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

作者：Maier I; Haasdonk B^*

来源：Applied Numerical Mathematics, 2014, 78: 31-48.

DOI：10.1016/j.apnum.2013.12.001

• Reduced basis method
• Model reduction
• Domain decomposition
• Iterative methods
• Dirichlet-Neumann coupling

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%26apos;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.

• 出版日期2014-4