An Online Efficient Two-Scale Reduced Basis Approach for the Localized Orthogonal Decomposition

We are concerned with employing Model Order Reduction (MOR) to efficiently solve parameterized multiscale problems using the Localized Orthogonal Decomposition (LOD) method. Like many methods, LOD follows idea of separating problem into localized fine-scale subproblems and an effective coarse-scale system derived from solutions local problems. While Reduced Basis (RB) method has already been used speed up solution problems, resulting coarse remained untouched, thus limiting achievable up. In this work we address issue by applying RB methodology a new two-scale formulation LOD. By reducing entire system, (TSRBLOD) approach, yields reduced order models that completely independent size mesh allowing efficient approximation even for very large domains. A rigorous posteriori estimator bounds model reduction error, taking account error both global system.