基于非线性辐射问题的非线性预处理非精确牛顿算法的研究
首发时间:2018-03-21
摘要:非精确牛顿算法(IN)被广泛用来求解通过非线性偏微分方程离散得到的大型非线性系统F(X*)=0,但是对于高度非线性的辐射运输问题难以用IN算法求解。文章以非线性辐射问题为例,先运用标准的有限体积法离散得到大型非线性系统,再使用非线性预处理非精确牛顿算法(NPIN)求解该大型非线性系统得到数值解。经过测试此算法的性能是比较好的。
关键词: 计算数学 并行计算 非线性预处理 高度非线性问题 非精确牛顿算法
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A Nonlinear preconditioned Inexact Newton Method for Nonlinear Radiation Problem
Abstract:The inexact Newton algorithm is widely used to solve the large-scale nonlinear system F(X*)=0, which is discreted by the nonlinear partial differential equation. However, inexact Newton methods often fail to achieve the desired convergent rate when the system is resulted by highly nonlinear radiation transport problems. In this paper, we introduce a nonlinear preconditioned inexact Newton method for the numerical results show that the approach shows a significantly improved performance for nonlinear radiation problems, when compared to the classical inexact Newton method.
Keywords: Computational Mathematics Parallel computing Nonlinear preprocessing Highly nonlinear problem Inexact Newton algorithm
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基于非线性辐射问题的非线性预处理非精确牛顿算法的研究
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