Towards Perturbation-Induced Static Pivoting on GPU-Based Linear Solvers

Linear system solving is a key tool for computational power system studies, e.g., optimal power flow, transmission switching, or unit commitment. CPU-based linear system solver speeds, however, have saturated in recent years. Emerging research shows that GPU-based linear system solvers are beginning to achieve notable speedup over CPU-based alternatives in some applications. Due to the architecture of GPU memory access, numerical pivoting represents the new bottleneck which prevents GPU-based solvers from running even faster. Accordingly, this paper proposes a matrix perturbation-based method to induce static pivoting. Using this approach, a series of perturbed, well-conditioned, pivot-free linear systems are solved in parallel on GPUs. Matrix expansion routines are then used to linearly combine the results, and the true solution is recovered to an arbitrarily high degree of theoretical accuracy. We showcase the validity of our approach on distributed-slack AC power flow solve iterations associated with the PGLib 300-bus test case.
Comment: submitted to PESGM 2024