Single scale wavelet approximations in layout optimization

The standard structural layout optimization problem in 2D elasticity is sol ved using a wavelet based discretization of the displacement field and of t he spatial distribution of material. A fictitious domain approach is used t o embed the original design domain within a simpler domain of regular geome try. A Galerkin method is used to derive discretized equations, which are s olved iteratively using a preconditioned conjugate gradient algorithm. A sp ecial preconditioner is derived for this purpose. The method is shown to co nverge at rates that are essentially independent of discretization size, an advantage over standard finite element methods, whose convergence rate dec ays as the mesh is refined. This new approach may replace finite element me thods in very large scale problems, where a very fine resolution of the sha pe is needed. The derivation and examples focus on 2D-problems but extensio ns to 3D should involve only few changes in the essential features of the p rocedure.