For large-scale applications modelled as Partial Differential Equations (PDEs) there is an increasing need to solve problems expressed in terms of equilibria with constraints. For many of these problems, optimization methods that mimic geometric considerations (e.g. in contact mechanics), thus preserving feasibility by ensuring that iterates remain on the constraint manifold, are particularly attractive. PDE constrained optimization has a strong impact on various engineering and scientific applications (e.g. automotive and aerospace industries, chemical processing, material science, biotechnology, etc.). In turn, these applications lead to many exciting research problems for which the appropriate mathematical treatment and the development of robust and efficient solution strategies requires the integration of tools from several mathematical subdisciplines (e.g. the theory of optimization and optimal control in a functional analytic setting, the theory of PDEs, numerical analysis, and scientific computing). A particular class of PDE constrained optimization problems with many important practical applications arises in structural mechanics, where there is a general need for more mathematically rigorous and numerically accurate computational strategies. In this talk, I will present an adaptive multi-scale approach for the computational modelling of large-scale dynamic structures assembled from linear-elastic bodies in mutual contact with friction. The adaptive multi-scale approach enables us to carry out simulations at a complexity normally associated with the cost of modelling the entire structure by a simple continuum model whilst incorporating small scale effects, such as openings of gaps and slippage between individual components, using a systematic and locally optimal criterion. Comparisons of the numerical results with data from experimental tests and from practical observations illustrate the capability of the multi-scale algorithm in predicting the behaviour of large-scale masonry structures.
Current 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996