A functional for dynamic finite-element solutions in electromagnetics

A new functional is introduced that satisfies Maxwell's equations, provides minimization, and eliminates spurious solutions. An analytical method is developed that provides a means of evaluating functional forms. The analytical method confirms the effective functional form as the fundamental cause underlying the difficulties with spurious solutions that are not completely eliminated under all circumstances. It is shown that the curl-curl "functional" form allows for the existence of an improper gradient behavior in a general field expansion. The new functional is shown to be self adjoint and positive definite, thus providing an error minimization. Numerical results are obtained that demonstrate the effectiveness of the new functional to prevent spurious solutions using node-based elements.