This dissertation is about efficient computation of the electromagnetic fields with the locally corrected Nyström (LCN) method as a point-based boundary element method (BEM). The concept of surface integral equations is discussed and the electric field integral equation (EFIE) is derived from the Maxwell’s equations. Due to its point-based nature, the LCN discretization of the EFIE has some advantages over discretizing the EFIE by the method-of-moments (MoM) which is an element-based BEM. On the other hand, due to maturity of the MoM, a large body of work is available to resolve the numerical issues arising in MoM while there has been less work related to the relatively new LCN. To combine the benefits of the LCN method and the classical Rao-Wilton-Glisson MoM, equivalence between these BEMs are established and their exact relationships are derived. Both the vector-potential EFIE and the mixed-potential EFIE are covered. Various aspects of achieving HO convergence to the correct answer using high-order (HO) LCN method are discussed. In particular, the patch size limitation, predicting the optimal degrees of freedom, and the effect of dynamic range in the solution are discussed both analytically and numerically to provide concrete motivations towards HO LCN. The benefits of an HO BEM can not be realized unless an HO geometry representation is used in conjunction with the BEM. Non-uniform rational b-spline (NURBS) surfaces are the most widely adopted HO geometry modelling technique in various disciplines due to their many advantages. However, a typical mesh created out of NURBS surfaces contain both triangular and quadrilateral elements while formulating LCN based on Gaussian quadrature rules on triangular elements have limitations. As a result, the LCN community has mostly adopted LCN based on curvilinear quadrilateral modelling of the geometry. A new class of Newton-Cotes quadrature rules for triangles is proposed to facilitate incorporating NURBS surfaces into the HO LCN. / May 2016

Electromagnetic scattering from a rough two dimensional homogeneous scatterer has been computationally modeled. The scatterer is intended to simulate reflection from a two interface multilayer. The rough scatterer was created from Gaussian random points centered about an ideal interface. The points were connected with a third order spline interpolant which accounts for correlation between neighboring surface atoms. The scalar electric field integral equation (EFIE) and magnetic field integral equation (MFIE) were solved using the Nystrom method to obtain the reflected intensity as a function of observation angle. Verification of the accuracy of the code was obtained by means of comparison with well-known analytic solutions and approximations. The predicted Nevot-Croce factor drop in reflectance was found to be in general agreement with the computed decrease in reflectance due to surface roughness. However, an angle dependent difference was also noticed, indicating the Nevot-Croce factor might need revision. The code is being modified to run on a supercomputing cluster where longer, more realistic surfaces can be analyzed to determine whether an improved roughness correction factor is needed.

In 1919 Anton Nyström became the first person in Sweden to publish a comprehensive defense of homosexuality. He believed that its classification as a mental illness was erroneous and that Sweden's law against homosexual sex was both irrational and cruel. Nyström was a physician whose work in the medical area dealt primarily with dermatology, psychiatry and human sexuality; however he was also a prolific historian, who took a staunchly anti-Christian view in his analysis of how Christianity affected European culture, especially in the area of sexual morality. In fact, much of Nyström's medical texts dealing with human sexuality consisted of anti-Christian cultural and historical commentary. The object of this "C-uppsats" is to analyze Nyström's pamphlet, Om Homosexualitet och Hermafroditi: Belysning af Missförstådda Existenser and illustrate how its defensive structure was consistent with the pattern used by the author in his other books and articles on human sexuality. Specifically, that irrational and neurotic Christian beliefs caused both mental and physical suffering and were the source of deleterious forms of morality. Additionally, this paper will also show that the solution Nyström had for the problem of negative and erroneous attitudes towards homosexuality was to replace the sodomitic view of homosexuality with one based upon a more rational and naturalistic belief system, the basis of which could be found in the pre-Christian cultures of Europe, most especially in Greece. This new conception was to be constructed primarily out of historical example and cultural analyses. For Nyström, history writing was used both as a weapon to fight the source of negative attitudes towards homosexuality, as well as a tool that could be used to build a positive cultural model which would be beneficial for homosexuals.