Convergence analysis for cellular automata applied to truss design

Abstract

Traditional parallel methods for structural design, as well as modern preconditioned iterative linear solvers, do not scale well. This paper discusses the application of massively scalable cellular automata (CA) techniques to structural design, specifically trusses. There are two sets of CA rules, one used to propagate stresses and strains, and one to perform design updates. These rules can be applied serially, periodically, or concurrently, and Jacobi or Gauss‐Seidel style updating can be done. These options are compared with respect to convergence, speed, and stability for an example, problem of combined sizing and topology design of truss domain structures. The central theme of the paper is that the cellular automaton paradigm is tantamount to classical block Jacobi or block Gauss‐Seidel iteration, and consequently the performance of a cellular automaton can be rigorously analyzed and predicted.