TY - JOUR

T1 - A nonlinear elimination preconditioner for fully coupled space-time solution algorithm with applications to high-rayleigh number thermal convective flow problems

AU - Yang, Haijian

AU - Hwang, Feng Nan

N1 - Publisher Copyright:
© 2019 Global-Science Press.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Domain decomposition

KW - Fluid flow

KW - Heat transfer

KW - Nonlinear elimination

KW - Parallel computing

KW - Space-time

UR - http://www.scopus.com/inward/record.url?scp=85113317145&partnerID=8YFLogxK

U2 - 10.4208/CICP.OA-2018-0191

DO - 10.4208/CICP.OA-2018-0191

M3 - 期刊論文

AN - SCOPUS:85113317145

SN - 1815-2406

VL - 26

SP - 749

EP - 767

JO - Communications in Computational Physics

JF - Communications in Computational Physics

IS - 3

ER -