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Digital
Library of the European Council for Modelling and Simulation |
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Title: |
Thermistor Problem: Multi-Dimensional Modelling,
Optimization And Approximation |
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Authors: |
Ciro D'Apice,
Umberto De Maio, Peter I. Kogut |
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Published in:
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(2018). ECMS 2018
Proceedings Edited by: Lars Nolle, Alexandra
Burger, Christoph Tholen,
Jens Werner, Jens Wellhausen European Council for
Modeling and Simulation. doi:
10.7148/2018-0005 ISSN:
2522-2422 (ONLINE) ISSN:
2522-2414 (PRINT) ISSN:
2522-2430 (CD-ROM) 32nd European Conference on Modelling and Simulation, Wilhelmshaven, Germany, May 22nd
– May 265h, 2018 |
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Citation
format: |
Ciro D'Apice, Umberto De Maio, Peter I. Kogut (2018). Thermistor Problem: Multi-Dimensional Modelling,
Optimization And Approximation, ECMS 2018
Proceedings Edited by: Lars Nolle, Alexandra
Burger, Christoph Tholen,
Jens Werner, Jens Wellhausen European Council for
Modeling and Simulation. doi:
10.7148/2018-0348 |
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DOI: |
https://doi.org/10.7148/2018-0348 |
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Abstract: |
We consider a problem of an optimal control in coefficients
for the system of two coupled elliptic equations also known as thermistor problem which provides a simultaneous
description of the electric field u = u(x) and temperature θ(x). The coef-ficients
of operator div (A(x) ∇ θ(x)) are used
as the controls in L∞(Ω). The optimal control prob-lem
is to minimize the discrepancy between a given distribution θd ∈ Lr(Ω)
and the temperature of thermistor θ ∈ W01,γ (Ω) by choosing an appropri-ate
anisotropic heat conductivity matrix B. Basing on the perturbation theory of extremal problems and the concept of fictitious
controls, we propose an “approximation approach” and discuss the ex-istence of the so-called quasi-optimal and optimal
solutions to the given problem. |
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