Clustering solver for displacement-based numerical homogenization

Based on strain-clustering via k-means, we decompose computational domain into clusters of possibly disjoint cells. Assuming cells in each cluster take the same strain, we reconstruct displacement field. We further propose a new way to condensate the governing equations of displacement-based finite element method to reduce the complexity while maintain the accuracy. Numerical examples are presented to illustrate the efficiency of the clustering solver. Numerical convergence studies are performed for the examples. Avoiding complexities which is common in existing clustering analysis methods, the proposed clustering solver is easy to implement, particularly for numerical homogenization using commercial softwares.