AH-TDMA: An Adaptive Heterogeneous Tridiagonal Matrix Algorithm on the New Sunway Supercomputer

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The solution of tridiagonal linear systems is used in in various fields and plays a crucial role in numerical simulations. However, there is few efficient solver for tridiagonal linear systems on the new Sunway supercomputer. Based on a three-dimensional heat conduction problem, we propose an adaptive heterogeneous tridiagonal matrix algorithm (AH-TDMA). Our major innovations include: (1) To address computational hotspots within AH-TDMA, a multi-level parallel approach involving MPI+Athread has been adopted. (2) An adaptive data partitioning scheme has been set up to achieve load balance. (3) Employing direct memory access and establishing shared space between registers and main memory, instead of employing discrete memory access, is done to enhance memory access efficiency. (4) The optimization of the loop structure has been made in adjusting the sequencing of the dual-layered loops to reduce communication overhead. The experimental results show that, with one core group, the AH-TDMA achieves a speedup of 99.6 times for hotspot and total time speedup up to 59.4 times compared to the Parallel and Scalable Library for Tridiagonal Matrix Algorithm (PaScal TDMA). The AH-TDMA is scalable up to 2048 core groups, with a parallel efficiency of 69.2%.