Parallel node placement method by bubble simulation

An efficient Parallel Node Placement method by Bubble Simulation (PNPBS), employing METIS-based domain decomposition (DD) for an arbitrary number of processors is introduced. In accordance with the desired nodal density and Newton's Second Law of Motion, automatic generation of node sets by bubble simulation has been demonstrated in previous work. Since the interaction force between nodes is short-range, for two distant nodes, their positions and velocities can be updated simultaneously and independently during dynamic simulation, which indicates the inherent property of parallelism, it is quite suitable for parallel computing. In this PNPBS method, the METIS-based DD scheme has been investigated for uniform and non-uniform node sets, and dynamic load balancing is obtained by evenly distributing work among the processors. For the nodes near the common interface of two neighboring subdomains, there is no need for special treatment after dynamic simulation. These nodes have good geometrical properties and a smooth density distribution which is desirable in the numerical solution of partial differential equations (PDEs). The results of numerical examples show that quasi linear speedup in the number of processors and high efficiency are achieved.