Maxwell's vector field equations represent significant challenges for the numerical solution of electric and magnetic fields in complex geometries. With increasing complexity in the design of electromagnetic devices, it becomes imperative to develop compact algorithms for electrodynamic calculations that will generate high accuracy with minimal computational time. We solve the field equations for the example of a two-dimensional photonic crystal using the finite element method with Hermite interpolation polynomials. We demonstrate that the Hermite interpolation polynomials, due to their derivative continuity across elements, yield accurate predictions of the fields in a photonic crystal at a much lower computational cost than conventional approaches to this problem.
Worcester Polytechnic Institute
Major Qualifying Project
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