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A Quasi-optimal Sparse Grids Procedure for Groundwater Flows

  • Joakim Beck
  • Fabio Nobile
  • Lorenzo Tamellini
  • Raúl TemponeEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 95)

Abstract

In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work “On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods” to a Darcy problem where the permeability is modeled as a lognormal random field. We propose an explicit a-priori/a-posteriori procedure for the construction of such quasi-optimal grid and show its effectiveness on a numerical example. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution and an efficient nested quadrature rule with respect to the Gaussian weight.

Keywords

Interpolation Point Sparse Grid Permeability Field Polynomial Chaos Expansion Homogeneous Dirichlet Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The second and third authors have been supported by the Italian grant FIRB-IDEAS (Project n. RBID08223Z) “Advanced numerical techniques for uncertainty quantification in engineering and life science problems”. Support from the VR project “Effektiva numeriska metoder för stokastiska differentialekvationer med tillämpningar” and King Abdullah University of Science and Technology (KAUST) AEA project “Predictability and Uncertainty Quantification for Models of Porous Media” is also acknowledged. The fourth author is a member of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Joakim Beck
    • 1
  • Fabio Nobile
    • 2
    • 3
  • Lorenzo Tamellini
    • 2
    • 3
  • Raúl Tempone
    • 1
    Email author
  1. 1.Applied Mathematics and Computational ScienceKAUSTThuwalSaudi Arabia
  2. 2.CSQI – MATHICSEEcole Politechnique Fédérale LausanneLausanneSwitzerland
  3. 3.MOX, Department of Mathematics “F. Brioschi”Politecnico di MilanoMilanItaly

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