Solving three-dimensional layout optimization problems using fixed scale wavelets

The layout optimization problem in three-dimensional elasticity is solved with a meshless, wavelet-based solution scheme. A fictitious domain approach is used to embed the design domain into a simple regular domain. The material distribution and displacement field are discretized over the fictitious domain using fixed-scale, shift-invariant wavelet expansions. A discrete form of the elasticity problem is solved using a wavelet-Galerkin technique during each iteration of the layout optimization sequence. Approximate solutions are found with an efficient preconditioned conjugate gradient (PCG) solver using non-diagonal preconditioners which lead to convergence rates that are insensitive to the level of resolution. The convergence and memory management properties of the PCG algorithm make the analysis of large-scale problems possible. Several wavelet-based layout optimization examples are included.