论文标题
在反热传导问题中识别异质电导率
Identification of the heterogeneous conductivity in an inverse heat conduction problem
论文作者
论文摘要
这项工作涉及在稳态热传导边界值问题中确定非均匀的热电导率曲线的问题，并在整个域中的国家知识中，在$ \ mathbb {r}^n $中的有界域上的混合dirichlet-neumann边界条件。我们开发一种基于变异方法的方法，导致最佳方程式，然后将其投影到有限的维空间中。离散化产生了一个线性，但虽然严重不良的方程式，然后通过适当的临时惩罚机正规化，导致a产生广义的tikhonov-phillips功能。没有对电导率施加平稳性假设。对于电导率只能采用两个规定值（两种材料的情况）的情况的数值示例表明，该方法能够产生精确解决方案的很好的重建。
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$, from the knowledge of the state over the whole domain. We develop a method based on a variational approach leading to an optimality equation which is then projected into a finite dimensional space. Discretization yields a linear although severely ill-posed equation which is then regularized via appropriate ad-hoc penalizers resulting a in a generalized Tikhonov-Phillips functional. No smoothness assumptions are imposed on the conductivity. Numerical examples for the case in which the conductivity can take only two prescribed values (a two-materials case) show that the approach is able to produce very good reconstructions of the exact solution.
