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 26 articles )

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  1. Khan, Arbaz; Powell, Catherine E.; Silvester, David J.: Robust preconditioning for stochastic Galerkin formulations of parameter-dependent nearly incompressible elasticity equations (2019)
  2. Bespalov, Alex; Rocchi, Leonardo: Efficient adaptive algorithms for elliptic PDEs with random data (2018)
  3. Crowder, Adam J.; Powell, Catherine E.: CBS constants & their role in error estimation for stochastic Galerkin finite element methods (2018)
  4. Eigel, Martin; Marschall, Manuel; Schneider, Reinhold: Sampling-free Bayesian inversion with adaptive hierarchical tensor representations (2018)
  5. Guignard, Diane; Nobile, Fabio: A posteriori error estimation for the stochastic collocation finite element method (2018)
  6. Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch.: Large deformation shape uncertainty quantification in acoustic scattering (2018)
  7. Anker, Felix; Bayer, Christian; Eigel, Martin; Ladkau, Marcel; Neumann, Johannes; Schoenmakers, John: SDE based regression for linear random PDEs (2017)
  8. Ballani, Jonas; Kressner, Daniel; Peters, Michael D.: Multilevel tensor approximation of PDEs with random data (2017)
  9. Dölz, J.; Harbrecht, H.; Schwab, Ch.: Covariance regularity and (\mathcalH)-matrix approximation for rough random fields (2017)
  10. Eigel, Martin; Pfeffer, Max; Schneider, Reinhold: Adaptive stochastic Galerkin FEM with hierarchical tensor representations (2017)
  11. Newsum, Craig J.; Powell, Catherine E.: Efficient reduced basis methods for saddle point problems with applications in groundwater flow (2017)
  12. Powell, C. E.; Silvester, D.; Simoncini, V.: An efficient reduced basis solver for stochastic Galerkin matrix equations (2017)
  13. Rauhut, Holger; Schwab, Christoph: Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations (2017)
  14. Bachmayr, Markus; Schneider, Reinhold; Uschmajew, André: Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations (2016)
  15. Bespalov, Alex; Silvester, David: Efficient adaptive stochastic Galerkin methods for parametric operator equations (2016)
  16. Eigel, Martin; Merdon, Christian: Local equilibration error estimators for guaranteed error control in adaptive stochastic higher-order Galerkin finite element methods (2016)
  17. Eigel, Martin; Merdon, Christian; Neumann, Johannes: An adaptive multilevel Monte Carlo method with stochastic bounds for quantities of interest with uncertain data (2016)
  18. Guignard, Diane; Nobile, Fabio; Picasso, Marco: A posteriori error estimation for elliptic partial differential equations with small uncertainties (2016)
  19. Hall, Eric Joseph; Hoel, Håkon; Sandberg, Mattias; Szepessy, Anders; Tempone, Raúl: Computable error estimates for finite element approximations of elliptic partial differential equations with rough stochastic data (2016)
  20. Kunoth, Angela; Schwab, Christoph: Sparse adaptive tensor Galerkin approximations of stochastic PDE-constrained control problems (2016)

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