A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/109135

Title:	A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation
Authors:	黃楓南;Hwang, Feng-Nan;Su, Yi-Cheng;Cai, Xiao-Chuan
Contributors:	理學院數學系
Keywords:	Adaptive nonlinear elimination;Algorithms;Density upwinding finite difference;Dynamical systems;Inexact Newton;Local high nonlinearity;Mathematical analysis;Mathematical models;Newton methods;Nonlinearity;Partitioning;Shock wave;Subspaces;Transonic flow
Date:	2015-03-01
Issue Date:	2026-04-23 16:10:00 (UTC+8)
Publisher:	Elsevier Ltd.;United Kingdom: Elsevier Ltd
Abstract:	摘要： •New adaptive right nonlinear elimination preconditioner for inexact Newton algorithm proposed.•Three major ingredients include: subspace correction, global update, and determination of partition.•Key idea is to remove local nonlinearity before performing global Newton update.•Intermediate solution used to select adaptively the to-be-eliminated components.•Numerical examples used to demonstrate robustness and efficiency of the algorithm. We propose and study a right-preconditioned inexact Newton method for the numerical solution of large sparse nonlinear system of equations. The target applications are nonlinear problems whose derivatives have some local discontinuities such that the traditional inexact Newton method suffers from slow or no convergence even with globalization techniques. The proposed adaptive nonlinear elimination preconditioned inexact Newton method consists of three major ingredients: a subspace correction, a global update, and an adaptive partitioning strategy. The key idea is to remove the local high nonlinearity before performing the global Newton update. The partition used to define the subspace nonlinear problem is chosen adaptively based on the information derived from the intermediate Newton solution. Some numerical experiments are presented to demonstrate the robustness and efficiency of the algorithm compared to the classical inexact Newton method. Some parallel performance results obtained on a cluster of PCs are reported. 出版者： United Kingdom: Elsevier Ltd 出版日期： 2015-03-30 出處： Computers & fluids, 2015-03, Vol.110 (C), p.96-107 版權： 2014 Elsevier Ltd 識別號： ISSN: 0045-7930 識別號： ISSN: 1879-0747 識別號： EISSN: 1879-0747 識別號： DOI: 10.1016/j.compfluid.2014.04.005
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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