Dynamic Load Balancing for the Parallel, Adaptive, Multigrid Solution of Implicit Phase-Field Simulations

In this paper we assess the performance of a selection of load balancing strategies for a parallel, adaptive multigrid solver that has been developed for the implicit solution of phase-field problems. The strategies considered include a number of standard approaches and a new technique that we propose specifically for multigrid solvers. This technique takes account of the sequential nature of the grid correction used in multiplicative multilevel algorithms such as multigrid. The paper focuses on two phase-field example problems which model the rapid solidification of an undercooled binary alloy: using isothermal and non-isothermal models respectively. We undertake a systematic comparison of the different load-balancing strategies for a selection of different adaptive mesh scenarios. We conclude that the optimal choice of load-balancing strategy depends critically on the computation to communication ratio of the parallel multigrid solver, and that in the computation-dominated limit our proposed technique is typically the most effective of those considered.