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A moving mesh fictitious domain approach for shape optimizationproblems

Published online by Cambridge University Press:  15 April 2002

Raino A.E. Mäkinen ,
Tuomo Rossi  and
Jari Toivanen
Raino A.E. Mäkinen
Affiliation:
Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (MaE), 40351 Jyväskylä, Finland. ([email protected])
Tuomo Rossi
Affiliation:
Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (MaE), 40351 Jyväskylä, Finland. ([email protected])
Jari Toivanen
Affiliation:
Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (MaE), 40351 Jyväskylä, Finland. ([email protected])
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Abstract

A new numerical method based on fictitious domain methods for shapeoptimization problems governed by the Poisson equation is proposed.The basic idea is to combine the boundary variation technique, in whichthe mesh is moving during the optimization, and efficient fictitiousdomain preconditioning in the solution of the (adjoint) state equations.Neumann boundary value problems are solved using an algebraic fictitiousdomain method. A mixed formulation based on boundary Lagrangemultipliers is used for Dirichlet boundary problems and the resultingsaddle-point problems are preconditioned with block diagonal fictitiousdomain preconditioners. Under given assumptions on the meshes, thesepreconditioners are shown to be optimal with respect to the conditionnumber. The numerical experiments demonstrate the efficiency ofthe proposed approaches.

Keywords

Shape optimizationfictitious domain methodpreconditioningboundary variation techniquesensitivity analysis.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 1 , January 2000 , pp. 31 - 45
Copyright
© EDP Sciences, SMAI, 2000

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