A number of minisymposia will be scheduled during the parallel sessions. Each minisymposium should consist of a multiple of three 20 minute presentations.

If you are interested in organising a minisymposium, in any branch of Numerical Analysis or a cognate area, please contact the conference committee.

• Please supply the title of your proposed minisymposium along with a brief abstract and a tentative list of speakers.
• Please note that individuals are limited to one presentation, either a minisymposium talk or a contributed talk.
• Organisers are encouraged to ensure that the speakers represent a broad spectrum of research experience.
• Authors will advised of acceptance of proposals by email shortly after submission.
• The deadline for submission of minisymposium topics HAS BEEN EXTENDED TO April 14th 2023.
Abstracts from contributors should be submitted by April 30th 2023

Multiscale and Polytopal Discretisation Methods for Complicated Domains and Heterogeneous Structures

Organisers: Zhaonan Dong (Inria and CERMICS) and Roland Maier (Friedrich Schiller University Jena)
List of speakers: Anna Persson (Uppsala), Barbara Verfürth (Bonn), Zhaonan Dong (INRIA Paris), Andreas Rupp (Lappeenranta–Lahti University of Technology), Moritz Hauck (Augsburg), Theophile Chaumont-Frelet (Inria Sophia Antipolis), Omar Duran (Bergen), Lorenzo Mascotto (Milano-Bicocca), Géraldine Pichot (Inria), Gabriel Barrenechea (Strathclyde), Andrea Cangiani (SISSA)

Abstract: It is well-known that classical finite element discretisations can reach their limits in the presence of complicated domains and heterogeneous structures. In the past decade, multiscale methods and polytopal discretisation methods for the approximate solution of partial differential equations have received increasing attention in order to overcome the limitations of classical approaches. Besides, these methods generally aim at reducing computational costs when computing an approximate solution. In this minisymposium, we aim to gather researchers from the two communities who are interested in constructing and analysing multiscale methods and polytopal methods in the context of, e.g., multiphysics models or nonlinear problems in the presence of heterogeneous (micro-)structures and/or complicated domains.

Recent advances in computational PDEs for uncertainty quantification

Organisers: Alex Bespalov (University of Birmingham), Michele Ruggeri (University of Strathclyde)
List of speakers: Alex Bespalov (University of Birmingham), Sergey Dolgov (University of Bath), Ivan Graham (University of Bath), Anastasia Istratuca (University of Edinburgh), Michael Multerer (USI Lugano), Thomas Round (University of Birmingham), Andrea Scaglioni (TU Wien), Laura Scarabosio (Radboud University), David Silvester (University of Manchester)

Abstract: Partial differential equations (PDEs) with parametric or uncertain inputs are ubiquitous in mathematical models of physical phenomena and in engineering applications. Due to insufficient or imprecise measurements, some of the inputs (e.g., domain, coefficients, forcing terms, boundary and/or initial conditions) may not be fully known a priori. Therefore, it is very important to incorporate this uncertainty into the model and to design bespoke numerical algorithms in order to make simulations realistic and at the same time computationally feasible. The efficient numerical solution of PDE problems stemming from uncertainty quantification models presents a number of theoretical and practical challenges, and a wide variety of techniques have been studied in recent years giving rise to the emerging field of computational uncertainty quantification. These methodologies include the Monte Carlo method and its variants, stochastic Galerkin and collocation methods, multilevel and multifidelity strategies, Bayesian inference approaches, model order reduction, and tensor-formatted numerical linear algebra techniques. This minisymposium aims to give an overview of some of the recent advances in numerical methods for uncertainty quantification, with a particular focus on the mathematical foundations of novel computational strategies for high-dimensional PDEs with uncertain inputs.

Novel discretisation and solution methods for wave propagation problems

Organisers: Théophile Chaumont-Frelet (Inria, France), Victorita Dolean (University of Strathclyde)
List of speakers: Camille Carvalho (INSA Lyon, France), Mark Fry (University of Strathclyde), Roland Maier (University of Jena, Germany), Axel Modave (CNRS, ENSTA, France), Emile Parolin (Inria Paris, France), Monica Nonino (University of Vienna, Austria), Joshua Bannister (UCL)

Abstract: The efficient computation of wave propagation and scattering problems on modern multiprocessor computers has long been considered one of the ‘hard problems’ in numerical PDEs/scientific computing and is also of huge importance in applications - e.g., in seismic imaging and electromagnetics.

These wave problems are difficult to solve numerically because the solutions are often highly oscillatory and very fine discretisations are needed to resolve them, leading to large system matrices. This mini-symposium gathers specialists in different aspects of wave propagation problems (discretisation or solution methods) tackling different methodological or applicative aspects of these problems.

