INTEMP: Inverse Methods

Project Topic

Inverse methods for determining the temperature in hot glasses.

Project Description

The most important parameter in almost all stages of the glass production and glass processing is the temperature. During the melting the temperature influences the homogeneity of the glass melt. Undesired cracks could be the result of a wrong cooling of the glass. Thus, the knowledge of the right temperature is important to guarantee the quality of the final products.

Indirect measurements are very often the only way to measure the temperature inside hot glasses or glass melts. Glass is a semitransparent material. The coupling of heat conduction and thermal radiation results from a mathematical point of view in a high-dimensional non-linear system of partial differential equations. For the inverse temperature reconstruction different approaches will be considered:

The spectral remote sensing is based on the formal solution of the radiative transfer equation. One has to solve a non-linear integral equation of first kind which is ill-posed. Regularization techniques are required. The analysis of different regularizations and alternative approximation approaches for solving the integral equation are part of the INTEMP project.

Knowing boundary temperatures and heat fluxes from measurements one can ask for the reconstruction of the initial temperature profile. The solution and mathematical analysis of this new inverse problem will be a second part of INTEMP.

Project Members

Project Chair

• Dr. Norbert Siedow, Sect. Transport Processes, Fraunhofer Institute for Industrial Mathematics (ITWM)

Participating Research Groups

• Sect. Transport Processes, Fraunhofer Institute for Industrial Mathematics (ITWM)
• Technomathematics Group, Department of Mathematics

Scientific Personnel

• Dr. Norbert Siedow (Fraunhofer Institute for Industrial Mathematics (ITWM))
• Prof. Dr. Rene Pinnau (Technomathematics Group)
• Sergiy Pereverzyev (Fraunhofer Institute for Industrial Mathematics (ITWM))

External Cooperation

Project Events and Achievements

• Project start date: November 1st, 2005
• Project end date: December 31st, 2007

Project Publications

Asymptotic and Discrete Concepts for Optimal Control in Radiative Transfer

Michael Herty, Rene Pinnau, G. Thömmes. Submitted, 2006

Regularized Fixed-Point Iterations for Nonlinear Inverse Problems

Sergiy S. Pereverzyev, Rene Pinnau, Norbert Siedow. In: Inverse Problems. Volume 22, P. 1--22, 2006

Initial temperature reconstruction for a nonlinear heat equation

Sergiy S. Pereverzyev, Rene Pinnau, Norbert Siedow. In: Inverse Problems in Science and Engineering. Submitted, 2006

On Optimal Control Problems in Radiative Transfer

Michael Herty, Rene Pinnau, Mohammed Seaid. Submitted, 2005