Optimal control and inverse problems in radiative heat transfer

该项目的主要目标是推导和研究有效的数学方法，用于解决辐射主导过程的最优控制和识别问题，这些过程由非线性积分微分系统或扩散型近似描述。这些工艺例如与玻璃生产或燃气涡轮机燃烧室的布置相关。由于其模拟已经非常复杂和耗时，由于辐射，该项目的主要重点将是基于伴随变量的优化算法的研究，这将适用于全辐射传热系统以及扩散型近似。与黑箱优化算法相比，这允许在任意精细离散化的优化和模拟工作之间保持平衡。特别重点将是不同的数值方法，允许在合理的计算成本解决三维问题的调查。除了优化，我们还将研究从边界测量重建初始温度的新方法，因为它的精确知识对于任何令人满意的模拟都是强制性的。特别是，我们将开发一种快速，无导数的方法来解决反问题，这样我们就可以使用许多不同的模型来模拟辐射过程。

The main objective of this project is the derivation and investigation of efficient mathematical methods for the solution of optimal control and identification problems for radiation dominant processes, which are described by a nonlinear integro-differential system or diffusive type approximations. These processes are for example relevant in glass production or in the layout of gas turbine combustion chambers. Since already their simulation is very complex and time consuming due to the radiation, the main focus of the project will be on the investigation of optimization algorithms based on the adjoint variables, which will be applied to the full radiative heat transfer system as well as to diffusive type approximations. In contrast to black-box optimization algorithms, this allows to keep a balance between the optimization and simulation effort for arbitrary fine discretizations. Special focus will be on the investigation of different numerical methods which allow to solve three dimensional problems at reasonable computational costs. In addition to the optimization we will also study new approaches to the reconstruction of the initial temperature from boundary measurements, since its precise knowledge is mandatory for any satisfactory simulation. Especially, we will develop a fast, derivative-free method for the solution of the inverse problem, such that we can use many different models for the simulation of the radiative process.