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 55 articles )

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  1. Bespalov, Alex; Loghin, Daniel; Youngnoi, Rawin: Truncation preconditioners for stochastic Galerkin finite element discretizations (2021)
  2. Bespalov, Alex; Praetorius, Dirk; Ruggeri, Michele: Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin finite element method (2021)
  3. Bespalov, Alex; Rocchi, Leonardo; Silvester, David: T-IFISS: a toolbox for adaptive FEM computation (2021)
  4. Dai, Dihan; Epshteyn, Yekaterina; Narayan, Akil: Hyperbolicity-preserving and well-balanced stochastic Galerkin method for shallow water equations (2021)
  5. Donoghue, Geoff; Yano, Masayuki: Spatio-stochastic adaptive discontinuous Galerkin methods (2021)
  6. Khan, Arbaz; Bespalov, Alex; Powell, Catherine E.; Silvester, David J.: Robust a posteriori error estimation for parameter-dependent linear elasticity equations (2021)
  7. Khan, Arbaz; Powell, Catherine E.: Parameter-robust stochastic Galerkin mixed approximation for linear poroelasticity with uncertain inputs (2021)
  8. Bachmayr, Markus; Dahmen, Wolfgang: Adaptive low-rank approximations for operator equations: accuracy control and computational complexity (2020)
  9. Bespalov, Alex; Xu, Feng: A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case (2020)
  10. Bochmann, Maximilian; Kämmerer, Lutz; Potts, Daniel: A sparse FFT approach for ODE with random coefficients (2020)
  11. Dolgov, Sergey; Anaya-Izquierdo, Karim; Fox, Colin; Scheichl, Robert: Approximation and sampling of multivariate probability distributions in the tensor train decomposition (2020)
  12. Eigel, Martin; Marschall, Manuel; Multerer, Michael: An adaptive stochastic Galerkin tensor train discretization for randomly perturbed domains (2020)
  13. Eigel, Martin; Marschall, Manuel; Pfeffer, Max; Schneider, Reinhold: Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations (2020)
  14. Gerster, Stephan; Herty, Michael: Entropies and symmetrization of hyperbolic stochastic Galerkin formulations (2020)
  15. Khodadadian, Amirreza; Parvizi, Maryam; Heitzinger, Clemens: An adaptive multilevel Monte Carlo algorithm for the stochastic drift-diffusion-Poisson system (2020)
  16. Kubínová, Marie; Pultarová, Ivana: Block preconditioning of stochastic Galerkin problems: new two-sided guaranteed spectral bounds (2020)
  17. Uschmajew, André; Vandereycken, Bart: Geometric methods on low-rank matrix and tensor manifolds (2020)
  18. Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele: Convergence of adaptive stochastic Galerkin FEM (2019)
  19. Bespalov, Alex; Praetorius, Dirk; Rocchi, Leonardo; Ruggeri, Michele: Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs (2019)
  20. Crowder, Adam J.; Powell, Catherine E.; Bespalov, Alex: Efficient adaptive multilevel stochastic Galerkin approximation using implicit a posteriori error estimation (2019)

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