A parallel discrete surface integral equation method for the analysis of three-dimensional microwave circuit devices with planar symmetry

It has been found that the discrete integral equation (DSI) technique is a highly effective technique for the analysis of microwave circuits and devices. In the present paper, a technique that exploits planar symmetries is described, namely, planar symmetry is recognized for three-dimensional geometries which can be uniquely described by a projection onto a two-dimensional plane. To this end, the three-dimensional model is described by a two-dimensional grid. Furthermore, due to regularity along the third-dimension the sparse matrices used for the field updates need only be computed for the two-dimensional grid. This results in a significant savings in storage, increasing potential problem sizes that can be solved by orders of magnitude. Based on the planar DSI algorithm, a highly scalable parallel algorithm is presented. The parallel algorithm is based on a spatial discretization of the two-dimensional mesh. By treating the update matrices as a subassembly of matrices, the matrix-vector multiplications are easily done in parallel requiring only minimal interprocessor communication. Finally, the robustness and efficiency of the algorithm is illustrated through a number of examples.