Recent advances in the approximation of variational inequalities

Organisers: Mira Schedensack (Leipzig University), Philip Lederer (University of Twente)
List of speakers: Carsten Carstensen (HU Berlin), Alexei Gazca (University of Freiburg), Mira Schedensack (Leipzig University), Andreas Schröder (Paris Lodron University Salzburg), Philip Lederer (University of Twente), Dond Asha Kisan (Indian Institute of Science Education and Research Thiruvananthapuram), Jan Ellmenreich (TU Vienna)

Abstract: Variational inequalities arise in many mechanical problems, e.g., for non-Newtonian fluids or elasto-plasticity. The approximation of solutions is a challenging task due to the non-linearity in the problem and the possible arrising saddle point structure. The obstacle problem resp. the Bingham problem are the two simplest instances of variational inequalities of first resp. second kind. This minisymposium is intended to bring together researchers from the respective fields who are experts on numerical analysis for these problems and to address recent developments.

Saddle point problems: solvers and preconditioners

Organisers: Erin Carson (Charles University), Ieva Daužickaitė (Charles University)
List of speakers: Karolína Benková (University of Edinburgh), Luca Bergamaschi (University of Padua), Ieva Daužickaitė (Charles University), Frédéric Nataf (Sorbonne University), John Pearson (University of Edinburgh), Jemima Tabeart (University of Oxford)

Abstract: Solving a saddle point system of linear equations is a necessary step in numerous computational problems and is known to be a challenging task. This motivates a continuous stream of work on efficient solvers and suitable preconditioners. In their design process, we need to take into account various problem dependent conditions, for example, constraints on time and memory available for the computations, required accuracy of the solution, or the structure of the saddle point matrix. This minisymposium is meant to discuss advances towards efficient solution of saddle point problems arising in a collection of applications.

Numerical methods for fractional-derivative problems

Organisers: Natalia Kopteva (Limerick), Yubin Yan (Chester)
List of speakers: Lehel Banjai (Heriot-Watt), Markus Faustmann (TU Wien), Sebastian Franz (TU Dresden), Charlie Green (Chester), Sean Kelly (University of Limerick), Natalia Kopteva (Limerick), Ercília Sousa (Coimbra), Yubin Yan (Chester), Zhi Zhou (Hong Kong Polytechnic)

Abstract: In recent years there has been an explosion in the number of published papers dealing with numerical methods for fractional-derivative problems, but the rigorous analysis of such methods has many open questions. This mini-symposium brings together several fractional-derivative experts to present and discuss recent developments in this fast-changing area.

Recent advances in finite element methods

Organisers: Mark Ainsworth (Brown University), Charles Parker (University of Oxford)
List of speakers: Mark Ainsworth (Brown University), Charles Parker (University of Oxford), Pablo Brubeck (University of Oxford), Francis Aznaran (University of Oxford), Kaibo Hu (University of Oxford)

Abstract: The minisymposium is focused on recent advances in the theory of finite element methods including structure preserving methods, discrete complexes and commuting diagram properties of finite elements, stable high order methods through to efficient implementations. The minisymposium brings together both young and experienced experts working in these areas and will highlight some of the recent advances in the field.

Spectral methods and orthogonal polynomials

Organisers: Timon Gutleb (Oxford), Ioannis Papadopoulos (Imperial), Marco Fasondini (Leicester)
List of speakers: Georgia Bradshaw (Manchester), Matthew Colbrook (Cambridge), Timon Gutleb (Oxford), Sheehan Olver (Imperial), Ioannis Papadopoulos (Imperial), Tianyi Pu (Imperial), Richard Mikael Slevinsky (Manitoba, Canada), Nick Trefethen (Oxford), Geoff Vasil (Edinburgh), Marcus Webb (Manchester), Kuan Xu (USTC, China), Wenqi Zhu (Oxford)

Abstract: The theory of orthogonal polynomials has played a foundational role in recent advances in spectral methods and fast algorithms for the solution of differential, integral and fractional-order equations. This minisymposium aims to showcase and further increase the interplay between orthogonal polynomials, spectral methods and applications.

Advances in solvers and preconditioning for PDE problems

Organisers: Niall Bootland (STFC Rutherford Appleton Laboratory), Sean Hon (Hong Kong Baptist University)
List of speakers: Andrés Miniguano-Trujillo (University of Edinburgh and Heriot-Watt University), Andy Wathen (University of Oxford), Isabella Furci (University of Genoa), Niall Bootland (STFC Rutherford Appleton Laboratory), Sean Hon (Hong Kong Baptist University)

Abstract: The computational solution of PDE problems is central to many areas in the physical sciences and more widely in modern applications. State-of-the-art approaches often rely on being able to solve very large linear systems efficiently. Solvers must be carefully designed and often an effective choice of preconditioner must be devised. Such methods may typically exploit sparsity or other structure within the linear systems to give the most efficient solution on a given computer architecture. This minisymposium brings together researchers working on solvers and preconditioning for PDE problems and showcases recent advances in both theory and practice.

