论文标题
一种基于局部角色的方法，用于求解辐射扩散问题的线性系统
A local character based method for solving linear systems of radiation diffusion problems
论文作者
论文摘要
辐射扩散问题是一种{时间依赖性}非线性方程。为了求解辐射扩散方程，在每个时间步骤中都在非线性迭代中获得许多线性系统。线性方程的成本主导着辐射扩散应用的数值模拟，例如惯性限制融合等。{通常，}迭代方法用于求解{a}真实应用中的线性系统。 {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. 在本文中，提出了局部{基于字符}的方法来解决辐射扩散问题的线性系统。提出的方法包括三个步骤：首先，构建了局部域（代数域）；其次，解决了本地域上的子系统；最后，将解决整个系统。给出了两种构建本地域的方法。一个基于空间梯度，另一个基于残差。进行了二维热传导模型问题的数值测试，并进行了两个实际应用模型，即多组辐射扩散方程和三个温度能量方程。测试结果表明，可以使用基于局部字符的方法大大减少解决线性系统的解决方案时间。
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.
