Parallel implementation of domain decomposition methods for the electromagnetic analysis of guided wave systems

Abstract

A domain decomposition method is introduced to facilitate the efficient and rigorous computation of electromagnetic phenomena in structures that are electrically large in one dimension. These large structures are decomposed into many smaller regions by placing partitions throughout the structure, then numerical solutions are generated within each region. Field continuity conditions are applied at the partitions between regions after the numerical solutions are generated to form the solution of the entire structure. By partitioning the large structure into smaller independent regions, the boundary value problem is rendered solvable on a workstation environment, but is also made suitable for massively-parallel computation. Finite element techniques, used for the numerical solutions in this paper, have several levels of parallelism that can be taken advantage of in a parallel environment. Repetitious or nearly periodic structures can be analyzed much more efficiently, since the numerical solutions in unique regions need only be generated once, rather than every time they occur in the total structure. Examples demonstrate the accuracy of the method in a 'finite' periodic structure, and explore the trends in computation time on the Connection Machine (CM-2).