PDEs in Data Science

Organisers: Lisa Maria Kreusser (Bath), Jonas Latz (Heriot-Watt)
List of speakers: Jeremy Budd (Caltech), Ariane Fazeny (FAU Erlangen-Nürnberg), Leon Bungert (TU Berlin), Yves van Gennip (TU Delft), Stefan Klus (Heriot-Watt), Lisa Maria Kreusser (Univ. Bath), Jonas Latz (Heriot-Watt Univ.), Matthew Thorpe (Univ. Manchester), Simon Urbainczyk (Heriot-Watt Univ.)

Abstract: Partial differential equations are often used to model physical or biological systems and processes and a large part of numerical analysis has always been concerned with the approximation of PDE solutions. On the other hand, PDEs can appear as solution strategies for hard problems, say, in image denoising, where the parabolic Rudin-Osher-Fatemi PDE can be solved to remove noise from an image whilst reconstructing/retaining edges in the image. In recent years, PDEs have become more prevalent also in more generic data science tasks: such as regression or classification. There, a classifier or regressor shall be found that solves an appropriate PDE (e.g., Laplace or Allen-Cahn) whilst taking the data into account at the same time. This minisymposium will connect current research in PDE-based data science, including: graphical and continuous models, asymptotic and non-asymptotic analyses, numerical methods, stochastic and Bayesian techniques, as well as applications.

Recent advances in multilevel, multiscale, and parallel in time methods

Organisers: Hussam Al Daas (STFC, Rutherford Appleton Laboratory), Felix Kwok (Universitè Laval)
List of speakers: Bastien Chaudet-Dumas (University of Geneva), Victorita Dolean (University of Strathclyde and University Côte d’Azur), Philip Freese (University of Hamburg), Conor McCoid (Universitè Laval), Tyrone Rees (STFC, Rutherford Appleton Laboratory), Lambert Theisen (University of Stuttgart)

Abstract: As computing clusters with thousands to millions of cores become increasingly common, it is important to design highly scalable parallel solvers and preconditioners such as multigrid, domain decomposition and multiscale methods that are appropriate to the application of interest and which remain efficient as the number of cores increases. The need for parallelization is particularly important for time-dependent PDEs, where sequential integration of the problem becomes more and more of a bottleneck as the number of available cores continues to increase. This minisymposium brings together experts in different aspects of parallel and multilevel solvers to discuss their latest advances in the subject.

Recent advances in the robust solution of singularly perturbed differential equations

Organisers: Niall Madden (University of Galway), Torsten Linß (FeU Hagen)
List of speakers: Abdolreza Amiri (Strathclyde), Bosco Garcia Archilla (Sevilla), Alan Hegarty (Limerick), Róisín Hill (Limerick), Petr Knobloch (Praha), Torsten Linß (Hagen), Scott MacLachlan (St John's), Niall Madden (Galway), Christian Merdon (Berlin), Julia Novo (Madrid)

Abstract: Singularly perturbed differential equations, in which a small parameter multiplies the highest-order derivative, occur widely in mathematical modelling. Typically, their solution exhibit boundary and/or interior layers. Classical methods are usually unsatisfactory for such problems: they may provide numerical solutions that are unstable, or fail to resolve features of interest, or both. The development of specialised methods, which overcome these problems, and whose analysis entirely accounts for the small parameter, has long been the focus of research in numerical mathematics. This mini-symposium will feature some of the most recent developments in this field, including the development of specialised discretizations, meshing methods, and linear solvers.

Mathematical and Computational Foundations of AI

Organisers: Des Higham (University of Edinburgh), Ivan Tyukin (King's College London)
List of speakers: Alexander Bastounis (University of Leicester), Lucas Beerens (University of Edinburgh), Nicolas Boullé (University of Cambridge), Des Higham (University of Edinburgh), Martin Lotz (University of Warwick), Dayana Savostianova (Gran Sasso Science Institute), Ivan Tyukin (King's College London), Tiffany Vlaar (Mila and McGill University)

Abstract: For the vast potential of Artificial Intelligence (AI) to be realised, we must deepen our understanding of the theoretical foundations, identify and overcome existing methodological barriers and, where necessary, develop new algorithms and analyses. Numerical analysts are well-placed to make significant and lasting impact in these directions. This minisymposium will cover a range of topics where ideas from numerical analysis and related areas of mathematics can be applied to challenges in AI. These topics include initialization, training and post-processing of deep learning networks; derivation of approximation theory results; and the use of PDE learning techniques. They also include the design of practical "adversarial attack" algorithms that reveal vulnerabilities in existing AI systems and theoretical results to shed light on the accuracy-robustness tradeoff. This summary was not written by an AI chatbot.

