scholarly journals DETECTING AN OBSTACLE IMMERSED IN A FLUID BY SHAPE OPTIMIZATION METHODS

2011 ◽  
Vol 21 (10) ◽  
pp. 2069-2101 ◽  
Author(s):  
MEHDI BADRA ◽  
FABIEN CAUBET ◽  
MARC DAMBRINE
Keyword(s):  
Shape Optimization ◽  
Least Squares ◽  
Stokes Equations ◽  
Neumann Boundary ◽  
Nonlinear Least Squares ◽  
Identification Problem ◽  
Optimization Methods ◽  
Riesz Operator ◽  
Shape Derivatives ◽  
Shape Hessian

The paper presents a theoretical study of an identification problem by shape optimization methods. The question is to detect an object immersed in a fluid. Here, the problem is modeled by the Stokes equations and treated as a nonlinear least-squares problem. We consider both the Dirichlet and Neumann boundary conditions. Firstly, we prove an identifiability result. Secondly, we prove the existence of the first-order shape derivatives of the state, we characterize them and deduce the gradient of the least-squares functional. Moreover, we study the stability of this setting. We prove the existence of the second-order shape derivatives and we give the expression of the shape Hessian. Finally, the compactness of the Riesz operator corresponding to this shape Hessian is shown and the ill-posedness of the identification problem follows. This explains the need of regularization to numerically solve this problem.

A COMPARISON OF OPTIMIZATION METHODS FOR FITTING CURVES TO INFRARED BAND ENVELOPES

1966 ◽  
Vol 44 (24) ◽  
pp. 3031-3050 ◽  
Author(s):  
J. Pitha ◽  
R. Norman Jones
Keyword(s):  
Least Squares ◽  
Computation Time ◽  
Direct Methods ◽  
Nonlinear Least Squares ◽  
Optimization Methods ◽  
Infrared Band ◽  
Band Shape ◽  
Analytical Functions ◽  
Degree Of Convergence ◽  
Better Than

A comparison has been made of seven numerical methods of fitting infrared absorption band envelopes with analytical functions using nonlinear least squares approximations. Gauss and Cauchy (Lorentz) band shape functions are used, and also sum and product combinations of the two. The methods have been compared with respect to both the degree of convergence and to the computation time needed to achieve an acceptable fit.The most effective method has matched the overlap envelope of a steroid spectrum containing 16 bands; this necessitated the optimization of 65 variables. More complex spectra can be dealt with by a "moving subspace" modification in which only the parameters of a group of adjacent bands are adjusted at one time. Automatic computer programs have been written for five of the methods, and for the moving subspace modification. These will be published elsewhere.If the computed curve is convoluted with the spectral slit function before making the least squares calculations, the distortion of the observed spectrum caused by the finite spectral slit width can be corrected. In some cases this method of diminishing the slit distortion is better than direct methods, particularly when dealing with strongly overlapped bands.

scholarly journals On the Resolution of an Inverse Problem by Shape Optimization Techniques

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Chahnaz Zakia Timimoun
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Shape Optimization ◽  
Stokes Equations ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
The Body ◽  
Cost Functional

In this work, we want to detect the shape and the location of an inclusion ω via some boundary measurement on ∂Ω. In practice, the body ω is immersed in a fluid flowing in a greater domain Ω and governed by the Stokes equations. We study the inverse problem of reconstructing ω using shape optimization methods by defining the Kohn-Vogelius cost functional. We aim to study the inverse problem with Neumann and mixed boundary conditions.

scholarly journals Seismic Image Restoration Using Nonlinear Least Squares Shape Optimization

2013 ◽  
Vol 18 ◽  
pp. 732-741 ◽  
Author(s):  
Mathieu Gilardet ◽  
Sebastien Guillon ◽  
Bruno Jobard ◽  
Dimitri Komatitsch
Keyword(s):  
Shape Optimization ◽  
Image Restoration ◽  
Least Squares ◽  
Nonlinear Least Squares ◽  
Seismic Image

Improvement of Efficiency by Design Optimization of a Centrifugal Pump Impeller

2014 ◽  
Author(s):  
Sayed Ahmed Imran Bellary ◽  
Abdus Samad
Keyword(s):  
Shape Optimization ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Weighted Average ◽  
Optimization Methods ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
Hydraulic Efficiency ◽  
Pump Impeller ◽  
Design Variables

Shape optimization of centrifugal impeller blades has been performed through numerical analysis and implementation of multiple surrogate based optimization methodology. Design variables which are used to define blade angles at leading and trailing edges were introduced to increase the hydraulic efficiency of the impeller. The efficiency was selected as an object function and the optimization was performed using a surrogate base optimization methods. A three-dimensional simulation using Reynolds-averaged Navier Stokes equations for the performance analysis was carried out after designing the geometries of the impellers at the design points selected from the design space which was defined by the lower and upper limits of the variables. Throughout the shape optimization, the hydraulic efficiency was increased by decreasing losses near the blade surfaces and impeller passage. Among different surrogates, a weighted average model produced better results. The application of the multiple surrogate methods not only improved quality of single objective optimization but also gives the feedback of the fidelity of the optimization models.

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