虚构解方法程序验证

对求解偏微分方程问题的程序的严格验证,一直以来由于其精确解有限,较难进行,针对这种情况,本文给出了一种新的程序验证方法,虚构解方法,该方法旨在解决大型科学计算程序如何较严格地进行程序验证这一问题;该方法通过构造虚构解,修改原控制方程,然后通过对计算结果的分析处理达到对程序的精确验证;文中给出了一组通用的虚构解的选取办法,解决了虚构解方法验证过程中确定虚构解的问题;同时还给出了运用该方法对非结构二维Euler计算程序进行验证的具体例子,网格收敛分析结果表明该方法是一种有效的程序验证方法,并且具有较好的通用性。

Code Verification via the Method of Manufactured Solutions

Robust code verification of Partial Differential Equation(s)(or PDE(s)) sovers has some difficulty for a limit num of PDE exact solutions, for such problems, a new algorithm, method of manufactured solutions is detailed, which is born to solve the big science/engineering computing program verification problems. The verification process can be discribed as manufacturing the exact solutions of the PDE(s), modifying the control equations, and then analysing the results. In the paper, the methods of choicing the manufactured solutions is presented, which is made the verification becoming easier. Also an example of the verification of 2D solver by such algorithm is given, the results indicate that the methods is a valid way to verification of the PDE solvers.