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An A Priori Error Estimate for Interior Penalty Discretizations of the Curl-Curl Operator on Non-Conforming Meshes
(2014)Research ReportReport -
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Efficient computation of all speed flows using an entropy stable shock-capturing space-time discontinuous Galerkin method
(2014)Research ReportWe present a shock-capturing space-time Discontinuous Galerkin method to approximate all speed flows modeled by systems of conservation laws with multiple time scales. The method provides a very general and computationally efficient framework for approximating such systems on account of its ability to incorporate large time steps. Numerical examples ranging from computing the incompressible limit (robustness with respect to Mach number) ...Report -
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Isolated Execution on Many-core Architectures
(2014)We explore how many-core platforms can be used to enhance the security of future systems and to support important security properties such as runtime isolation using a small Trusted Computing Base (TCB). We focus on the Intel Single-chip Cloud Computer (SCC) to show that such properties can be implemented in current systems. We design a system called SEMA which offers strong security properties while maintaining high performance and ...Report -
Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients
(2014)SAM Research ReportStrong convergence rates for (temporal, spatial, and noise) numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the scientific literature. Weak convergence rates for numerical approximations of such SEEs have been investigated since about 11 years and are far away from being well understood: roughly speaking, no essentially sharp weak convergence rates ...Report -
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Multi-level Monte Carlo finite volume method for shallow water equations with uncertain parameters applied to landslides-generated tsunamis
(2014)SAM Research ReportTwo layer Savage-Hutter type shallow water PDEs model flows such as tsunamis generated by rockslides. On account of heterogeneities in the composition of the granular matter, these models contain uncertain parameters like the ratio of densities of layers, Coulomb and interlayer friction. These parameters are modeled statistically and quantifying the resulting solution uncertainty (UQ) is a crucial task in geophysics. We propose a novel ...Report