Novel strategies for second-kind integral equations to analyze perfect electric conductors

Güler, Sadri
In this thesis, the magnetic-field integral equation (MFIE) for three-dimensional perfectly conducting objects is studied with a particular focus on the solutions of the formulation with the method of moments employing low-order discretization elements. Possible discretization functions and their applications in the testing of MFIE while considering different numbers of testing points are analyzed for accurate and efficient solutions. Successful results are obtained by using rotational Buffa-Christiansen testing functions when the electric current density is expanded with Rao-Wilton-Glisson functions. The same mixed discretization scheme is also employed in the context of the combined-field integral equation (CFIE). In order to successfully handle internal resonances in the mixed-discretized CFIE, projection of testing spaces of EFIE and MFIE via Gram matrices is required. Inversion of Gram matrices is discussed in terms of computational requirements in the context of large-scale problems analyzed with the multilevel fast multipole algorithm (MLFMA). Finally, a novel MFIE implementation with double-layer modeling is presented to mitigate internal resonances without resorting to CFIE. Accuracy of the proposed formulation is improved via inner-layer selection, post-processing, and accurate discretization techniques. All discussions are presented and supported via numerical results involving canonical objects.