Theory of sparse grid interpolation

Basic explenations on sparse grid interpolation are coming soon.

In the meantime, you can check the following publications by the author of this package and collaborators:

  • A Peer-review paper on the adaptive sparse grid-finite elements approximation of the random diffusion Poisson problem: [FS21];

  • A preprint on the approximation of the Stochastic Landau-Lifshitz-Gilbert problem with a-priori determined sparse grid and rates of convergence: [ADF+24]. The sparse grid (equivalently, the multi-index set) of the interpolant is determined based on a general theory we developed to analyze the regularity of nonlinear parametric PDEs with Gaussian noise;

  • The (soon to be published) PhD thesis, which comprises the previous two papers, some theoretical extensions, and more comments on SGMethods: [Sca24].

References

[ADF+24]

Xin An, Josef Dick, Michael Feischl, Andrea Scaglioni, and Thanh Tran. Sparse grid approximation of nolinear SPDEs: the Landau–Lifshitz–Gilbert equation. 2024. Under review. arXiv:2310.11225.

[FS21]

Michael Feischl and Andrea Scaglioni. Convergence of adaptive stochastic collocation with finite elements. Comput. Math. Appl., 98:139–156, 2021. URL: https://doi.org/10.1016/j.camwa.2021.07.001, doi:10.1016/j.camwa.2021.07.001.

[Sca24]

Andrea Scaglioni. Sparse grid approximation of stochastic PDEs: Adaptivity and approximation of the stochastic Landau–Lifshitz–Gilbert equation. PhD thesis, TU Wien, 2024. Soon to appear.