超高速求解守恒律方程组的快速扫掠方法
Fast Sweeping Methods for Hyperbolic Systems of Conservation Laws at Steady State
AI总结：
本文提出一种快速扫掠方法，用于高效计算守恒律方程组的稳态解，通过特征线信息流和Rankine-Hugoniot条件捕捉激波，结合收敛分析和数值实验验证方法有效性。
摘要：
快速扫掠方法已成为计算静态Hamilton-Jacobi方程解的有用工具。通过借鉴这些方法的核心思想，本文描述了一种计算守恒律方程组稳态解的新方法。通过利用特征线上的信息流，这些快速扫掠方法可以非常高效地计算解。此外，这些方法通过直接施加Rankine-Hugoniot激波条件来精确捕捉激波。我们为几个一维和二维示例提供了收敛分析和数值实验，以说明该方法的使用和优势。
英文摘要：
Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton-Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of conservation laws. By exploiting the flow of information along characteristics, these fast sweeping methods can compute solutions very efficiently. Furthermore, the methods capture shocks sharply by directly imposing the Rankine-Hugoniot shock conditions. We present convergence analysis and numerics for several one- and two-dimensional examples to illustrate the use and advantages of this approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
