A fast algorithm for particle simulations
Journal of Computational Physics
Multiwavelets for Second-Kind Integral Equations
SIAM Journal on Numerical Analysis
Composite wavelet bases for operator equations
Mathematics of Computation
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Etude de Problème d'Optimal Design
Proceedings of the 7th IFIP Conference on Optimization Techniques: Modeling and Optimization in the Service of Man, Part 2
Computational Optimization and Applications
Wavelet Galerkin Schemes for Boundary Integral Equations---Implementation and Quadrature
SIAM Journal on Scientific Computing
Compression Techniques for Boundary Integral Equations---Asymptotically Optimal Complexity Estimates
SIAM Journal on Numerical Analysis
Efficient treatment of stationary free boundary problems
Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
On Convergence in Elliptic Shape Optimization
SIAM Journal on Control and Optimization
A new fictitious domain method in shape optimization
Computational Optimization and Applications
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The present paper is dedicated to the verification of sufficient second order conditions for shape optimization problems that arise from stationary free boundary problems. We assume that the state satisfies the Dirichlet problem for the Poisson equation and track the Neumann data at the free boundary. The gradient and Hessian of the shape functional under consideration are computed. By analyzing the shape Hessian in case of matching data a sufficient criterion for its strict coercivity is derived. Strict coercivity implies stable minimizers and, in case of a Ritz-Galerkin method, existence and convergence of approximate shapes. By a fast boundary element method we realize an efficient numerical algorithm to solve the free boundary problem. Numerical experiments are carried out in three spatial dimensions.