A new parallelization strategy for solving time-dependent 3D Maxwell equations using a high-order accurate compact implicit scheme

With progress in computer technology there has been renewed interest in a time-dependent approach to solving Maxwell equations. The commonly used Yee algorithm (an explicit central difference scheme for approximation of spatial derivatives coupled with the Leapfrog scheme for approximation of temporal derivatives) yields only a second-order of accuracy. On the other hand, an increasing number of industrial applications, especially in optic and microwave technology, demands high-order accurate numerical modelling. The standard way to increase accuracy of the finite difference scheme without increasing the differential stencil is to replace a 2nd-order accurate explicit scheme for approximation of spatial derivatives with the 4th-order accurate compact implicit scheme. In general, such a replacement requires additional memory resources and slows the computations. However, the curl-based form of Maxwell equations allows us to construct an effective parallel algorithm with the alternating domain decomposition (ADD) minimizing the communication time. We present a new parallel approach to the solution of three-dimensional time-dependent Maxwell equations and provide a theoretical and experimental analysis of its performance. Copyright © 2006 John Wiley & Sons, Ltd.