非线性预条件是一种改善求解强非线性问题牛顿法收敛性质的全局化技术，其核心思想是替换非线性函数或改变未知量。在数值模拟中，我们常常要求解离散后得到的大规模非线性系统，因而该技术有着重要的应用价值。基于科学计算工具箱PETSc，本项目拟研究非线性预条件并行算法的设计及其应用：(1)针对机翼绕流跨声速全速势模型，本项目结合Newton-Krylov算法、Schwarz预条件和非线性预条件等技术，构造并行的核心求解算法。在跨声速的情况时，该算法通过移除激波附近局部强非线性的方式来加速收敛，而不需要像传统的牛顿类算法经历冗长的残量停滞期；(2)目前没有文献报告非线性预条件技术在燃烧领域的研究成果，本项目拟研究如何利用基于物理场分裂的非线性预条件技术，求解由Navier-Stokes方程和Shvab-Zeldovich方程耦合的具有强非线性的火焰面模型问题，以达到显著减少牛顿迭代数的目的。

Nonlinear preconditioning is a globalization technique for improving global convergence properties of Newton's method applied to systems of equations with unbalanced nonlinearities, and the key idea is to replace nonlinear functions or change unknowns. In the numerical simulation, we often solve large systems of equations arising from discretization of nonlinear partial differential equations (PDEs) , therefore, it plays an important role in applications. In this project, we study the design and applications of nonlinearly preconditioned parallel algorithms based on PETSc (Portable, Extensible Toolkit for Scientific Computation): (1) for transonic full potential flow around airfoils, we design a parallel algorithm by combining the Newton-Krylov method, the Schwarz method as preconditioners and nonlinear preconditioning techniques. In the transonic case, the algorithm accelerates convergence by removing local strong nonlinearities near the shock, which differs from the traditional Newton-like algorithm suffering from a lengthy residual stagnation period. (2) there are no any results reported about applications of nonlinear preconditioning in combustion, so we plan to apply nonlinear preconditioning techniques with physics-based field-split partitioning to solve the flame sheet model with strong nonlinearities, coupling the Navier-Stokes equation with a Shvab-Zeldovich formulation, so that the number of nonlinear iterations can be dramatically reduced.