Time domain support operator method on unstructured grids

Nowadays, much effort on FDTD is to push the Yee grid onto a nonorthogonal, nonsmooth, and unstructured grid. Among the techniques used, the support operator method (SOM) is attractive because the discrete operators derived preserve the fundamental properties of their original continuum models (Hyman, J.M. and Shashkov, M., Comp. Math. Appl., vol.33, no.4, p.81-104, 1997; Appl. Num. Math., vol.25, p.413-42, 1997). In SOM, a discrete approximation is defined for a first order differential operator that satisfies the appropriate integral identity. This initial discrete operator, called the natural operator, then supports the construction of other discrete operators, using discrete formulations of the identities for differential operators. SOM has been applied to solve Maxwell-Heaviside equations in structured grids (Hyman and Shashkov, Los Alamos National Lab., Report LA-UR-98-1032; Proc. 4th Int. Conf. on Math. and Num. Aspects of Wave Propag., 1998). We extend it to all unstructured quadrilateral grids, and give the stability analysis of this method.