High Accuracy Electrodynamic Calculations using Hermite Finite Elements

Pandey, Siddhant

Student Work

High Accuracy Electrodynamic Calculations using Hermite Finite Elements

Public Deposited

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.

This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator