The validity of the equivalent differential equation (also called modified equation or differential approximation) for representing shock solutions of high order schemes is investigated through a comparison of exact a...
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We present a novel method to tackle the multi-class classification problem with sparse grids and show how the computational procedure can be split into an Offline phase (pre-processing) and a very rapid Online phase. ...
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Classical Gaussian quadrature rules achieve exponential convergence for univariate functions that are infinitely smooth and where all derivatives are uniformly bounded. The aim of this paper is to construct generalize...
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In this work we propose novel algorithms for storing and evaluating sparse grid functions, operating on regular (not spatially adaptive), yet potentially dimensionally adaptive grid types. Besides regular sparse grids...
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In this contribution we show that it is possible to get the macroscopic fluid equations of a lattice Boltzmann scheme with an external force using the Taylor expansion method. We validate this general expansion by a d...
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We investigate the stochastic collocation method for parametric, elliptic partial differential equations (PDEs) with lognormally distributed random parameters in mixed formulation. Such problems arise, e.g., in uncert...
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Since "A combination technique for the solution of sparse grid problems" Griebel et al. (1992), the sparse grid combination technique has been successfully employed to approximate sparse grid solutions of mu...
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