Technological advances have greatly improved our quality of life. However, they bring with them a
huge surge in energy requirements which in turn puts at risk our entire bio-sphere. It is of paramount
importance to predict these risks and to develop better solutions for the future. One of the central tasks is the accurate simulation of multiphase flow above and under ground. The risk analysis and uncertainty quantification, as well as the assimilation of data require statistical tools and efficient solvers for stochastic and deterministic PDEs as well as for the associated inverse problems.
The key features that make it extremely hard to predict these physical phenomena accurately are the multiple time and length scales that arise, as well as the lack of and uncertainty in data. Because of the highly varying scales involved, the resolution of all scales is currently impossible even on the largest supercomputers. While there is a fairly long history of empirically successful robust computational techniques for certain multiscale problems, the rigorous (numerical) analysis of such methods is of extremely high current interest.
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Introduction
The Householder Symposium XVIII on Numerical Linear Algebra was held on 12-17 June 2011, at the
Granlibakken Conference Center and Lodge in Tahoe City, California, on the northwest shore of Lake
Tahoe. The meeting was the eighteenth in a series, previously called the Gatlinburg Symposia. It was hosted by Lawrence Berkeley National Laboratory and was in cooperation with SIAM. At the meeting, the 14th Householder Award for the best thesis in numerical linear algebra since January 1, 2008 was presented.