The radiation diffusion problem is a kind of time-dependent nonlinear equations. For solving the radiation diffusion equations, many linear systems are obtained in the nonlinear iterations at each time step. The cost of linear equations dominates the numerical simulation of radiation diffusion applications, such as inertial confinement fusion, etc. Usually, iterative methods are used to solve the linear systems in a real application. Moreover, the solution of the previous nonlinear iteration or the solution of the previous time step is typically used as the initial guess for solving the current linear equations. Because of the strong local character in ICF, with the advancing of nonlinear iteration and time step, the solution of the linear system changes dramatically in some local domain, and changes mildly or even has no change in the rest domain.

In this paper, a local character-based method is proposed to solve the linear systems of radiation diffusion problems. The proposed method consists of three steps: firstly, a local domain (algebraic domain) is constructed; secondly, the subsystem on the local domain is solved; and lastly, the whole system will be solved. Two methods are given to construct the local domain. One is based on the spatial gradient, and the other is based on the residual. Numerical tests for a two-dimensional heat conduction model problem, and two real application models, the multi-group radiation diffusion equations and the three temperature energy equations, are conducted. The test results show that the solution time for solving the linear system can be reduced dramatically by using the local character-based method.

辐射扩散问题是一类与时间有关的非线性方程。为了求解辐射扩散方程，在每个时间步长的非线性迭代中获得了许多线性系统。线性方程组的成本支配着辐射扩散应用（例如惯性约束融合等）的数值模拟。通常，在实际应用中使用迭代方法求解线性系统。而且，通常将先前非线性迭代的解或先前时间步的解用作求解当前线性方程的初始猜测。由于ICF具有很强的局部特性，随着非线性迭代和时间步长的发展，线性系统的解在某些局部域中发生了巨大变化，而在其余域中则发生了温和甚至没有变化。

本文提出了一种基于局部特征的方法来解决辐射扩散问题的线性系统。所提出的方法包括三个步骤：首先，构造一个局部域（代数域）；其次，解决了本地域上的子系统。最后，整个系统将得到解决。给出了两种构造本地域的方法。一种基于空间梯度，另一种基于残差。进行了二维热传导模型问题的数值测试，以及两个实际的应用模型，即多组辐射扩散方程和三个温度能量方程。测试结果表明，使用基于局部字符的方法可以大大减少求解线性系统的时间。