Shape Optimizations of Metallic Sheets Using a Multigrid Approach

We present a novel multigrid approach for the shape optimizations of corrugated metallic sheets by using genetic algorithms (GAs) and the multilevel fast multipole algorithm (MLFMA). The overall mechanism is obtained by an efficient integration of GAs and MLFMA, while the optimizations are improved by applying multiple grids at different layers. We show that the multigrid approach provides more effective optimizations than the conventional no-grid optimizations that employ the discretization nodes directly. The multigrid optimizations become useful especially as the problem size grows and no-grid optimizations demonstrate poor performances.