A Dirichlet-Neumann reduced basis method for homogeneous domain decomposition problems

摘要

Reduced basis methods allow efficient model reduction of parametrized partial differential equations. In the current paper, we consider a reduced basis method based on an iterative Dirichlet-Neumann coupling for homogeneous domain decomposition of elliptic PDE's. We gain very small basis sizes by an efficient treatment of problems with a-priori known geometry. Moreover iterative schemes may offer advantages over other approaches in the context of parallelization. We prove convergence of the iterative reduced scheme, derive rigorous a-posteriori error bounds and provide a full offline/online decomposition. Different methods for basis generation are investigated, in particular a variant of the POD-Greedy procedure. Experiments confirm the rigor of the error estimators and identify beneficial basis construction procedures.