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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)749-767
Number of pages19
JournalCommunications in Computational Physics
Volume26
Issue number3
DOIs
StatePublished - 2019

Keywords

  • Domain decomposition
  • Fluid flow
  • Heat transfer
  • Nonlinear elimination
  • Parallel computing
  • Space-time

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