The Origin of Spurious Solutions in Computational Electromagnetics
Abstract
It is commonly believed that the divergence equations in the Maxwell equations are "redundant" for transient and timeharmonic problems, therefore most of the numerical methods in computational electromagnetics solve only two firstorder curl equations or the secondorder curlcurl equations. This misconception is the true origin of spurious modes and inaccurate solutions in computational electromagnetics. By studying the divcurl system this paper clarifies that the firstorder Maxwell equations are not "overdetermined," and the divergence equations must always be included to maintain the ellipticity of the system in the space domain, to guarantee the uniqueness of the solution and the accuracy of the numerical methods, and to eliminate the infinitely degenerate eigenvalue. This paper shows that the common derivation and usage of the secondorder curlcurl equations are incorrect and that the solution of Helmholtz equations needs the divergence condition to be enforced on an associated part of the boundary. The divcurl method and the leastsquares method introduced in this paper provide rigorous derivation of the equivalent secondorder Maxwell equations and their boundary conditions. The nodebased leastsquares finite element method (LSFEM) is recommended for solving the firstorder full Maxwell equations directly. Examples of the numerical solutions by LSFEM are given to demonstrate that the LSFEM is free of spurious solutions.
 Publication:

Journal of Computational Physics
 Pub Date:
 April 1996
 DOI:
 10.1006/jcph.1996.0082
 Bibcode:
 1996JCoPh.125..104J