Optimal control in radiative transfer

A tracking-type optimal control problem for the radiative transfer equation (RTE) is studied, where we consider the source term in the RTE as control variable. Necessary and sufficient optimality conditions are derived. Numerical methods for the model equation and its adjoint are presented. Computational results based on a steepest descent method are given for two test examples underlining the feasibility of our approach.

[1]  R. Pinnau,et al.  Newton's method for optimal temperature-tracking of glass cooling processes , 2007 .

[2]  Claude Bardos,et al.  Optimal control approach in inverse radiative transfer problems: the problem on boundary function , 2000 .

[3]  Axel Klar,et al.  Efficient numerical methods for radiation in gas turbines , 2004 .

[4]  M. Modest.  Radiative heat transfer , 1993 .

[5]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[6]  C. T. Kelley,et al.  A Fast Multilevel Algorithm for the Solution of Nonlinear Systems of Conductive-Radiative Heat Transfer Equations in Two Space Dimensions , 1999, SIAM J. Sci. Comput..

[7]  C. D. Levermore,et al.  Moment closure hierarchies for kinetic theories , 1996 .

[8]  INITIAL TEMPERATURE RECONSTRUCTION FOR A NONLINEAR HEAT EQUATION : APPLICATION TO RADIATIVE AND CONDUCTIVE HEAT TRANSFER . , 2005 .

[9]  G. Thömmes,et al.  Optimal boundary control of glass cooling processes , 2004 .

[10]  Sandro Manservisi,et al.  On some optimal control problems for the heat radiative transfer equation , 2000 .

[11]  M. K. Choudhary,et al.  Mathematical modeling in the glass industry : An overview of status and needs , 1997 .

[12]  Jean Charles Gilbert,et al.  Numerical Optimization: Theoretical and Practical Aspects , 2003 .

[13]  J. Frédéric Bonnans,et al.  Numerical Optimization: Theoretical and Practical Aspects (Universitext) , 2006 .

[14]  C. Kelley.  Existence and uniqueness of solutions of nonlinear systems of conductive-radiative heat transfer equations , 1996 .

[15]  A. Klar,et al.  NUMERICAL METHODS AND OPTIMAL CONTROL FOR GLASS COOLING PROCESSES , 2002 .

[16]  P. Spellucci.  Nonlinear (local) optimization. The state of the art , 2001 .

[17]  Axel Klar,et al.  Numerical Solvers for Radiation and Conduction in High Temperature Gas Flows , 2005 .

[18]  A. Klar,et al.  Efficient Preconditioning of Linear Systems Arising from the Discretization of Radiative Transfer Equation , 2003 .

[19]  M. Laitinen,et al.  Integro-differential equation modelling heat transfer in conducting, radiating and semitransparent materials , 1998 .

[20]  W. Fiveland.  Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures , 1984 .

[21]  Axel Klar,et al.  Simplified P N approximations to the equations of radiative heat transfer and applications , 2002 .

[22]  D. Mihalas,et al.  Foundations of Radiation Hydrodynamics , 1985 .

[23]  Peter Spellucci,et al.  Numerische Verfahren der nichtlinearen Optimierung , 1993 .