An Efficient Load Balancing Scheme for Parallel <i>p</i> -Adaptive DGTD Method With Local Time Stepping Strategy

The time-domain discontinuous Galerkin (DGTD) method with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaptive and local time stepping (LTS) strategies, widely employed for simulating various electromagnetic wave phenomena, faces challenges in achieving optimal performance in parallel computing environments due to load imbalance among computational nodes caused by the dynamic change of base order. To address this issue, an adaptive load balancing adjustment strategy is proposed. The proposed load balancing strategy, based on the element diffusion model, achieves balanced computational loads by reasonably selecting and adjusting the interface elements among the computational nodes. Without the need of repartitioning the entire computational domain, the solution time consumed by the proposed method for the load balancing is reduced. Several multiscale electromagnetic examples are given to demonstrate that with the proposed load balancing method, fewer load balancing time overheads and enhanced scalability of the parallel DGTD algorithm with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaptive and LTS strategies are achieved, compared with widely used ParMETIS repartitioning method.