Domain decomposition of finite element models using dijkstra’s algorithm

The paper proposes an algorithm for decomposing regions of a finite element model (FEM) for the integration of unified cellular structures in the design of lightweight parts. In this algorithm, the considered FEM region is represented as a graph for the purpose of decomposition. Based on this graph, the procedure for identifying break points and the criteria for splitting FEM regions at narrowed areas are described. The use of Dijkstra’s algorithm is justified for determining the weights of vertices located in constricted regions of the FEM. An example of the algorithm’s operation is provided, demonstrating its applicability in the design of lightweight parts with cellular structures.

1. Polozkov Yu.V. Problems of design and shaping of lightweight parts in additive manufacturing. Mathematical Methods in Engineering and Technology: proceedings of the International Scientific Conference, Minsk, October 10–12, 2017. St. Petersburg; 2017. Vol. 10. pp. 61–65 (in Russian).

2. Kovaleva I.L., Makanov D.V., Polozkov Yu.V. Clustering of subdomains for the integration of cellular structures into monolithic parts. Innovative Technologies, automation and mechatronics in mechanical and instrument engineering: proceedings of the XI International scientific and practical conference, April 5, 2023. Minsk; 2023. pp. 64–65 (in Russian). Available at: https://rep.bntu.by/handle/data/142244 (accessed 01.10.2025).

3. Prihozhy A.A., Karasik O.N. Competing all–pairs shortest paths algorithms for sparse / dense graphs: implementation and comparison. System analysis and applied information science. 2024;4:4–12 (in Russian). https://doi.org/10.21122/2309-4923-2024-4-4-12.