Honors College Thesis

 

Finite Element and Finite Difference Methods for Maxwell’s Equations in Metamaterials Public Deposited

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https://ir.library.oregonstate.edu/concern/honors_college_theses/x059cd51j

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  • In this thesis, we consider Maxwell's Equations and their numerical discretization using finite difference and finite element methods. We first describe Maxwell's equations in linear dielectrics and then present finite difference and finite element methods for this case. We then describe Maxwell's equations in linear metamaterials using the Lorentz and Drude models. Finally, we construct a finite element method for Maxwell's Equations in a Lorentz metamaterial. An exact solution of the model system, involving both partial differential equations of the Maxwell system and ordinary differential equations describing the response of the Lorentz metamaterial, is constructed. Finite element simulations are then performed and tested against this exact solution to demonstrate the accuracy of the method.
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