Comlab

This lecture is about the extension of our CAD-Free platform to the simulation and sensitivity analysis for design and control of multi-model configurations. We present the different ingredients of the platform using simple models for the physic of the problem. This presentation enables for an easy evaluation of coupling, design and control strategies.

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Sensitivity analysis has been performed using automatic differentiation in direct or reverse modes and finite difference or complex variable methods. This former approach is interesting for cases where only one control parameter is involved as we can evaluate the state and sensitivity in real time with only one evaluation.

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We show that for some class of applications, incomplete sensitivities can be evaluated dropping the state dependency which leads to a drastic cost reduction.

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The design concerns the structural characteristic of the model and our control approach is based in perturbating the inflow incidence by a time dependent flap position described by a dynamic system encapsulating a gradient based minimization algorithm expressed as dynamic system. This approach enables for the definition of various control laws for different minimization algorithm.

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We present dynamic minimization algorithms based on the coupling of several heavy ball method. This approach enables for global minimization at a cost proportional to the number of balls times the cost of one steepest descent minimization.

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Two and three dimension flutter problem simulation and control are presented and the sensitivity of the different parameters in the model is discussed.

This seminar has been cancelled.

Krylov subspace methods offer good possibilities for the solution of

large sparse linear systems of equations.For general systems, some of

the popular methods often show an irregular type of convergence

behavior and one may wonder whether that could be improved or not. Many

suggestions have been made for improvement and the question arises

whether these corrections are cosmetic or not. There is also the

question whether the irregularity shows inherent numerical instability.

In such cases one should take extra care in the application of

smoothing techniques. We will discuss strategies that work well and

strategies that might have been expected to work well.

This work forms part of a larger research project to develop efficient

low-dissipative high-order numerical techniques for high-speed

turbulent flow simulation, including shock wave interactions with

turbulence. The requirements on a numerical method are stringent.For

the turbulence the method must be capable of resolving accurately a

wide range of length scales, whilst for shock waves the method must be

stable and not generate excessive local oscillations. Conventional

methods are either too dissipative, or incapable of shock capturing.

Higher-order ENO, WENO or hybrid schemes are too expensive for

practical computations. Previous work of Yee, Sandham & Djomehri

(1999) developed high-order shock-capturing schemes which minimize the

use of numerical dissipation away from shock

waves. The objective of the present study is to further minimize the

use of numerical dissipation for shock-free compressible turbulence

simulations.

In 1983 Pantoja described a stagewise construction of the exact Newton

direction for a discrete time optimal control problem. His algorithm

requires the solution of linear equations with coefficients given by

recurrences involving second derivatives, for which accurate values are

therefore required.

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Automatic differentiation is a set of techniques for obtaining derivatives

of functions which are calculated by a program, including loops and

subroutine calls, by transforming the text of the program.

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In this talk we show how automatic differentiation can be used to

evaluate exactly the quantities required by Pantoja's algorithm,

thus avoiding the labour of forming and differentiating adjoint

equations by hand.

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The cost of calculating the newton direction amounts to the cost of

solving one set of linear equations, of the order of the number of

control variables, for each time step. The working storage cost can be made

smaller than that required to hold the solution.