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A moving mesh fictitious domain approach for shape optimization problems. (English) Zbl 0948.65064
The authors propose a numerical method based on fictitious domain methods for shape optimization problems governed by the Poisson equation. The basic idea of the method 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 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. The numerical experiments demonstrate the efficiency of the proposed approaches.
MSC:
65K10Optimization techniques (numerical methods)
49J20Optimal control problems with PDE (existence)
49M29Methods involving duality in calculus of variations