Web-splines solution of 3D electromagnetic problems

Abstract

This dissertation proposes the weighted extended basis splines (web-splines) approach in the finite element method (FEM) for electrostatic, electromagnetic, and bioheat problems for radially symmetric and three dimensional (3D) structures. The most important advantage of this new method is that it does not need mesh generation which overcomes some of the drawbacks of using meshes and piecewise-uniform or linear trial functions. In this thesis, the theoretical development of web-spline formulations has been done. The mathematical contributions have been supported by the simulations in both electrostatic and electromagnetic wave problems for inhomogeneous boundary conditions in cylindrical coordinates for the first time. Furthermore, this newly developed computational approach is employed to calculate the steady-state temperature distribution in a normal human eye. As a first step, the human eye is evaluated in two dimensions (2D). The simulation results which are verified using the values reported in the literature, point out to better efficiency in terms of the accuracy level. Next, to give a more precise representation of the actual human eye, 3D modeling is simulated using these new finite elements in conjunction with linear, quadratic and cubic b-splines. Grid convergence number estimates are derived for both sets of simulations. It is shown that this method reaches higher precision in a shorter period of time with fewer nodes. Finally, FEM with web-spline computer modeling have been applied to human eye to study the intraocular temperature during microwave irradiation. Our findings indicate that web-spline solutions improve the computational methods for health care.