TC2 Optimal design of structures O.Pantz Convex Optimization Exercise I. Optimization of a heater. We want to optimize the temperature T of a room Ω by the mean of a heater
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Exercise I. Optimization of a heater. We want to optimize the temperature T of a room Ω by the mean of a heater ω whose heat flux v ∈ L(ω) is controlled. An air stream of velocity u fills the room. We assume that the air is incompressible, that is u is assumed to be divergence free. Moreover, u is also assumed to be regular. The temperature on the boundary of the room is equal to the external temperature, assumed to be zero. The temperature in the room satisfies the following convection-diffusion equation −∆T + u · ∇T = 1ωv.
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TC2 Optimal design of structures O.Pantz Convex Optimization Exercise I. Optimization of a heater. We want to optimize the temperature T of a room Ω by the mean of a heater
Exercise I. Optimization of a heater. We want to optimize the temperature T of a room Ω by the mean of a heater ! whose heat flux v ∈ L(!) is controlled. An air stream of velocity u fills the room. We assume that the air is incompressible, that is u is assumed to be divergence free. Moreover, u is also assumed to be regular. The temperature on the boundary of the room is equal to the external t...
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