A quasi-Newton interior point algorithm applied to constrained optimum design in computational fluid dynamics

Herskovits, José; Laporte, Emmanuel; Tallec, Patrick Le; Santos, G.

doi:10.1080/12506559.1996.10511239

Cited by 7 publications

(10 citation statements)

References 4 publications

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“…It can be also further generalized by replacing in the Newton step the Hessian ~~ + L >' 1 ~~ by an adequate positive definite approximation B constructed I for example by a BFGS updating procedure. The general Herskovits algorithm [23,24] then updates the solution (z, >.) through the following steps: i) Newton's prediction Solve the linearized equations of optimality In practice, the above one-dimensional problem is usually solved by an Armijo technique computing the first element in the sequence {I, v, V 2 , V 3 , ..• } such that…”

Section: Herskovits' Algorithm Without Equality Constraintsmentioning

confidence: 99%

“…Such a behavior is usually respected in practice. The detailed implementation of the above algorithm is described in [24).…”

Section: Herskovits' Algorithm Without Equality Constraintsmentioning

confidence: 99%

“…idata(24) double precision data(9) Set real parameters to zero call dzerov(data,9) data(2)=1. Od-4 data(5)=1.0dO do 100 i=1,24 idata(i)=O 100 continue idata(l1)=l idata(12)=0 idata(13)=0 idata(14)=0 idata(16)=1 idata (17) =1 return end…”

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confidence: 99%

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Numerical Methods in Sensitivity Analysis and Shape Optimization

Laporte

Tallec

2003

Modeling and Simulation in Science, Engineering and Technology

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Section: Herskovits' Algorithm Without Equality Constraintsmentioning

confidence: 99%

“…Such a behavior is usually respected in practice. The detailed implementation of the above algorithm is described in [24).…”

Section: Herskovits' Algorithm Without Equality Constraintsmentioning

confidence: 99%

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Numerical Methods in Sensitivity Analysis and Shape Optimization

Laporte

Tallec

2003

Modeling and Simulation in Science, Engineering and Technology

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“…In this paper we employ a SAND formulation for both approaches and solve the optimization problems employing the Feasible Arc Interior Point Algorithm, FAIPA, a line search interior-point algorithm for nonlinear optimization. See [32], [33], [42], [37], [6] for a general discussion of the SAND formulation, [5], [34], [12], [13] for some other issues and applications and [20], [34], [21] for details about FAIPA.…”

Section: Introductionmentioning

confidence: 99%

Inductor shape optimization for electromagnetic casting

Canelas

Roche

Herskovits

2009

Struct Multidisc Optim

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International audienceThe design of inductors in electromagnetic shaping of molten metals consists in looking for the position and the shape of a set of electric wires such that the induced electromagnetic field makes a given mass of liquid metal acquire a predefined shape. In this paper we formulate an inverse optimization problem where the position and shape of the inductors are defined by a set of design variables. In a first formulation of the inverse optimization problem we minimize the difference between the target and the equilibrium shapes while in a second approach we minimize the L 2 norm of a fictitious surface pressure that makes the target shape to be in mechanical equilibrium. Geometric constraints that prevent the inductors from penetrating the liquid metal are considered in both formulations. The optimization problems are solved using FAIPA, a line search interior-point algorithm for nonlinear optimization. Some examples are presented to show the effectiveness of the proposed approaches

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“…Herein, we have calculated exact derivatives for all the functions of the discretized model. For more details about FAIPA see [10,11,24].…”

Section: Numerical Examplesmentioning

confidence: 99%

Shape optimization for inverse electromagnetic casting problems

Canelas

Roche²,

Herskovits

2011

Inverse Problems in Science and Engineering

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In this paper we present an algorithm for inverse optimization problems concerning electromagnetic casting of molten metals. We are interested in locating suitable inductors around the molten metal so that the equilibrium shape be as near as possible to a desired target shape. A Simultaneous Analysis and Design (SAND) mathematical programming formulation is stated for the inverse problem. The resulting optimization problem is solved with FAIPA, a feasible directions interior-point algorithm. INTRODUCTIONThe industrial technique of electromagnetic casting allows for contactless heating, shaping and controlling of chemical aggressive, hot melts. The main advantage over the conventional crucible shape forming is that the liquid metal does not come into contact with the crucible wall, so there is no danger of contamination. This is very important in the preparation of very pure specimens in metallurgical experiments, as even small traces of impurities, such as carbon and sulphur, can affect the physical properties of the sample. Industrial applications are, for example, electromagnetic shaping of aluminum ingots using soft-contact confinement of the liquid metal, electromagnetic shaping of components of aeronautical engines made of superalloy materials (Ni,Ti, . . . ), control of the structure solidification, etc.The direct problem is to determine the resulting liquid metal shape for a given external current distribution. The model considered here concerns a vertically falling molten metal column shaped by an externally applied magnetic field created by a set of inductors. In general, the direct problem can be solved either directly studying the equilibrium

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A quasi-Newton interior point algorithm applied to constrained optimum design in computational fluid dynamics

Cited by 7 publications

References 4 publications

Numerical Methods in Sensitivity Analysis and Shape Optimization

Numerical Methods in Sensitivity Analysis and Shape Optimization

Inductor shape optimization for electromagnetic casting

Shape optimization for inverse electromagnetic casting problems

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