A Nonlinear Additive Schwarz Preconditioned Inexact Newton Method for Shocked Duct Flow
A Nonlinear Additive Schwarz Preconditioned Inexact Newton Method for Shocked Duct Flow
复制标题
DOI：
--
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
X. Cai;D. Keyes;D. Young
中科院分区：
文献类型：
--
作者：
X. Cai;D. Keyes;D. Young
最近在[CK 00]中引入了一种非线性预处理不精确牛顿算法（PIN），用于求解非线性偏微分方程离散化产生的大型稀疏非线性方程组。在PIN中，非线性系统F（u）= 0转化为一个新的非线性系统F（u）= 0，它与原系统具有相同的解.对于某些应用，新函数F（u）的非线性更加平衡，因此，不精确牛顿法收敛得更快。在本文中，我们将使用非线性添加剂施瓦茨算法作为预条件子，并专注于性能的PIN的可压缩激波管问题，这是已知的一个困难的测试情况下，不精确牛顿型算法。
A nonlinearly preconditioned inexact Newton algorithm (PIN) was recently introduced, in [CK00], for solving large sparse nonlinear system of equations arising from the discretization of nonlinear partial di erential equations. In PIN the nonlinear system F (u) = 0 is transformed into a new nonlinear system F(u) = 0, which has the same solution as the original system. For certain applications the nonlinearities of the new function F(u) are more balanced and, as a result, the inexact Newton method converges faster. In this paper, we shall use the nonlinear additive Schwarz algorithm as the preconditioner and focus on the performance of PIN for a compressible shock tube problem, which is known to be a diÆcult test case for inexact Newton type algorithms.