A Scalable Semi‐Implicit Barotropic Mode Solver for the MPAS‐Ocean
Hyun‐Gyu Kang, Katherine J. Evans, Mark Petersen, Philip W. Jones, Siddhartha Bishnu
Abstract
Abstract A scalable semi‐implicit barotropic mode solver for the ocean component of the model for prediction across scales has been implemented as a competitor to an existing explicit‐subcycling scheme to allow faster and more stable simulations while not sacrificing accuracy. The semi‐implicit solver adopts the pipelined preconditioned bi‐conjugate gradient stabilization algorithm as an iterative solver in conjunction with the restricted additive Schwarz preconditioner that accelerates the convergence rate of the iterative solver. The preconditioner is constructed from a linearized barotropic system that also reorders the system for optimal performance, while the semi‐implicit solver deals with the fully nonlinear barotropic system that requires reassembly of the coefficient matrix for every time step. Several numerical experiments, from simple one‐dimensional tests to three‐dimensional real‐world tests, demonstrate that the semi‐implicit solver has almost the same accuracy and better parallel scalability compared with the existing scheme while allowing faster and more stable simulations. The semi‐implicit solver accelerates the barotropic mode up to 2.9 times faster than the existing scheme on 16,320 processors, leading to an overall runtime speedup of 1.9.