Advancements in Etherodimensional Coupling: Exploring Reduced Lagrange Multipliers and Reduced Distributed Lagrange Multipliers Methods
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We discuss novel advancements in etherodimensional coupling through the exploration of Reduced Lagrange Multipliers (RLM) and Reduced Distributed Lagrange Multipliers (RDLM) methods. Complex multiphysics problems often involve the interaction between two or more phases that have different intrinsic dimensions. The RLM and RDLM methods provide a way to define in a systematic and mathematically consistent way the coupling across etherogeneous dimensions, and to solve the resulting coupled problem in a computationally efficient way. The RLM and RDLM methods streamline the Lagrange multipliers and the distributed Lagrange multipliers approaches by introducing a geometrically reduced order model, significantly enhancing computational efficiency while maintaining accuracy. This method is particularly beneficial for problems where the interface dynamics are complex but can be effectively captured by a lower-dimensional representation. Our presentation will outline the theoretical frameworks of these methods, complemented by detailed algorithmic overviews and computational analyses. Practical applications in numerical simulations will be highlighted, showcasing the effectiveness of RLM and RDLM.
