Grunnleggende konsepter
Matrix perturbation-based method for static pivoting in GPU-based linear solvers.
Sammendrag
The content discusses the challenges faced by GPU-based linear system solvers due to numerical pivoting and proposes a matrix perturbation-based approach to induce static pivoting. By solving a series of perturbed linear systems in parallel on GPUs, the original solution can be accurately reconstructed. The paper showcases the application of this method in distributed-slack AC power flow solve iterations. Key highlights include:
Introduction to linear system solving in computational power systems.
Comparison between CPU-based and emerging GPU-based linear system solvers.
Challenges of numerical pivoting on GPUs and the need for static pivoting.
Proposal of a matrix perturbation-based method for inducing static pivoting.
Utilization of Neumann series matrix expansion for optimal reconstruction.
Theoretical accuracy achieved through a linear combination of perturbed solutions.
Methodology summary outlining the steps involved in perturbation-induced static pivoting.
Test results demonstrating the effectiveness of the proposed approach on a 300-bus distributed slack power flow problem using Newton-Raphson.
Sitater
"None of the tested packages delivered significant GPU acceleration for our test cases."
"Pivoting on the GPU is prohibitively expensive, and avoiding pivoting is paramount for GPU speedups."