The Generalized Multiscale Finite Element Method (GMsFEM) is an advanced computational technique designed to efficiently solve complex multiscale problems in various fields such as engineering and applied sciences. GMsFEM enhances the traditional finite element method by incorporating detailed fine-scale information into a coarser-scale model. This is achieved through the construction of local basis functions that capture essential fine-scale features, enabling accurate simulations without the prohibitive computational cost of resolving all scales directly. GMsFEM is particularly useful for applications involving heterogeneous materials and porous media, where accurate representation of multiple scales is essential. By effectively bridging the gap between microscopic and macroscopic phenomena, GMsFEM provides a robust framework for improving the accuracy and efficiency of numerical simulations in multiscale modeling.
Simple GMsFEM examples (under construction): GMsFEM from scracth in Julia