Accurate matrix-free time-domain method in unstructured meshes

In this paper, we develop 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. 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. Numerical experiments on a variety of unstructured meshes have validated the accuracy and generality of the proposed method.