FICTITIOUS DOMAINS METHODS WITH DISTRIBUTED LAGRANGE MULTIPLIERS PART II: APPLICATION TO THE SOLUTION OF SHAPE OPTIMIZATION PROBLEMS-Reference-Cited by-同舟云学术

FICTITIOUS DOMAINS METHODS WITH DISTRIBUTED LAGRANGE MULTIPLIERS PART II: APPLICATION TO THE SOLUTION OF SHAPE OPTIMIZATION PROBLEMS

Published:2001-04 Issue:03 Volume:11 Page:549-563
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

HASLINGER JAROSLAV¹,MAITRE JEAN-FRANCOIS²,TOMAS LAURENT³

Affiliation:

1. Department of Metal Physics, Charles University Ke Karlovu 5, 121 16 Praha 2, Czech Republic

2. UMR CNRS 5585, Ecole Centrale de Lyon BP 163, 69131 Ecully Cedex, France

3. Alstom Power Hydro-Hydraulic Engineering Department, 82 Avenue Léon Blum BP 75, 38041 Grenoble Cedex 9, France

Abstract

The distributed Lagrange multipliers based fictitious domain method for the numerical computation of state problems presented in Part I is now used in the frame of shape optimization. Practical aspects of this approach are discussed. In general it is shown that the resulting minimization problem is nonsmooth, due to the locking effect. Two possible regularization techniques are described and the results of one numerical example is shown.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202501000970

Reference3 articles.

1. Numerical realization of a fictitious domain approach used in shape optimization. Part I: Distributed controls

2. Fictitious domain/mixed finite element approach for a class of optimal shape design problems

3. FICTITIOUS DOMAINS METHODS WITH DISTRIBUTED LAGRANGE MULTIPLIERS PART I: APPLICATION TO THE SOLUTION OF ELLIPTIC STATE PROBLEMS

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Shape optimization with immersed interface finite element method;International Journal for Numerical Methods in Engineering;2022-08-26

2. Shape optimization using a NURBS-based interface-enriched generalized FEM;International Journal for Numerical Methods in Engineering;2017-01-31

3. On shape sensitivities with heaviside-enriched XFEM;Structural and Multidisciplinary Optimization;2016-12-24

4. Material Design Using a NURBS-based Shape Optimization;57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference;2016-01-01

5. A gradient-based shape optimization scheme using an interface-enriched generalized FEM;Computer Methods in Applied Mechanics and Engineering;2015-11