在ICF等许多重要应用领域的数值模拟中，需要求解各类复杂的非线性方程组。这些方程组的求解占据数值模拟绝大部分时间开销。目前，在ICF等数值模拟应用中，求解各类非线性方程组以Picard方法为主。该方法属于不动点迭代，具有程序实现简单等优点，但其收敛速度较慢。如何提高Picard方法的收敛速度，成为影响ICF等数值模拟效率的关键。近期，关于不动点迭代过程的一类加速算法—Anderson加速引起广泛关注。Anderson加速已在相关领域得到成功应用。然而，由于健壮性和适应性等问题，难以将该算法直接有效地应用于ICF等数值模拟。本项目将结合ICF等数值模拟应用，开展Anderson加速算法的健壮性和适应性研究。同时，将以该算法为基础，研究和发展新的迭代算法和预处理方法。期望通过本项目实施，能够显著加速ICF等数值模拟应用中相关迭代收敛速度，从而有效提高数值模拟效率。

It is necessary to solve all kinds of complex nonlinear equations in the numerical simulations of many important application areas, such as inertial confinement fusion (ICF). The solution for these nonlinear equations dominants the whole time cost of the numerical simulations. At present, the main method for solving nonlinear equations in ICF numerical simulations is Picard iteration. Picard method is a kind of fixed point iteration. This kind of method has many advantages, including easily implemented, etc. However, the convergence rate of the method is slow. Therefore, the key problems concerning the efficiency of ICF numerical simulation is how to improve the convergence rate of Picard method. Recently, one kind of acceleration method for fixed point iteration — Anderson acceleration attracts much attention. Anderson acceleration has been used successfully in some related areas. However, it is difficult to apply this algorithm directly to ICF numerical simulation because of robustness, applicability and some other problems. In this project, some research about Anderson acceleration’s robustness and applicability will be done by combining some important applications including ICF. At the same time, by basing on Anderson acceleration algorithm, some new iterative methods and preconditioning techniques will be developed. It is expected that, with the implementation of the project, the convergence rate of related iterations in ICF numerical simulation can be accelerated dramatically so that the whole efficiency of the numerical simulation can be improved effectively.