Pipeline Implementation of Cellular Automata for Structural Design on Message-Passing Multiprocessors

The inherent structure of cellular automata is trivially parallelizable and can directly benefit from massively parallel machines in computationally intensive problems. This paper presents both synchronous and pipeline parallel implementations of cellular automata on distributed memory (message-passing) architectures. A structural design problem is considered to study the performance of the various cellular automata implementations. The synchronous parallel implementation is a mixture of Jacobi and Gauss-Seidel style iteration, where it is more Jacobi like as the number of processors increase. Therefore, it exhibits divergence because of the mathematical characteristics of Jacobi matrix iteration for the structural problem as the number of processors increases. The proposed pipeline implementation preserves convergence by simulating a pure Gauss-Seidel iteration. Numerical results for analysis and design of a cantilever plate made of composite material show that the pipeline update scheme is convergent and successfully generates optimal designs.