The origin of spurious solutions in computational electromagnetics
The authors discuss the belief that the divergence equations in Maxwell's equations are redundant and that consequently many numerical methods solve only the first-order curl equations or the second order curl-curl equations, giving rise therefore to the possibility of spurious modes and inaccurate solutions in the numerical solution of problems of electromagnetic theory. They show that this belief is untrue and that the divergence equations are in fact relevant and suggest a more suitable formulation of the second-order curl-curl equations. A least squares formulation is introduced, suitable for finite element methods, which generates a system which does not give rise to spurious solutions. An analysis is developed which introduces extra potentials into Maxwell's equations and shows that they must be zero and hence that the system consisting of Maxwell's equations, together with the associated divergence and boundary equations is not overdetermined. A least squares formulation is constructed which is suitable for use with time harmonic fields and reasons are given as to why it is highly suitable for numerical solutions. The method is illustrated by two circular waveguide problems involving respectively two semi-circular cylinders of different electromagnetic properties and an off-centre circular core.
scientific article; zbMATH DE number 881907