Numerical Analysis: Computational electromagnetics in complex environments
The Yee scheme is still the main workhorse for computational electromagnetics in industry. In this project we study how to improve two weaknesses of the Yee scheme when applied to problems with complicated geometry: its inability to cope with boundaries not aligned with the grid, especially curved boundaries; and small geometric features, such as obstacles and holes, that are of smaller size than the grid spacing. These weaknesses stem from the use of a staggered Cartesian grid which is coincidently, also a major reason for the popularity of the method. It gives relatively low dispersion, a low memory footprint, and allows easy implementation on distributed memory architectures. Our approach has been to stick to the Yee grid structure as much as possible and primarily modify the coefficients in the method to achieve the desired improvements. We thus develop new stencils and and analyze the results with respect to accuracy and stability.