APPLICATION OF DYNAMIC LOAD BALANCING FOR EFFICIENT GENERATION OF FRACTAL BASINS OF ATTRACTION ON SUPERCOMPUTER SYSTEMS

Leontyeva Tatyana Vladimirovna, Bryutova Sofia Danilovna

Generating fractal basins of attraction for Lagrange points using Newton's method is an important but extremely computationally complex task in nonlinear dynamics, depending on the efficiency of parallelisation. At the initial stage, it was established that traditional static data decomposition causes a significant load imbalance due to the irregular complexity of fractal boundaries. As a result, the scalability of the algorithm on a supercomputer cluster decreased sharply, reaching only 5.8% with 448 cores. To solve the problem, a dynamic Master/Worker architecture with a fine-grained task pool and point-to-point MPI exchange was adapted. Performance analysis and overhead profiling were performed. The application of the dynamic method provided stable efficiency of 32–34% when scaling to hundreds of cores, which is 5.7 times higher than the original approach. The generation time for an 8K image was reduced from 25 to 4.4 minutes. The proposed approach demonstrates the effective use of supercomputer resources for a wide class of tasks with irregular computational structures.

Keywords:fractal structure, Newton's method, three-body problem, load balancing, dynamic scheme, master-worker, parallel code acceleration, High-performance computing (HPC).