Face-based Selection of Corners in 3D Substructuring

In most recent substructuring methods, a fundamental role is played by the coarse space. For some of these methods (e.g. BDDC and FETI-DP), its definition relies on a 'minimal' set of coarse nodes (sometimes called corners) which assures invertibility of local subdomain problems and also of the global coarse problem. This basic set is typically enhanced by enforcing continuity of functions at some generalized degrees of freedom, such as average values on edges or faces of subdomains. We revisit existing algorithms for selection of corners. The main contribution of this paper consists of proposing a new heuristic algorithm for this purpose. Considering faces as the basic building blocks of the interface, inherent parallelism, and better robustness with respect to disconnected subdomains are among features of the new technique. The advantages of the presented algorithm in comparison to some earlier approaches are demonstrated on three engineering problems of structural analysis solved by the BDDC method.

Tomorrow's cities: a framework to assess urban resilience

Urbanisation is one of the great driving forces of the twenty-first century. Cities generate both productivity and creativity, and the benefits offered by high-density living and working contribute to sustainability. Cities comprise multiple components, forming both static and dynamic systems that are interconnected directly and indirectly on a number of levels. Bringing together large numbers of people within a complex system can lead to vulnerability from a wide range of hazards, threats and trends. The key to reducing this vulnerability is the identification of critical systems and determination of the implications of their failure and their interconnectivities with other systems. One emerging approach to these challenges focuses on building resilience – defined here as the degree to which a system can continue to function effectively in a changing environment. This paper puts forward a framework designed to help engineers, planners and designers to support cities in understanding the hazards, threats and trends that can make them vulnerable, and identify focus areas for building resilience into the systems, which allow it to function and prosper. Four case studies of cities whose resilience was tested by recent extreme weather events are presented, seeking to demonstrate the application of the proposed framework.