Shape Optimization under Uncertainty from a Stochastic Programming Point of View: Stochastic Programming
Autor Harald Helden Limba Engleză Paperback – 28 iul 2009
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Specificații
ISBN-13: 9783834809094
ISBN-10: 3834809098
Pagini: 134
Ilustrații: 148 p. 39 illus., 26 illus. in color.
Dimensiuni: 148 x 210 x 20 mm
Greutate: 0.19 kg
Ediția:2009
Editura: Vieweg+Teubner Verlag
Colecția Vieweg+Teubner Verlag
Seria Stochastic Programming
Locul publicării:Wiesbaden, Germany
ISBN-10: 3834809098
Pagini: 134
Ilustrații: 148 p. 39 illus., 26 illus. in color.
Dimensiuni: 148 x 210 x 20 mm
Greutate: 0.19 kg
Ediția:2009
Editura: Vieweg+Teubner Verlag
Colecția Vieweg+Teubner Verlag
Seria Stochastic Programming
Locul publicării:Wiesbaden, Germany
Public țintă
ResearchCuprins
Solution of the Elasticity PDE.- Stochastic Programming Perspective.- Solving Shape Optimization Problems.- Numerical Results.
Notă biografică
Dr. Harald Held completed his doctoral thesis at the Department of Mathematics at the University of Duisburg-Essen. He is now a Research Scientist at Siemens AG, Corporate Technology.
Textul de pe ultima copertă
Optimization problems are relevant in many areas of technical, industrial, and economic applications. At the same time, they pose challenging mathematical research problems in numerical analysis and optimization.
Harald Held considers an elastic body subjected to uncertain internal and external forces. Since simply averaging the possible loadings will result in a structure that might not be robust for the individual loadings, he uses techniques from level set based shape optimization and two-stage stochastic programming. Taking advantage of the PDE’s linearity, he is able to compute solutions for an arbitrary number of scenarios without significantly increasing the computational effort. The author applies a gradient method using the shape derivative and the topological gradient to minimize, e.g., the compliance . and shows that the obtained solutions strongly depend on the initial guess, in particular its topology. The stochastic programming perspective also allows incorporating risk measures into the model which might be a more appropriate objective in many practical applications.
Harald Held considers an elastic body subjected to uncertain internal and external forces. Since simply averaging the possible loadings will result in a structure that might not be robust for the individual loadings, he uses techniques from level set based shape optimization and two-stage stochastic programming. Taking advantage of the PDE’s linearity, he is able to compute solutions for an arbitrary number of scenarios without significantly increasing the computational effort. The author applies a gradient method using the shape derivative and the topological gradient to minimize, e.g., the compliance . and shows that the obtained solutions strongly depend on the initial guess, in particular its topology. The stochastic programming perspective also allows incorporating risk measures into the model which might be a more appropriate objective in many practical applications.
Caracteristici
Shape Optimization