Time-Domain Method Having a Naturally Diagonal Mass Matrix Independent of Element Shape for General Electromagnetic Analysis—2-D Formulations

Abstract

In this paper, we present a new time-domain method that has a naturally diagonal mass matrix and thereby a strict linear computational complexity per time step, regardless of whether the discretization is a structured grid or an unstructured mesh. This property is obtained independent of the element shape used for discretization. No interpolations, projections, and mass lumping are required. The accuracy and stability of the proposed method are both theoretically guaranteed. In addition, no dual mesh is needed and the tangential continuity of the fields is satisfied across the element interface. The flexible framework of the proposed method also allows for a straightforward extension to higher order accuracy in both electric and magnetic fields. Numerical experiments have been conducted on a variety of unstructured triangular-element meshes. Correlations with analytical solutions and the time-domain finite-element method have validated the accuracy and generality of the proposed new time-domain method.