Accurate and stable matrix-free time-domain method independent of element shape for general electromagnetic analysis

Abstract

In this paper, we present a new time-domain method that is naturally matrix free, i.e., requiring no matrix solution, regardless of whether the discretization is a structured grid or an unstructured mesh. Its matrix-free property is independent of the element shape used for discretization, and its implementation is straightforward. No interpolations, projections, and mass lumping are required. The accuracy and stability of the proposed method are theoretically analyzed and shown to be 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 validated the accuracy and generality of the proposed matrix-free method.