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Higher-order convex approximations of Young measures in optimal control
(2001)FIM's preprintsReport -
Multilevel higher order Quasi-Monte Carlo Bayesian Estimation
(2016)Research reports / Seminar for Applied MathematicsReport -
Numerical approximation of statistical solutions of incompressible flow
(2015)Research ReportWe present a finite difference-(Multi-level) Monte Carlo algorithm to efficiently compute statistical solutions of the two dimensional Navier-Stokes equations, with periodic bound- ary conditions and for arbitrarily high Reynolds number. We propose a reformulation of statistical solutions in the vorticity-stream function form. The vorticity-stream function for- mulation is discretized with a finite difference scheme. We obtain a convergence ...Report -
Sparse wavelet methods for option pricing under stochastic volatility
(2004)Research ReportReport -
Electromagnetic Wave Scattering by Random Surfaces: Shape Holomorphy
(2016)Research reports / Seminar for Applied MathematicsReport -
QMC integration for lognormal-parametric, elliptic PDEs: local supports imply product weights.
(2016)Research reports / Seminar for Applied MathematicsReport -
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Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs
(2011)Research ReportsThe numerical approximation of parametric partial differential equations is a computational challenge, in particular when the number of involved parameter is large. This paper considers a model class of second order, linear, parametric, elliptic PDEs on a bounded domain D with diffusion coefficients depending on the parameters in an affine manner. For such models, it was shown in [11, 12] that under very weak assumptions on the diffusion ...Report -
Multi-Level Monte Carlo Finite Volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium
(2014)Research ReportWe consider the very challenging problem of efficient uncertainty quantification for acoustic wave propagation in a highly heterogeneous, possibly layered, random medium, characterized by possibly anisotropic, piecewise log-exponentially distributed Gaussian random fields. A multi-level Monte Carlo finite volume method is proposed, along with a novel, bias-free upscaling technique that allows to represent the input random fields, generated ...Report