The conformal perfectly matched layer for electrically large curvilinear higher order finite element methods in electromagnetics - Smull, Aaron P., author; Notaros, Branislav, advisor; Pezeshki, Ali, committee member; Estep, Donald, committee member (Colorado State University. Libraries, 2017)
The implementation of open-region boundary conditions in computational electromagnetics for higher order finite element methods presents a well known set of challenges. One such boundary condition is known as the perfectly matched layer. In this thesis, the generation of perfectly matched layers for arbitrary convex geometric hexahedral meshes is discussed, using a method that can be implemented without differential operator based absorbing boundary conditions or coupling to boundary integral equations. A method for automated perfectly matched layer element generation is presented, with geometries based on surface projections from a convex mesh. Material parameters are generated via concepts from transformation electromagnetics, from complex-coordinate transformation based conformal PML's in existing literature. A material parameter correction algorithm is also presented, based on a modified gradient descent optimization algorithm Numerical results are presented with comparison to analytical results and commercial software, with studies on the effects of discretization error of the effectiveness of the perfectly matched layer. Good agreement is found between simulated and analytical results, and between simulated results and commercial software.
Keywords: finite element method; perfectly matched layer; computational electromagnetics; scattering; numerical methods