2016/06/27 by Phanish Suryanarayana, Suryanarayana, Phanish, Phanisri P. Pratapa +3 · 3 citations
Chemistry · Computer Science · #Advanced NMR Techniques and Applications #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1606.08740
openalex publication_date 2016/06/27 · openalex created_date 2022/10/03 · openalex updated_date 2026/08/01
We present the Alternating Anderson-Richardson (AAR) method: an efficient and\nscalable alternative to preconditioned Krylov solvers for the solution of\nlarge, sparse linear systems on high performance computing platforms.\nSpecifically, we generalize the recently proposed Alternating Anderson-Jacobi\n(AAJ) method (Pratapa et al., J. Comput. Phys. (2016), 306, 43--54) to include\npreconditioning, discuss efficient parallel implementation, and provide serial\nMATLAB and parallel C/C++ implementations. In serial applications to\nnonsymmetric systems, we find that AAR is comparably robust to GMRES, using the\nsame preconditioning, while often outperforming it in time to solution; and\nfind AAR to be more robust than Bi-CGSTAB for the problems considered. In\nparallel applications to the Helmholtz and Poisson equations, we find that AAR\nshows superior strong and weak scaling to GMRES, Bi-CGSTAB, and Conjugate\nGradient (CG) methods, using the same preconditioning, with consistently\nshorter times to solution at larger processor counts. Finally, in massively\nparallel applications to the Poisson equation, on up to 110,592 processors, we\nfind that AAR shows superior strong and weak scaling to CG, with shorter\nminimum time to solution. We thus find that AAR offers a robust and efficient\nalternative to current state-of-the-art solvers, with increasing advantages as\nthe number of processors grows.\n