Stability of the DSI algorithm on a chevron grid

摘要

The development of time domain electromagnetic solvers for nonorthogonal grids is an area of current research interest, stemming from the need to simulate complex geometries in a wide variety of applications. A notable example is the discrete surface integral (DSI) algorithm which solves the Maxwell curl equations in the time domain using a 3d, unstructured, mixed-polyhedral grid. Although this method is an extension of the time proven Yee algorithm, little is known about the numerical properties of the method when discretized on these more general grids. Dispersion relations for the DSI algorithm can be derived using 2d idealized grids, such as the skewed mesh analysis done by Ray and Rambo for both triangles and quadrilaterals. The present work applies the same techniques used for the skewed mesh analysis to another idealized, but nonorthogonal, 2d grid.