# A moving mesh fictitious domain approach for shape optimization problems

Raino A.E. Mäkinen; Tuomo Rossi; Jari Toivanen

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 34, Issue: 1, page 31-45
- ISSN: 0764-583X

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topMäkinen, Raino A.E., Rossi, Tuomo, and Toivanen, Jari. "A moving mesh fictitious domain approach for shape optimization problems." ESAIM: Mathematical Modelling and Numerical Analysis 34.1 (2010): 31-45. <http://eudml.org/doc/197532>.

@article{Mäkinen2010,

abstract = {
A new numerical method based on fictitious domain methods for shape
optimization problems governed by the Poisson equation is proposed.
The basic idea is to combine the boundary variation technique, in which
the mesh is moving during the optimization, and efficient fictitious
domain preconditioning in the solution of the (adjoint) state equations.
Neumann boundary value problems are solved using an algebraic fictitious
domain method. A mixed formulation based on boundary Lagrange
multipliers is used for Dirichlet boundary problems and the resulting
saddle-point problems are preconditioned with block diagonal fictitious
domain preconditioners. Under given assumptions on the meshes, these
preconditioners are shown to be optimal with respect to the condition
number. The numerical experiments demonstrate the efficiency of
the proposed approaches.
},

author = {Mäkinen, Raino A.E., Rossi, Tuomo, Toivanen, Jari},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Shape optimization; fictitious domain method; preconditioning;
boundary variation technique; sensitivity analysis.; fictitious domain methods; shape optimization; Poisson equation; boundary variation technique; Lagrange multipliers; saddle-point problems; numerical experiments},

language = {eng},

month = {3},

number = {1},

pages = {31-45},

publisher = {EDP Sciences},

title = {A moving mesh fictitious domain approach for shape optimization problems},

url = {http://eudml.org/doc/197532},

volume = {34},

year = {2010},

}

TY - JOUR

AU - Mäkinen, Raino A.E.

AU - Rossi, Tuomo

AU - Toivanen, Jari

TI - A moving mesh fictitious domain approach for shape optimization problems

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 34

IS - 1

SP - 31

EP - 45

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

LA - eng

KW - Shape optimization; fictitious domain method; preconditioning;
boundary variation technique; sensitivity analysis.; fictitious domain methods; shape optimization; Poisson equation; boundary variation technique; Lagrange multipliers; saddle-point problems; numerical experiments

UR - http://eudml.org/doc/197532

ER -

## References

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