Localized Model Reduction for Parametric PDEs

Abstract

This thesis develops a method for approximately solving a parametric diffusion equation by combining techniques from local model order reduction and the reduced basis greedy method. The approach relies on partitioning the domain into subdomains where local approximation spaces can be constructed and later combined. The unknown boundary conditions on the local subdomains are handled with a boundary-to-interior mapping and an extended subdomain. A reduced basis greedy algorithm is used for the parameter dependence of the problem. Each approximation step is accompanied by error analysis. Numerical results show convergence of the error in agreement with the theoretical predictions.