A Nonlinear Elimination Preconditioner for Fully Coupled Space-Time Solution Algorithm with Applications to High-Rayleigh Number Thermal Convective Flow Problems
Year: 2019
Communications in Computational Physics, Vol. 26 (2019), Iss. 3 : pp. 749–767
Abstract
As the computing power of the latest parallel computer systems increases dramatically, the fully coupled space-time solution algorithms for the time-dependent system of PDEs obtain their popularity recently, especially for the case of using a large number 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. In the paper, we introduce and study some parallel nonlinear space-time preconditioned Newton algorithm for the space-time formulation of the thermal convective flows at high Rayleigh numbers. In particular, we apply an adaptive nonlinear space-time elimination preconditioning technique to enhance the robustness of the inexact Newton method, in the sense that an inexact Newton method can converge in a broad range of physical parameters in the multi-physical heat fluid model. In addition, at each Newton iteration, we find an appropriate search direction by using a space-time overlapping Schwarz domain decomposition algorithm for solving the Jacobian system efficiently. Some numerical results show that the proposed method is more robust and efficient than the commonly-used Newton-Krylov-Schwarz method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2018-0191
Communications in Computational Physics, Vol. 26 (2019), Iss. 3 : pp. 749–767
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Fluid flow heat transfer nonlinear elimination space-time domain decomposition parallel computing.