关键词: 广义最小残差算法, 分布式系统, 数据压缩, 通信优化

Abstract: The generalized minimal residuals(GMRES) method is one of the mainstream iterative algorithms for solving sparse linear systems,widely applied in circuit simulation,computational fluid dynamics,autonomous driving,and other fields.To efficiently solve large-scale sparse linear systems,researchers have developed distributed GMRES algorithms that use inter-node communication and distributed computing to achieve parallel solutions for large-scale problems.However,the sparse matrix-vector multiplication(SpMV) computation in distributed GMRES introduces significant communication demands for floating-point vectors,making the communication overhead of floating-point vectors a major performance bottleneck.Based on the restarted GMRES,this paper proposes a distributed restart GMRES(DR-GMRES) algorithm tailored for CPU-GPU heterogeneous systems,incorporating a collaborative computing model designed to align with the algorithm’s characteristics and heterogeneous architecture.Furthermore,for the communication requirements of floating-point vectors in SpMV and the numerical properties of GMRES’s inner-outer iterations,a two-layer hybrid compression strategy is proposed.This strategy combines lossy and lossless hybrid compression with inner-outer iteration hybrid compression to minimize the communication overhead of DR-GMRES while preserving acceptable solving accuracy.Additionally,a multi-buffer compressed communication architecture is designed to implement asynchronous data compression efficiently.Experimental results on 16 large-scale sparse linear systems demonstrate that,compared to the original distributed GMRES,the DR-GMRES algorithm based on hybrid data compression achieves an average speedup of ×3.37(with a maximum of ×8.02) with negligible impact on computational accuracy.Actual simulations experimentally verify that the DR-GMRES algorithm based on hybrid data compression achieves a ×3.09 acceleration in OSQP solving time over the baseline.

Key words: Generalized minimal residuals, Distributed system, Data compression, Communication optimization