Tesis doctoral de José María Tamayo Palau
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 usability of any antenna simulation software based on the mom has led to the development of a general mathematical model of an excitation port in the discretized space. With this new model, it is no longer necessary to adapt the mesh edges to the port.
Datos académicos de la tesis doctoral «Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations«
- Título de la tesis: Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations
- Autor: José María Tamayo Palau
- Universidad: Politécnica de catalunya
- Fecha de lectura de la tesis: 17/02/2011
Dirección y tribunal
- Director de la tesis
- Alexander Heldring
- Tribunal
- Presidente del tribunal: Juan ramón Mosig pérez
- guiseppe Vecchi (vocal)
- guy Vandenbosch (vocal)
- Manuel felipe Cátedra pérez (vocal)