Solving topology optimization problems using cellular automata and mortar finite element method

Currently topology optimization is widely used by engineers for different practical problems.  Researches by different authors offer algorithms of using cellular automata in these problems, and most recent publications introduce a mesh-refinement procedure to decrease numerical efforts.  In this article, we propose to apply a mortar finite element method for solving topology optimization problems using cellular automata.  This methodology enables us to handle the non-conforming meshes, which can arise in the refinement process.  We present a formulation of the algorithm and analyse its computational complexity by applying to a test problem.

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Mathematical Modeling and Computing, Vol. 7, No. 2, pp. 239–247 (2020)