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首页> 外文期刊>International Journal of Heat and Mass Transfer >A new algorithm for direct and backward problems of heat conduction equation
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A new algorithm for direct and backward problems of heat conduction equation

机译：导热方程正反问题的一种新算法

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Direct heat conduction problem (DHCP) and backward heat conduction problem (BHCP) are numerically solved by employing a new idea of fictitious time integration method (FTIM). The DHCP needs to consider the stability of numerical integration in the sense that the solution may be divergent for a specific time stepsize and specific spatial stepsize. The BHCP is renowned as strongly ill-posed because the solution does not continuously depend on the given data. In this paper, we transform the original parabolic equation into another parabolic type evolution equation by introducing a fictitious time variable, and adding a fictitious viscous damping coefficient to enhance the stability of numerical integration of the discretized equations by employing a group preserving scheme. When 10 numerical examples are amenable, we find that the FTIM is applicable to both the DHCP and BHCP. Even under seriously noisy initial or final data, the FTIM is also robust against disturbance. More interestingly, when we use the FTIM, we do not need to use different techniques to treat DHCP and BHCP as that usually employed in the conventional numerical methods. It means that the FTIM can unifiedly approach both the DHCP and BHCP, and the gap between direct problems and inverse problems can be smeared out.
机译：通过采用虚拟时间积分方法（FTIM）的新思想在数值上解决了直接热传导问题（DHCP）和向后热传导问题（BHCP）。从解决方案在特定时间步长和特定空间步长可能有所不同的意义上说，DHCP需要考虑数值积分的稳定性。 BHCP因病情严重而闻名，因为解决方案不连续依赖于给定的数据。在本文中，我们通过引入一个虚拟的时间变量，并添加一个虚拟的粘性阻尼系数，将原始的抛物型方程转换为另一个抛物型演化方程，从而通过采用群保存方案来增强离散化方程数值积分的稳定性。当有10个数值示例可用时，我们发现FTIM适用于DHCP和BHCP。即使在嘈杂的初始或最终数据下，FTIM也具有强大的抗干扰能力。更有趣的是，当我们使用FTIM时，我们不需要像常规数值方法中通常使用的那样使用不同的技术来处理DHCP和BHCP。这意味着FTIM可以统一处理DHCP和BHCP，并且可以消除直接问题和反问题之间的差距。

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