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Focal Report 5: Using Scenarios to Assess Risks
(2012)CSS Risk and Resilience ReportsThis report aims to shed some light on the interrelationship between (different types of) scenarios and risk assessment by looking more closely at risk management approaches in Denmark, the Netherlands, Germany and the United Kingdom. In turn, it aims to develop a more nuanced understanding of the value and limits of scenarios in risk assessment.Report -
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Dispersion Analysis of Plane Wave Discontinuous Galerkin Methods
(2012)Research ReportThe plane wave discontinuous Galerkin (PWDG) method for the Helmholtz equation was introduced and analyzed in [Gittelson, C., Hiptmair, R., and Perugia, I. Plane wave discontinuous Galerkin methods: Analysis of the h-version. Math. Model. Numer. Anal. 43 (2009), 297–331] as a generalization of the so-called ultra-weak variational formulation, see [O. Cessenat and B. Despr´es, Application of an ultra weak variational formulation of elliptic ...Report -
On the road between robust optimization and the scenario approach for chance constrained optimization problems
(2012)Report Institute of Automatic Control, ETH ZürichWe propose a new method for solving chance constrained optimization problems which lies between robust (or worst-case) optimization and scenario-based methods. Our method does not require prior knowledge of the underlying probability distribution as in standard robust optimization methods, nor is it based entirely on randomization as in the scenario approach. It instead involves solving a robust optimization problem with bounded uncertainty, ...Report -
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Experiments on steel columns under fire conditions
(2012)IBK BerichtMaterial and structural stability behaviour at elevated temperatures are key considerations for structural fire safety. This report describes experimental results of material coupon as well as structural stub and slender column furnace tests on carbon steel specimens at elevated temperatures. The tests were executed at the Technical University of Darmstadt, Germany, and at the ETH Zurich, Switzerland. The report is organized into eight ...Report -
Multilevel Monte-Carlo front tracking for random scalar conservation laws
(2012)SAM Research ReportWe consider random scalar hyperbolic conservation laws (RSCLs) in spatial dimension $d\ge 1$ with bounded random flux functions which are $\mathbb{P}$-a.s. Lipschitz continuous with respect to the state variable, for which there exists a unique random entropy solution (i.e., a measurable mapping from the probability space into $C(0,T;L^1(\mathbb{R}^d))$ with finite second moments). We present a convergence analysis of a Multi-Level ...Report -
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Geometric multiscale decompositions of dynamic low-rank matrices
(2012)SAM Research ReportThe present paper is concerned with the study of manifold-valued multiscale transforms with a focus on the Stiefel manifold. For this specific geometry we derive several formulas and algorithms for the computation of geometric means which will later enable us to construct multiscale transforms of wavelet type. As an application we study compression of piecewise smooth families of low-rank matrices both for synthetic data and also real-world ...Report