Migration of Ginkgo s Jacobi-Preconditioned CG Solver to Vector RISC-V

Abstract

[EN] The solution of large, sparse linear systems of equations lies at the core of many scientific and engineering computations, particularly those derived from the discretization of partial differential equations. Iterative methods such as Conjugate Gradient (CG), GMRES, and BiCGSTAB, combined with suitable preconditioners, offer high scalability and memory efficiency, yet their performance on modern CPU architectures depends critically on efficient utilization of vector units. This paper presents the development of SIMD implementations for several key computational kernels in the Ginkgo linear algebra library, namely the sparse matrix¿vector product, Jacobi preconditioner application, and Level-1 BLAS operations, targeting RISC-V architectures that support the RISC-V Vector Extension (RVV) 1.0 specification. We integrate these vectorized routines into Ginkgo¿s Jacobi-preconditioned CG solver and evaluate the performance of the resulting solver on the SpaceMiT K1 processor, a commercial multicore RISC-V CPU embedded into the BananaPi F3 board. Our experimental results using matrices from the SuiteSparse Matrix Collection demonstrate both the benefits of vectorization and the presence of a strong memory bandwidth bottleneck on the BananaPi F3 board that currently limits attainable speed-ups. Our findings highlight the potential of RVV-based SIMD acceleration for iterative solvers and outline directions for further optimization on emerging RISC-V hardware.