关于heat equation的一个不定常形状最优化问题的数值解
On the numerical solution of a time-dependent shape optimization problem for the heat equation
摘要：
本文研究了一个不定常形状识别问题的解。具体地说，我们考虑热方程的区域，其中包含一个不定常包含零温度。我们的目标是从给定的温度和热通量在域的外部边界检测这种包含。为此，对于外部边界处的给定温度，诺依曼数据的失配被最小化。然后，通过基于梯度的最优化方法来解决这个与不定常的形状最优化问题。数值结果验证了本方法。
英文摘要：
This article is concerned with the solution of a time-dependent shape identification problem. Specifically we consider the heat equation in a domain, which contains a time-dependent inclusion of zero temperature. The objective is to detect this inclusion from the given temperature and heat flux at the exterior boundary of the domain. To this end, for a given temperature at the exterior boundary, the mismatch of the Neumann data is minimized. This time-dependent shape optimization problem is then solved by a gradient-based optimization method. Numerical results are presented which validate the present approach.
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