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Titlebook: Sparse Grids and Applications - Miami 2016; Jochen Garcke,Dirk Pflüger,Guannan Zhang Conference proceedings 2018 Springer International Pu

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Scalable Algorithmic Detection of Silent Data Corruption for High-Dimensional PDEs, large errors are always detected, and the small errors that go undetected do not noticeably damage the solution. We also carry out scalability tests for a 5D scenario. We finally discuss how to deal with false positives and how to extend these ideas to more general quantities of interest.
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Conference proceedings 2018discretization scheme. The articles present recent advances in the numerical analysis of sparse grids in connection with a range of applications including computational chemistry, computational fluid dynamics, and big data analytics, to name but a few..
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1439-7358 numerical discretization scheme. The articles present recent advances in the numerical analysis of sparse grids in connection with a range of applications including computational chemistry, computational fluid dynamics, and big data analytics, to name but a few..978-3-030-09227-6978-3-319-75426-0Series ISSN 1439-7358 Series E-ISSN 2197-7100
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Comparing Nested Sequences of Leja and PseudoGauss Points to Interpolate in 1D and Solve the SchroeudoGauss points. PseudoGauss points are also nested. They are chosen to improve the accuracy of the Gram matrix. With both Leja and PseudoGauss points it is possible to add one point per level. We also compare Lebesgue constants for weighted Leja and PseudoGauss points.
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Sparse Grid Quadrature Rules Based on Conformal Mappings,rid setting, and we show that in certain settings, the convergence improvement can be exponential with growing dimension. Numerical examples demonstrate the benefits and drawbacks of the approach, as predicted by the theory.
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