A Nonlinear Elimination Preconditioner for Fully Coupled Space-Time Solution Algorithm with Applications to High-Rayleigh Number Thermal Convective Flow Problems (Communications in Computational Physics, 2019)
As the computing power of the latest parallel computer systems increasesdramatically, the fully coupled space-time solution algorithms for the time-dependentsystem of PDEs obtain their popularity recently, especially for the case of using a largenumber of computing cores. In this space-time algorithm, we solve the resulting large,space, nonlinear systems in an all-at-once manner and a robust and efficient nonlinear solver plays an essential role as a key kernel of the whole solution algorithm. Inthe paper, we introduce and study some parallel nonlinear space-time preconditionedNewton algorithm for the space-time formulation of the thermal convective flows athigh Rayleigh numbers. In particular, we apply an adaptive nonlinear space-time elimination preconditioning technique to enhance the robustness of the inexact Newtonmethod, in the sense that an inexact Newton method can converge in a broad rangeof physical parameters in the multi-physical heat fluid model. In addition, at eachNewton iteration, we find an appropriate search direction by using a space-time overlapping Schwarz domain decomposition algorithm for solving the Jacobian systemefficiently. Some numerical results show that the proposed method is more robust andefficient than the commonly-used Newton-Krylov-Schwarz method.
Keywords: Fluid flow; heat transfer; nonlinear elimination; space-time; domain decomposition; parallel computing.