Numerical Methods and Optimal Control for Glass Cooling Processes

Thömmes, Guido; Pinnau, René; Seaı̈d, Mohammed; Götz, Theresa; Klar, Axel

doi:10.1081/tt-120015512

Cited by 55 publications

(26 citation statements)

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“…During the last years the increased computing power in combination with the usage of the approximate models has allowed for the numerical treatment of such large-scale optimization problems. In particular, optimal boundary control problems for the SP 1 -system yielded encouraging results and were successfully employed for many applications [20,12,15,11]. Nevertheless, the mathematical analysis of this optimal boundary control problem is still open.…”

Section: Introductionmentioning

confidence: 99%

Analysis of optimal boundary control for radiative heat transfer modeled by the $SP_{n}$-system

Pinnau¹

2007

Communications in Mathematical Sciences

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Abstract. We present an analytic study of an optimal boundary control problem for the diffusive SP 1 -system modeling radiative heat transfer. The cost functional is of tracking-type and the control problem is considered as a constrained optimization problem, where the constraint is given by the nonlinear parabolic/elliptic SP 1 -system. We prove the existence, uniqueness and regularity of bounded states, which allows for the introduction of the reduced cost functional. Further, we show the existence of an optimal control, derive the first-order optimality system and analyze the adjoint system, for which we prove existence, uniqueness and regularity of adjoint states.

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Section: Introductionmentioning

confidence: 99%

Analysis of optimal boundary control for radiative heat transfer modeled by the $SP_{n}$-system

Pinnau¹

2007

Communications in Mathematical Sciences

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“…The SP N approximations were first proposed in [14] and theoretically studied in [19]. In [20,26], the SP N approximations have been extensively studied for radiative transfer in glass manufacturing, while in [13] they have been implemented for radiation in gas turbines. The SP N approximations have also been studied in [6] for internal radiation in crystal growth.…”

Section: Introductionmentioning

confidence: 99%

hp-adaptive discontinuous Galerkin methods for simplified PN
Giani
¹
,
Seaı̈d
²

2016
Computer Methods in Applied Mechanics and Engineering
11
0
0
0
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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractWe investigate the performance of a class of hp-adaptive discontinuous Galerkin methods for the numerical solution of simplified P N approximations of radiative transfer in non-grey semitransparent media. By introducing an optical scale and using asymptotic expansions in the radiative transfer equation we formulate the simplified P N approximations. The optical spectrum is decomposed in frequency bands and the simplified P N equations are solved for each frequency band. As a numerical solver for the simplified P N equations we consider a high-order discontinuous Galerkin method. The solver belongs to a class of finite element methods whose approximate solutions are discontinuous across inter-element boundaries; this property renders the method ideally suited for the hp-adaptivity. An error estimator is shown to provide reliable and practically useful upper bounds for the numerical errors independent of the optical scales used in the simulations. The proposed method is simple, fast and highly accurate. The performance of the method is analyzed on several applications in frequency-dependent radiative transfer. The aim of such a method compared to the conventional finite element methods is to solve the simplified P N equations efficiently and with a high level of accuracy on unstructured meshes with different elements. The obtained results demonstrate the ability of the proposed method to capture the main radiative features.

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“…in the field of glass cooling processes or the design of combustion chambers, pose several challenging problems for applied mathematicians and engineers and have been extensively studied during the last years [3,21,16,2,1,6,13]. Due to the high numerical complexity of the model equations which are given by the radiative heat transfer system for the radiative intensity, there is a strong need for sophisticated reduced order models.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic and discrete concepts for optimal control in radiative transfer

Herty¹,

Pinnau

Thömmes

2007

Z Angew Math Mech

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Optimal control problems for radiative transfer and for approximate models are considered. Following the approach first discretize, then optimize, the discrete SP N approximations are for the first time derived exactly, which can be used to study optimal control on reduced order models. Combining asymptotic analysis and the adjoint calculus yields diffusive-type approximations for the adjoint radiative transport equation in the spirit of the approach first optimize, then discretize.

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Numerical Methods and Optimal Control for Glass Cooling Processes

Cited by 55 publications

References 1 publication

Analysis of optimal boundary control for radiative heat transfer modeled by the $SP_{n}$-system

Analysis of optimal boundary control for radiative heat transfer modeled by the $SP_{n}$-system

hp-adaptive discontinuous Galerkin methods for simplified PN
Giani
¹
,
Seaı̈d
²

2016
Computer Methods in Applied Mechanics and Engineering
11
0
0
0
View full text Add to dashboard Cite

Asymptotic and discrete concepts for optimal control in radiative transfer

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Numerical Methods and Optimal Control for Glass Cooling Processes

Cited by 55 publications

References 1 publication

Analysis of optimal boundary control for radiative heat transfer modeled by the $SP_{n}$-system

Analysis of optimal boundary control for radiative heat transfer modeled by the $SP_{n}$-system

hp-adaptive discontinuous Galerkin methods for simplified PNGiani1, Seaı̈d2 2016Computer Methods in Applied Mechanics and Engineering11000View full textAdd to dashboardCite

Asymptotic and discrete concepts for optimal control in radiative transfer

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hp-adaptive discontinuous Galerkin methods for simplified PN
Giani
¹
,
Seaı̈d
²

2016
Computer Methods in Applied Mechanics and Engineering
11
0
0
0
View full text Add to dashboard Cite