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 - Haijian Yang & Feng-Nan Hwang
JO - Communications in Computational Physics
VL - 3
SP - 749
EP - 767
PY - 2019
DA - 2019/04
SN - 26
DO - http://doi.org/10.4208/cicp.OA-2018-0191
UR - https://global-sci.org/intro/article_detail/cicp/13145.html
KW - Fluid flow, heat transfer, nonlinear elimination, space-time, domain decomposition,
parallel computing.
AB - <p style="text-align: justify;">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.</p>