ALEA

ALEA - a python framework for spectral methods and low-rank approximations in uncertainty quantification. ALEA is intended as a research framework for numerical methods in Uncertainty Quantification (UQ). Its emphasis lies on: generalised polynomial chaos (gpc) methods; stochastic Galerkin FEM; adaptive numerical methods; tensor methods for UQ. Most of these areas are work in progress. The provided functionality will be extended gradually and demonstrated in related articles. The framework is written in python and uses FEniCS as its default FEM backend.


References in zbMATH (referenced in 42 articles )

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  1. Bespalov, Alex; Xu, Feng: A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case (2020)
  2. Dolgov, Sergey; Anaya-Izquierdo, Karim; Fox, Colin; Scheichl, Robert: Approximation and sampling of multivariate probability distributions in the tensor train decomposition (2020)
  3. Eigel, Martin; Marschall, Manuel; Multerer, Michael: An adaptive stochastic Galerkin tensor train discretization for randomly perturbed domains (2020)
  4. Eigel, Martin; Marschall, Manuel; Pfeffer, Max; Schneider, Reinhold: Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations (2020)
  5. Kubínová, Marie; Pultarová, Ivana: Block preconditioning of stochastic Galerkin problems: new two-sided guaranteed spectral bounds (2020)
  6. Uschmajew, André; Vandereycken, Bart: Geometric methods on low-rank matrix and tensor manifolds (2020)
  7. Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele: Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs (2019)
  8. Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele: Convergence of adaptive stochastic Galerkin FEM (2019)
  9. Crowder, Adam J.; Powell, Catherine E.; Bespalov, Alex: Efficient adaptive multilevel stochastic Galerkin approximation using implicit a posteriori error estimation (2019)
  10. Dolgov, Sergey; Scheichl, Robert: A hybrid alternating least squares-TT-cross algorithm for parametric PDEs (2019)
  11. Eigel, Martin; Neumann, Johannes; Schneider, Reinhold; Wolf, Sebastian: Non-intrusive tensor reconstruction for high-dimensional random PDEs (2019)
  12. Eigel, Martin; Schneider, Reinhold; Trunschke, Philipp; Wolf, Sebastian: Variational Monte Carlo -- bridging concepts of machine learning and high-dimensional partial differential equations (2019)
  13. Khan, Arbaz; Powell, Catherine E.; Silvester, David J.: Robust preconditioning for stochastic Galerkin formulations of parameter-dependent nearly incompressible elasticity equations (2019)
  14. Müller, Christopher; Ullmann, Sebastian; Lang, Jens: A Bramble-Pasciak conjugate gradient method for discrete Stokes equations with random viscosity (2019)
  15. Bespalov, Alex; Rocchi, Leonardo: Efficient adaptive algorithms for elliptic PDEs with random data (2018)
  16. Crowder, Adam J.; Powell, Catherine E.: CBS constants & their role in error estimation for stochastic Galerkin finite element methods (2018)
  17. Eigel, Martin; Marschall, Manuel; Schneider, Reinhold: Sampling-free Bayesian inversion with adaptive hierarchical tensor representations (2018)
  18. Guignard, Diane; Nobile, Fabio: A posteriori error estimation for the stochastic collocation finite element method (2018)
  19. Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch.: Large deformation shape uncertainty quantification in acoustic scattering (2018)
  20. Anker, Felix; Bayer, Christian; Eigel, Martin; Ladkau, Marcel; Neumann, Johannes; Schoenmakers, John: SDE based regression for linear random PDEs (2017)

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