An Efficient and Effective Preconditioner for the Discontinuous Galerkin Domain Decomposition Method of Surface Integral Equation

This letter proposes a new preconditioning technique based on a restricted additive Schwarz (RAS) approach to improve the efficiency of the discontinuous Galerkin surface integral equation method. The RAS preconditioning is implemented efficiently using an octree structure derived from the multilevel fast multipole algorithm and is constructed using near-field matrices associated with boxes at the finest level. Compared with existing domain decomposition preconditioning methods based on subdomain block matrices, the proposed RAS preconditioning significantly reduces computation time and memory requirements, while providing scalable convergence for iterative solutions. Numerical experiments are presented to demonstrate the performance of the proposed cost-effective preconditioning technique.