News and recent events

New preprint: in a joint work with Dirk Praetorius, Thomas Round, and Andrey Savinov, we have proposed and analysed a goal-oriented adaptive strategy for stochastic collocation finite element methods. The proposed strategy relies on novel reliable a posteriori estimates of the errors in approximating quantities of interest represented by linear and nonlinear goal functionals.
Preprint on arXiv
April 2024: Giving a talk at The Spring 2024 Finite Element Circus held at Brown University.
April 2024: Participating in the Semester Program "Numerical PDEs: Analysis, Algorithms, and Data Challenges" at The Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University in Providence, Rhode Island.
March 2024: Speaking at the kick-off workshop of the ANR funded project A posteriori error estimates for wave equations (APOWA) at INRIA Lille.
19 February 2024: Alex Diaz De La O from UCL visited us and gave a talk at the Optimisation & Numerical Analysis Seminar.
12 February 2024: Jonas Latz from the University of Manchester visited us and gave a talk at the Optimisation & Numerical Analysis Seminar.
New preprint: in a joint work with Andrey Savinov, we have performed the convergence analysis of an adaptive stochastic collocation algorithm for the stationary diffusion equation with parametric coefficient. The analysis covers problems with affine and nonaffine parametric coefficient dependence.
Preprint on arXiv
22 January 2024: Patrick Farrell from the University of Oxford visited us and gave a talk at the joint seminar in the Optimisation & Numerical Analysis and Applied Mathematics series.
November 2023: visiting Oxford's Numerical Analysis group and speaking at the Computational Mathematics and Applications Seminar. Many thanks to Yuji Nakatsukasa for hosting.
28 November 2023: Victorita Dolean Maini from the University of Strathclyde visited us and gave a talk at the Optimisation & Numerical Analysis Seminar.
21 November 2023: Charles Parker from the University of Oxford visited us and gave a talk at the Optimisation & Numerical Analysis Seminar.
14 November 2023: David Hewett from University College London visited us and gave a talk at the Optimisation & Numerical Analysis Seminar.
24 October 2023: Euan Spence from the University of Bath visited us and gave a talk at the Optimisation & Numerical Analysis Seminar.
September 2023: research visit by Raphaël Bulle from Laval University to work on adaptive algorithms for the numerical approximation of the fractional Laplacian (supported by the Research in Pairs grant of the London Mathematical Society).
Congratulations to Thomas Round, a PhD student in the group, on winning one of the UKIE SIAM prizes for best student presentations at The 29th Biennial Numerical Analysis Conference (University of Strathclyde, 27-30 June 2023).
June 2023: together with Michele Ruggeri we organised a minisymposium "Recent advances in computational PDEs for uncertainty quantification" at the latest edition of the Biennial Numerical Analysis Conference that took place at the University of Strathclyde in Glasgow.
Software release: the MATLAB toolbox Adaptive ML-SCFEM has been released. The toolbox is developed for computing and investigating adaptive stochastic collocation finite element approximations for elliptic PDE problems with random inputs. It is associated with our two recent papers on adaptive stochastic collocation finite elements.
Link to the software on GitHub
January 2023: giving a talk at the (virtual) Irish Numerical Analysis Forum.
September 2022: giving a talk at the 35th Chemnitz Finite Element Symposium.
August 2022: attending the conference Computational Methods in Applied Mathematics (CMAM 2022) at TU Vienna and speaking at the minisymposium "Computational stochastic PDEs".
New preprint: in a joint work with Dirk Praetorius and Michele Ruggeri, we have designed and analysed a goal-oriented adaptive algorithm that employs multilevel stochastic Galerkin FEM to approximate linear and nonlinear functionals of solutions to parametric elliptic PDEs.
Preprint on arXiv
June 2022: Ignacio Muga (Pontificia Universidad Católica de Valparaíso, Chile) visited us and gave a talk at the Applied Mathematics seminar series as part of his UK tour supported by the LMS Scheme 2 grant.
June 2022: speaking at the workshop Interplay of discretization and algebraic solvers: a posteriori error estimates and adaptivity at INRIA Paris.
May 2022: participating in the Thematic Programme on Computational Uncertainty Quantification and speaking at the workshop "Approximation of high-dimensional parametric PDEs in forward UQ" at the ESI in Vienna.
April 2022: speaking about our work on adaptive stochastic collocation FEM at the workshop "Adaptivity, High Dimensionality and Randomness" at The Erwin Schrödinger International Institute for Mathematics and Physics (ESI) in Vienna.
Talk recording
New preprint: in a joint work with David Silvester, we have completed the second part in the series of two papers on the error estimation and adaptivity for stochastic collocation FEM. The new preprint discusses a multilevel approximation strategy that employs individually tailored spatial discretisations across an adaptively enriched set of collocation points.
(Published in SIAM J. Sci. Comp.)
Link to the paper Preprint on arXiv
Software release: the latest update to Stochastic T-IFISS has been released. The update contains recent developments including a posteriori error estimation and adaptive algorithms for computing multilevel stochastic Galerkin approximations of steady-state diffusion problems with parametric uncertainty in coefficients.
Link to the software on GitHub
November 2021: giving a talk on a posteriori error estimation and adaptivity in stochastic finite element methods at Bath Numerical Analysis Seminar.
November 2021: speaking at the NASPDE workshop.
September 2021: research visit by David Silvester (University of Manchester). We have completed a new preprint (joint work with Feng Xu) developing a general adaptive solution strategy for stochastic collocation FEM. This strategy relies on novel reliable a posteriori error estimates proposed in this work.
(Published in SIAM J. Sci. Comp.)
Link to the paper Preprint on arXiv
June 2021: speaking at the Minisymposium in memory of Francisco-Javier Sayas within the CEDYA/CMA 2020 congress.
Talk slides
May 2021: giving a talk on adaptive stochastic Galerkin FEM at the Research Seminar of the Mathematics Department at Brunel University London.
Talk slides
New publication: in a joint with Dirk Praetorius and Michele Ruggeri we have analysed convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM applied to elliptic PDEs with parametric or uncertain inputs.
(Published in IMA J. Numer Anal.)
Link to the paper Preprint
February 2021: congratulations to Rawin Youngnoi who has successfully defended his PhD Thesis "Preconditioning techniques for elliptic partial differential equations with random data".
New preprint: together with Daniel Loghin and Rawin Youngnoi we have studied a class of truncation preconditioners for stochastic Galerkin discretisations of parametric elliptic PDEs: we have performed spectral analysis of the preconditioned matrices and established optimality of the preconditioners with respect to discretisation parameters.
(Published in SIAM J. Sci. Comput.)
Link to the paper 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.
(Published in SIAM/ASA J. Uncertain. Quantif.)
Link to the paper 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. (Published in the special issue "Development and Application of Open-Source Software for Problems with Numerical PDEs" 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.

Alex Bespalov

School of Mathematics

News and recent events