Reduced basis methods for heterogeneous domain decomposition


Thursday, 22 May, 2014 - 11:30

Speaker: Immanuel Maier (Stuttgart University)

Room: SISSA - Santorio A - room 133

Heterogeneous domain decomposition problems are constituted by differential equations of dierent types on different subdomains of the computational domain and their coupling on the interface between those subdomains. Such problems arise for example in environmental science, biology or food technologies. A classical example is the modelling of groundwater flow, where the distinction of free flow and flow through permeable material leads to a coupled system of the Stokes equation and the porous media equation. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-stage the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-stage as well as the accuracy of the reduced coupled system. We demonstrate the efficiency of the approach by numerical experiments dealing with groundwater flow scenarios.