发表机构
IFP Energies nouvelles; Univ. Lille, CNRS, Inria, UMR 8524 – Laboratoire Paul Painlevé（IFP能源新动力; 里尔大学、法国国家科学研究中心、法国国家信息与自动化研究所、UMR 8524 - 保罗·潘勒韦实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出预扁平化方法，结合非线性消元技术，加速牛顿法求解非线性代数系统，通过地球科学化学平衡问题的数值模拟验证了方法的有效性。
AI 中文摘要
本文提出一种名为“预扁平化（preflattening）”的新方法，用于加速牛顿类方法求解非线性代数系统。预扁平化之于非线性系统，正如预条件化（preconditioning）之于线性系统，其核心是将原系统转化为更适配牛顿法的等价系统。为此，我们引入“平坦度（flatness）”概念，使其对非线性系统的作用类似条件数对线性系统的作用。针对地球科学中受关注的化学平衡问题这一物理模型，我们将该策略与非线性消元（nonlinear elimination）技术结合，通过数值模拟验证了所提方法的价值。
英文摘要
In this paper, we propose a new approach called {\em preflattening} to speed up the resolution of nonlinear algebraic systems by Newton-type methods. Preflattening is meant to be for nonlinear systems what preconditioning is for linear ones. The idea is to transform the system into an equivalent one that is more favorable to Newton's method. To this end, we introduce the notion of {\em flatness}, which is intended to play for nonlinear systems a role similar to that of the condition number for linear systems. For a physical model of interest in the geosciences, namely the chemical equilibrium problem, we combine this strategy with the nonlinear elimination technique and demonstrate the value of the resulting approach through numerical simulations.
