A Fast Domain Decomposition Method for Solving Three-Dimensional Large-Scale Electromagnetic Problems

Abstract

An efficient algorithm based on domain decomposition method (DDM) and partial basic solution vectors (PBSV) technique is proposed for solving three-dimensional (3-D), large-scale, finite periodic electromagnetic problems, such as photonic or electromagnetic bandgap structures, frequency selective surfaces. The entire computational domain is divided into many smaller nonoverlapping subdomains. A Robin-type condition is introduced at the interfaces between subdomains to enforce the field continuity. With the help of a set of dual unknowns, each subdomain can be tackled independently. Because of geometric repetitions, all the sudomains can be classified into a few building blocks, which can be dealt with by an improved PBSV algorithm. Thus, the original problem becomes a much smaller one which involves the unknowns only at the interfaces. The resulting linear system of equations is solved by a block symmetric successive over relaxation (SSOR) preconditioned Krylov subspace method. Once the unknowns at the interfaces have been obtained, the final solution on each subdomain can easily be calculated independently. Some numerical examples are provided and show the method is scalable with the number of subdomains.