The refinement by superposition approach to hp-adaptivity for finite element simulations in computational electromagnetics
Date
2022
Authors
Corrado, Jeremiah, author
Notaros, Branislav M., advisor
Kirby, Michael, committee member
Ilic, Milan M., committee member
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Abstract
The Finite Element Method (FEM) is a versatile numerical tool for simulating the behavior of Partial Differential Equations (PDEs) over geometric models with arbitrary shapes and material parameters. Its applications are widespread as PDEs are used to model the behavior of almost all complex physical systems. Common PDEs include Schrödinger's equation which governs the evolution of quantum systems; the Navier-Stokes equations, which describe the behavior of fluids; and Maxwells Equations, which are a macroscopic description of all Electric and Magnetic Phenomena. When leveraged against Maxwells Equations, FEM allows engineers and scientists to rapidly design a wide range of Radio-Frequency (RF) devices such as antennas, RF filters, waveguides, and many others, all of which are important to the development of communications networks, sensing networks, and computing infrastructure. One open question within FEM research is how to maximize simulation efficiency (i.e., what is the best strategy to maximize the ratio of simulation accuracy to computational resource usage). A typical approach is to use a multi-step process beginning with a coarse (or low resolution) discretization of the geometric model in question, which uses a small number of computational resources. This model is then iteratively refined in an intelligent manner, only introducing more entropy where it is most needed to improve solution accuracy. After several iterations, this approach will have achieved a desirable balance between resource usage and solution accuracy. This work focuses on the development and testing of a simple and ergonomic implementation of h- and p-refinements for FEM. When used in tandem, these two refinement strategies are amenable to the above procedure and efficiently produce accurate results on challenging Computational Electromagnetics problems.
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Subject
anisotropic refinement
FEM
refinement by superposition
FEA
adaptive refinement
hp-refinement