On the Causes of Spurious Solutions in Electromagnetics

Abstract

The problem of spurious solutions in finite-element methods for electromagnetics is discussed with the explicit aim to re-open the discussion on this much debated subject. First, an overview is given of existing ideas about the causes of spurious solutions together with the solutions that are proposed. Subsequently it is concluded that the cause of spurious solutions may differ from what is usually suggested or claimed, and an alternative cause for spurious solutions is proposed. Finally, suggestions are given about how a finite-element method should be designed that is free of spurious solutions.