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 block synchronous and block pipeline (with asynchronous message passing) 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 becomes more Jacobi like as the number of processors increases. Therefore, it exhibits divergence because of the mathematical characteristics of Jacobi iteration matrix for the structural problem as the number of processors increases. The proposed pipeline implementation preserves convergence by simulating a pure Gauss-Seidel style row-wise 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.