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)