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

1996 ◽  
Vol 41 (2) ◽  
pp. 123-147
Author(s):  
Jana Daňková ◽  
Jaroslav Haslinger
Keyword(s):  
Shape Optimization ◽  
Numerical Realization ◽  
Fictitious Domain ◽  
Distributed Controls

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

2001 ◽  
Vol 11 (03) ◽  
pp. 521-547 ◽  
Author(s):  
JAROSLAV HASLINGER ◽  
JEAN-FRANCOIS MAITRE ◽  
LAURENT TOMAS
Keyword(s):  
Finite Element ◽  
Shape Optimization ◽  
Lagrange Multipliers ◽  
Optimal Shape ◽  
Fictitious Domain ◽  
Boundary Variation ◽  
Fictitious Domain Methods ◽  
Finite Element Discretizations ◽  
Element Discretizations ◽  
Variation Technique

Fictitious domain approaches are an attractive way to overcome the usual drawbacks of the so-called boundary variation technique for solving optimal shape problems. In the first part of this paper, we introduce fictitious domain methods with distributed Lagrange multipliers for elliptic state problems. Continuous formulations as well as their finite element discretizations are discussed. The second part of the paper will be devoted to the application of these methods to shape optimization.

scholarly journals A moving mesh fictitious domain approach for shape optimization problems

2000 ◽  
Vol 34 (1) ◽  
pp. 31-45 ◽  
Author(s):  
Raino A.E. Mäkinen ◽  
Tuomo Rossi ◽  
Jari Toivanen
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Moving Mesh ◽  
Fictitious Domain

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

2001 ◽  
Vol 11 (03) ◽  
pp. 549-563 ◽  
Author(s):  
JAROSLAV HASLINGER ◽  
JEAN-FRANCOIS MAITRE ◽  
LAURENT TOMAS
Keyword(s):  
Shape Optimization ◽  
Numerical Computation ◽  
Minimization Problem ◽  
Lagrange Multipliers ◽  
Optimization Problems ◽  
Fictitious Domain ◽  
Fictitious Domain Method ◽  
Numerical Example ◽  
Regularization Techniques ◽  
Locking Effect

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.

A new fictitious domain method in shape optimization

2007 ◽  
Vol 40 (2) ◽  
pp. 281-298 ◽  
Author(s):  
Karsten Eppler ◽  
Helmut Harbrecht ◽  
Mario S. Mommer
Keyword(s):  
Shape Optimization ◽  
Fictitious Domain ◽  
Fictitious Domain Method ◽  
Domain Method

Genetic algorithms and fictitious domain based approaches in shape optimization

1996 ◽  
Vol 12 (4) ◽  
pp. 257-264 ◽  
Author(s):  
J. Haslinger ◽  
D. Jedelsk�
Keyword(s):  
Genetic Algorithms ◽  
Shape Optimization ◽  
Fictitious Domain

The Isogeometric Shape Optimization Method Based on Finite Cell Method

2014 ◽  
Vol 621 ◽  
pp. 655-662
Author(s):  
Gang He ◽  
Zheng Yu Pan ◽  
Zhi Hui Zou ◽  
Deng Lin Zhu
Keyword(s):  
Shape Optimization ◽  
Optimization Design ◽  
Boundary Representation ◽  
Fictitious Domain ◽  
Computational Domain ◽  
Finite Cell Method ◽  
Cell Method ◽  
High Efficient ◽  
Complex Boundary ◽  
Finite Cell

Isogeometric analysis (IGA) method uses the same mathematical model in geometric design and engineering analysis, and is the most potential method to realize high accuracy and integrated optimization design. Finite Cell Method (FCM) introduces high order finite element method into fictitious domain method, and it has great advantages of complex boundary representation and high efficient convergence. In order to break through IGA’s limit on geomerty’s topology, IGA and FCM are combined together in this research. Function Heasivide and Dirac are used to approximate the computational domain and its first order derivative, then the stiffness matrix on the fictitious domain are calculated and the displacement in the shape with complex boundary is solved by IGA method. One order and two order implicit curves are used to the outer boundary representation of elastic optimization problem, and their coefficients are taken as design variable. The sensitivity formulas are deduced. MMA method is used to implement the IGA shape optimization based on FCM. The examples show that our method is efficient and the result is satisfied.

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