Multigrid Accelerated Cellular Automata for Structural Optimization: A 1-D Implementation
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Multigrid acceleration is typically used for the iterative solution of partial differential equations in physics and engineering. A typical multigrid implementation uses a base discretization method, such as finite elements or finite differences, and a set of successively coarser grids that is used for accelerating the convergence of the iterative solution on the base grid. The presented thesis extends the use of multigrid acceleration to the design optimization of a sample structural system and demonstrates it within the context of the recently introduced Cellular Automata paradigm for design optimization. Within the design context, the multigrid scheme is not only used for accelerating the analysis iterations, but is also used to help refine the design across multiple grid levels to accelerate the design convergence. A comparison of computational efficiencies achieved by different multigrid implementations, including the multigrid accelerated nested design iteration scheme, is presented. The method is described in its generic form which can be applicable not only to the Cellular Automata paradigm but also to more general finite element analysis based design schemes as well.
- Masters Theses