A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation
A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation
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DOI：
10.1016/j.compfluid.2014.04.005
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发表时间：
2015-03
影响因子：
2.8
通讯作者：
F. Hwang;Yixiao Su;X. Cai
中科院分区：
文献类型：
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作者：
F. Hwang;Yixiao Su;X. Cai
提出并研究了一类大型稀疏非线性方程组数值解的右预条件非精确牛顿法。目标应用是导数存在局部不连续的非线性问题，使得传统的非精确牛顿法即使采用全局化技术也存在缓慢收敛或不收敛的问题。提出的自适应非线性消除预条件不精确牛顿法主要包括子空间校正、全局更新和自适应划分策略三个部分。关键思想是在进行全局牛顿更新之前先去除局部高非线性。根据中间牛顿解的信息自适应地选择用于定义子空间非线性问题的划分。数值实验结果表明，与经典的非精确牛顿法相比，该算法具有较好的鲁棒性和效率。本文报道了在pc集群上获得的一些并行性能结果。
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.