In this article, we analyse the accuracy and computational complexity of estimators for expected functionals of the solution to multi-dimensional parabolic stochastic partial differential equations (SPDE) of Zakai-typ...
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In many contexts it is necessary to determine coefficients of a basis expansion of a function f(x1, …, xD) from values of the function at points on a sparse grid. Knowing the coefficients, one has an interpolant or a...
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Sparse grids enable accurate function approximation in higher-dimensional settings with a moderate number of grid points. In this paper, we introduce generalized versions of various efficient sparse grid algorithms in...
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Runaway electrons (RE) generated during magnetic disruptions present a major threat to the safe operation of plasma nuclear fusion reactors. A critical aspect of understanding RE dynamics is to calculate the runaway p...
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B-splines on sparse grids are a versatile method for higher-dimensional approximation, especially in smooth settings or if gradient information is advantageous. With increasing dimension, grid points on the boundary b...
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Accurate modeling of contamination in subsurface flow and water aquifers is crucial for agriculture and environmental protection. Here, we demonstrate a parallel algorithm to quantify the propagation of uncertainty in...
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In this work we present a residual based a posteriori error estimation for a heat equation with a random forcing term and a random diffusion coefficient which is assumed to depend affinely on a finite number of indepe...
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Coupled cluster theory provides hierarchical many-particle models and is presently considered as the ultimate benchmark in quantum chemistry. Despite its practical significance, a rigorous mathematical analysis of cou...
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In (Griebel and Hamaekers, Fast discrete Fourier transform on generalized sparse grids, Sparse grids and Applications, volume 97 of lecturenotes in computationalscience and engineering, pages 75–108, Springer, 2014...
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This work is a follow-up to our previous contribution ("Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic PDEs)", SIAM J. Numer. Anal.,...
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