Watershed load balancing technique for distributed memory parallelization of fast multipole methods with near-field preconditioning

The fast multipole method (FMM) has demonstrated great potential for accelerating the solution of integral equation systems. However, FMM´s reliance on iterative solution techniques, in conjunction with poorly conditioned systems resulting from typical electromagnetic problems, mandates the use of specialized preconditioning methods to improve convergence and reduce the overall solution time. Efficient parallelization and load balancing of the FMM algorithm and preconditioner is equally critical for reduction of solution time. The near-field preconditioner (NFP) (Carr, M. et al., IEEE Ant. Prop. Mag., 2004; Carr and Volakis, J.L., Proc. 2003 IEEE Int. Ant. Prop. Symp.) is one technique that is amenable parallelization. However the overlapping subdomain condition of the NFP presents a challenge for distributed memory parallelization. The paper describes a technique referred to as watershed load balancing (WLB) that employs image processing methods to form large, contiguous subdomains, reducing the total volume of overlap and therefore achieving improved parallelization efficiency while preserving the characteristics of the NFP.