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Optimization and Inverse Problems in Radiative Heat Transfer

  • René PinnauEmail author
  • Norbert Siedow
Chapter
Part of the International Series of Numerical Mathematics book series (ISNM, volume 160)

Abstract

We discuss the derivation and investigation of efficient mathematical methods for the solution of optimization and identification problems for radiation dominant processes, which are described by a nonlinear integrodifferential system or diffusive type approximations. These processes are for example relevant in glass production or in the layout of gas turbine combustion chambers. The main focus is on the investigation of optimization algorithms based on the adjoint variables, which are applied to the full radiative heat transfer system as well as to diffusive type approximations. In addition to the optimization we also study new approaches to the reconstruction of the initial temperature from boundary measurements, since its precise knowledge is mandatory for any satisfactory simulation. In particular, we 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.

Keywords

Radiative heat transfer SPnapproximation optimal boundary control inverse problem optimality conditions analysis numerics adjoints integro-differential equations reduced order modeling. 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of MathematicsTU KaiserslauternKaiserslauternGermany
  2. 2.Fraunhofer Institut für Techno- und WirtschaftsmathematikKaiserslauternGermany

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