-purpose scheme, the MLACA is a method independent of the kernel of the integral equation and is purely algebraic. It improves both efficiency and compression rate with respect to the previously existing single-level version, the ACA. Therefore, it represents an excellent alternative for the solution of the MoM system of large-scale electromagnetic problems. Secondly, the direct evaluation method, which has proved to be the main reference in terms of efficiency and accuracy, is extended to overcome the computation of the challenging 4-D hyper-singular integrals arising in the Magnetic Field Integral Equation (MFIE) and Combined Field Integral Equation (CFIE) formulations. The maximum affordable accuracy – machine precision – is obtained in a more than reasonable computation time, surpassing any other existing technique in the literature. Thirdly, the aforementioned hyper-singular integrals become near-singular when the discretized elements are very closely placed but not touching. It is shown how traditional integration rules fail to converge also in this case, and a possible solution based on more sophisticated integration rules, like the Double Exponential and the Gauss-Laguerre, is proposed. Finally, an effort to facilitate the…
*Advisors/Committee Members: [email protected] (authoremail), false (authoremailshow), Rius Casals, Juan Manuel (director).*

Subjects/Keywords: vertex adjacent integration; edge adjacent integration; adaptive cross approximation; impedance matrix compression; electromagnetism; numerical simulation; singular integrals; surface integral equations; fast solvers; method of moments (MOM); 517; 621.3

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APA (6^{th} Edition):

Tamayo Palau, J. M. (2011). Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations. (Thesis). Universitat Politècnica de Catalunya. Retrieved from http://hdl.handle.net/10803/6952

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Tamayo Palau, José María. “Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations.” 2011. Thesis, Universitat Politècnica de Catalunya. Accessed April 22, 2021. http://hdl.handle.net/10803/6952.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Tamayo Palau, José María. “Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations.” 2011. Web. 22 Apr 2021.

Vancouver:

Tamayo Palau JM. Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations. [Internet] [Thesis]. Universitat Politècnica de Catalunya; 2011. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/10803/6952.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Tamayo Palau JM. Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations. [Thesis]. Universitat Politècnica de Catalunya; 2011. Available from: http://hdl.handle.net/10803/6952

Not specified: Masters Thesis or Doctoral Dissertation