Update-grid reanalysis method based on NS-FEM for 3D heat transfer problems

Repeated modifications and iterative recalculations cost a great amount of computation time in the structural design process. Reanalysis is an efficient computational method that can ensure the accuracy of a solution in place of repeated full finite element analysis (FEA) and other numerical methods. In this study, an update-grid (UG) reanalysis (UGR) method is suggested to analyse three-dimensional (3D) heat transfer problems. Compared with other reanalysis methods, the suggested method easily establishes a mapping between initial meshes and modified meshes using the mapping relationship. Generally, a modified structure can be reanalysed by directly reusing transfer operators from the UR analysis. Therefore, the modified meshes can be solved by constructing a map from the initial meshes, even if the model is totally re-meshed. Moreover, considering the accuracy of the analysis, a node-based smoothed finite element method (NS-FEM) is used as the main solver. To evaluate the performance of the suggested method, several heat transfer problems are investigated. The results demonstrate that the UGR method is more accurate and efficient compared with the popular multi-grid (MG) preconditioned conjugate gradient (PCG) method.