Volume 26, Issue 3
A Nonlinear Elimination Preconditioner for Fully Coupled Space-Time Solution Algorithm with Applications to High-Rayleigh Number Thermal Convective Flow Problems

Haijian Yang & Feng-Nan Hwang

Commun. Comput. Phys., 26 (2019), pp. 749-767.

Published online: 2019-04

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  • 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.

  • Keywords

Fluid flow, heat transfer, nonlinear elimination, space-time, domain decomposition, parallel computing.

  • AMS Subject Headings

76D05, 65F08, 49M15, 65M55, 68W10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-26-749, author = {}, title = {A Nonlinear Elimination Preconditioner for Fully Coupled Space-Time Solution Algorithm with Applications to High-Rayleigh Number Thermal Convective Flow Problems}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0191}, url = {http://global-sci.org/intro/article_detail/cicp/13145.html} }
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