Structure-preserving discretisations of Hilbert complexes

Organisers: Kaibo Hu (University of Oxford), Deepesh Toshniwal (Delft University of Technology)
List of speakers: Marien Hanot (Université de Montpellier), Xuehai Huang (Shanghai University of Finance and Economics), Yizhou Liang (Universität Augsburg), Frederik Schnack (Technische Universität München), Erick Schulz (Plexim), Rafael Vazquez (EPFL)

Abstract: Finite element exterior calculus (FEEC) is a cohomological approach for constructing and analyzing numerical methods for solving partial differential equations. FEEC provides a general strategy to avoid subtle spurious convergence and obtain numerical methods that preserve key geometric and physical properties of the continuous problem. This involves the identification of a Hilbert cochain complex associated to the given PDE and the selection of finite element spaces that together form its cohomologically-equivalent subcomplex. This minisymposium will gather experts in the construction and application of such methods with the focus being both, methods that utilize traditional finite element spaces of low regularity as well as approaches that use spaces of smooth splines as finite elements.

Approximate Computing in Numerical Linear Algebra

Organisers: Nick Higham, Xiaobo Liu, Bastien Vieublé
List of speakers: Petr Vacek (Charles University), Hei Yin Lam (EPFL), Silviu-Ioan Filip (IRISA), Edouard Timsit (INRIA Paris), Martina Iannacito (University of Leuven), Xiaobo Liu (University of Manchester)

Abstract: Approximate computing techniques have become extremely popular and intensively used within numerical linear algebra algorithms. In particular, these involve the use of randomization, low-rank approximation, and low precision arithmetic as well as their combinations, all of which can provide significant gains in speed and energy and enlarge the scale of problems we are able to solve. This minisymposium is intended to bring together researchers in these areas to discuss recent advances in algorithms that exploit these approximate computing techniques for a wide range of numerical linear algebra computations, including matrix multiplication, direct and iterative linear solvers, and neural networks.

Recent advances in numerical approximation of eigenvalue problems

Organisers: Fleurianne Bertrand (University of Twente), Daniele Boffi (KAUST), Arbaz Khan (IIT Roorkee)
List of speakers: Daniele Boffi (KAUST), Fleurianne Bertrand (University of Twente), Umberto Zerbinati (Oxford University), Henrik Schneider (University of Duisburg-Essen), Tran Ngoc Tien (University of Jena), Linda Alzaben (KAUST), Arbaz Khan (IIT Roorkee), Philipp Zilk (University of the Bundeswehr Munich), Luka Grubišić (University of Zagreb), Harri Hakula (Aalto University)

Abstract: In science and engineering, there are many significant applications based on eigenvalue problems of partial differential equations, e.g., biological sensing, structure in condensed matter and photonic crystals, etc. The main aim of this minisymposium is to focus on numerical approximation of eigenvalues problems of PDEs. It provides opportunities to bring the pre-eminent researchers for discussing recent advances in eigenvalues problems.

Numerical methods for fully nonlinear partial differential equations

Organisers: Max Jensen (UCL), Iain Smears (UCL)
List of speakers: Olivier Bokanowski (Université Paris Cité), Roberto Ferretti (Roma Tre), Omar Lakkis (Sussex University), Yohance Osborne (UCL), Tristan Pryer (Bath), David Siska (Edinburgh University)

Abstract: Fully nonlinear partial differential equations are central building blocks of optimal control and game theory as well as of differential geometry, leading a rich field of theory- and application-driven research. This minisymposium responds to the significant progress in computational solution methods for fully nonlinear PDEs in recent years due to advances with mesh- and sampling-based methods as well as due to connections to reinforcement and deep learning.

Simulating Stochastic Differential Equations

Organisers: Alix Leroy (University of Edinburgh and Heriot-Watt University)
List of speakers: Alix Leroy (University of Edinburgh and Heriot-Watt University), Yiyi Tang (University of Strathclyde)

Abstract: Computing numerical solutions to stochastic differential equations (SDEs) is challenging in terms of both finite-time convergence and long-time stability. This minisymposium will explore new algorithms to tackle issues arising with (a) classes of SDEs with non-Lipschitz drift coefficients, (b) Langevin dynamics, and (c) Markov Chain Monte Carlo methods. The minisymposium will also present applications of these ideas in molecular dynamics, neural network training and Bayesian inference.