News and recent events

  • PhD opportunity: Adaptivity and machine learning techniques for PDE problems with uncertain inputs.
  • New preprint: together with Daniel Loghin and Rawin Youngnoi we have introduced and analysed a new class of preconditioners for stochastic Galerkin discretisations of parametric elliptic PDEs. We call them truncation preconditioners.
    Preprint on arXiv
  • New preprint: together with Dirk Praetorius and Michele Ruggeri we have analysed a novel a posteriori error estimator for multilevel stochastic Galerkin approximations. We have also proposed, implemented, and empirically compared three adaptive algorithms driven by this error estimator for solving elliptic PDEs with parametric or uncertain inputs.
    Preprint on arXiv
  • 12 February 2020: Carolina Urzua Torres (University of Oxford) visited us and gave a talk at the Optimisation & Numerical Analysis Seminar.
  • 30 January 2020: Kody Law (The University of Manchester) visited us and gave a talk at the Applied Mathematics Seminar.
  • January 2020: research visit by Michele Ruggeri (Vienna University of Technology).
  • 14 November 2019: Gabriel Barrenechea (University of Strathclyde) visited us and gave a talk at the Applied Mathematics Seminar.
  • September 2019: speaking at the RMMM 2019 conference in Vienna; visiting the research group of Dirk Praetorius at Vienna University of Technology.
  • New preprint: together with Leonardo Rocchi and David Silvester we wrote a short review paper about T-IFISS - a MATLAB toolbox for studying adaptive finite element solution algorithms for deterministic and parametric elliptic PDEs. (To appear in a special issue of Comput. Math. Appl.)
    Link to the paper      Preprint on arXiv
  • June 2019: attending two remarkable conferences, MAFELAP 2019 at Brunel University (Uxbridge, UK) and the Biennial Numerical Analysis Conference at the University of Strathclyde (Glasgow, UK).
  • May 2019: congratulations to Leonardo Rocchi who has successfully defended his PhD Thesis "Adaptive algorithms for partial differential equations with parametric uncertainty".
  • 25-26 April 2019: together with Daniel Loghin and Kris van der Zee we organised the workshop "Scientific computation using machine-learning algorithms: recent mathematical advances and applications" at the University of Nottingham.
  • New preprint: in a joint work with Feng Xu, we have proposed and numerically tested an adaptive algorithm for the numerical solution of elliptic PDE problems with non-affine parametric representation of coefficients. (Published in Comput. Math. Appl.)
    Link to the paper      Preprint on arXiv
  • Software update: the latest update to Stochastic T-IFISS has been released to include the recently developed novel a posteriori error estimation techniques and adaptive algorithms for computing stochastic Galerkin approximations of steady-state diffusion problems with parametric uncertainty in coefficients.
    Link to the software
  • New preprint: together with Dirk Praetorius, Leonardo Rocchi and Michele Ruggeri we have performed convergence analysis of adaptive stochastic Galerkin FEM applied to elliptic PDEs with parametric or uncertain inputs. (Published in SIAM J. Numer. Anal.)
    Link to the paper      Preprint on arXiv
  • New preprint: together with Arbaz Khan, Catherine Powell, and David Silvester we have performed a posteriori error analysis of stochastic Galerkin approximations for parameter-dependent linear elasticity equations. In addition, we have developed an adaptive algorithm that employs proxies for the error reduction associated with certain enrichments of approximations spaces. (To appear in Math. Comp.)
    Preprint on arXiv
  • 24-26 September 2018: giving a talk at the Chemnitz FEM Symposium 2018 (Chemnitz, Germany).
  • September 2018: visiting Vienna University of Technology (TU Wien) to collaborate with Dirk Praetorius and his research group.
  • New preprint: in a joint work with Timo Betcke, Alexander Haberl, and Dirk Praetorius, we have proposed an adaptive mesh-refinement algorithm for numerical solution of the boundary integral formulations of the Helmholtz equations in 2D and 3D. We have proved that the associated adaptive boundary element method converges with optimal algebraic rates.
    (Published in Comput. Methods Appl. Mech. Engrg.)
    Link to the paper      Preprint on arXiv
  • 28-29 June 2018: research visit by Michele Ruggeri (University of Vienna).
  • New preprint: together with Dirk Praetorius, Leonardo Rocchi and Michele Ruggeri we have designed and implemented an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to elliptic PDEs with parametric or uncertain inputs. Our adaptive refinement strategy employs the error reduction indicators computed for spatial and parametric components of the primal and dual solutions. (Published in Comput. Methods Appl. Mech. Engrg.)
    Link to the paper      Preprint on arXiv
  • April - May 2018: participating in the Scientific Programme "Uncertainty quantification for complex systems: theory and methodologies" at the Isaac Newton Institute for Mathematical Sciences in Cambridge.
  • March 2018: research visit to Vienna University of Technology (TU Wien) to collaborate with Dirk Praetorius and his research group.
  • 14-15 February 2018: Martin Eigel (WIAS, Berlin) visited us and gave a talk at the Optimisation and Numerical Analysis Seminar.