FMM-accelerated hybrid boundary node method for multi-domain problems

This work presents a fast implementation of the multi-domain hybrid boundary node method (HdBNM) for numerical solution of the Laplaceʹs equation. The preconditioned GMRES is employed to solve the overall system of equations. At each iteration step of the GMRES, the matrix–vector multiplication is split into smaller scale ones at the sub-domain level, and thus accelerated by the fast multipole method independently within individual sub-domains. The computed matrix–vector products at the sub-domain level are then assembled into an overall vector using the equilibrium and continuity conditions at the interfaces. Our method is tested by benchmark examples for three-dimensional potential problems, and high accuracy and efficiency are observed.