Multigrid Accelerated Cellular Automata for Structural Design Optimization: A 1-D Implementation
Mostafa Abdalla, Sunwook Kim, Zafer Gürdal · 2004
Multigrid acceleration [1] is typically used for the iterative solution of partial differential equations in sciences and engineering. A typical implementation utilizes a base discretization, such as a finite element or a finite difference grid, and a set of successively coarser grids that is used for accelerating the convergence of the iterative solution on the base grid. The present work extends the use of the Multigrid acceleration to the design optimization of a sample structural system consisting of a 1-D beam, and demonstrates it within the context of recently introduced numerical analysis and design scheme based on the Cellular Automata (CA) paradigm [2]. Within the design context, the Multigrid scheme is not only used to accelerate the analysis iterations, but is also used to help refine the design across multiple grid levels to accelerate the overall design convergence.