The origin of spurious solutions in computational electromagnetics
type: Item
instance of: scholarly article
title: The origin of spurious solutions in computational electromagnetics
zbMATH Open document ID: 0848.65086
author: Bo-Nan Jiang
author: J. Wu
author: Louis A. Povinelli
published in: Journal of Computational Physics
publication date: 1996-07-02T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 78A50
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 35Q60
zbMATH DE Number: 881907
zbMATH Keywords: computational electromagnetics
zbMATH Keywords: divergence equations
zbMATH Keywords: Maxwell's equations
zbMATH Keywords: curl equations
zbMATH Keywords: least squares
zbMATH Keywords: finite element methods
zbMATH Keywords: spurious solutions
zbMATH Keywords: waveguide
reviewed by: Ll. G. Chambers
MaRDI profile type: Publication
OpenAlex ID: W1963572177
Wikidata QID: Q56057386
DOI: 10.1006/JCPH.1996.0082
description: scientific article; zbMATH DE number 881907