2026 Volume 34 Pages 1084-1093
Many scientific and engineering applications require solving a sequence of large, sparse, and symmetric positive definite linear systems with the same coefficient matrix. To accelerate such a sequential solution process on a GPU platform, we study the Error vector Sampling-based Subspace Correction (ES-SC) preconditioner in combination with the Conjugate Gradient (CG) method. We implement the ES-SC-CG solver on a GPU platform and adapt the workflow for the GPU execution, while constructing the baseline preconditioner once on a CPU before solving the sequence. A main contribution of this work is a new integration of ES-SC with a GPU-oriented sparse approximate inverse preconditioner, SD-AINV, resulting in ES-SC-SD-AINV-CG. For comparison, we also evaluate ES-SC combined with a multicolored incomplete Cholesky type preconditioner (MC-IC), which provides a practical parallel counterpart of the incomplete Cholesky preconditioner used in prior CPU-oriented settings. Across ten test matrices, ES-SC reduces the total iteration counts across all test cases, and the iteration reduction remains effective when combined with SD-AINV. In terms of time-to-solution, ES-SC-SD-AINV-CG improves the total elapsed time for eight out of ten matrices compared with the SD-AINV-CG baseline, whereas ES-SC-MC-IC-CG does not consistently reduce elapsed time despite strong iteration reduction, due to higher per-iteration costs. A detailed time breakdown of the solution process where ES-SC is fully activated further indicates that the additional cost introduced by the SC preconditioner is a decisive factor: elapsed time is reduced only when the iteration reduction is sufficiently large to compensate for the increased per iteration overhead.
