High Accuracy Electrodynamic Calculations using Hermite Finite ElementsPublic Deposited
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We show that the present approaches for the solution of Maxwell's equations have limitations that can be overcome through the use of C1-continuous Hermite interpolation polynomials. Our approach yields better accuracy by several orders of magnitude than comparable applications of edge-based vector finite element method (VFEM). We reexamine the issue of removing spurious unphysical zero-frequency solutions. (i) We investigate the group theory of fields in an empty cubic metallic cavity to explain the accidental degeneracy. (ii) We show that the inclusion of a smaller dielectric cube within the cubic cavity leads to the removal of accidental degeneracy. The method delineated here should be effective in solving scalar-vector coupled field problems, such as modeling quantum cavity well lasers.
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