Adaptive Moving and Anisotropic Meshes for the Numerical Approximation of PDEs

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Adaptive Moving and Anisotropic Meshes for the Numerical Approximation of PDEs

 09 - 13 May 2022

ICMS, Bayes Centre, Edinburgh

  • Chris Budd, University of Bath
  • Weizhang Huang, The University of Kansas
  • Jens Lang, TU Darmstadt
  • Simona Perotto, Politecnico of Milano


A major bottleneck in current scientific computing practice is the difficulty of resolving small scale structures without excessive computational cost. Adaptive mesh methods afford the possibility of achieving much better resolution, and thus of providing much more accurate predictions, in an efficient manner. Adaptive mesh movement and anisotropic mesh adaptation have emerged as areas of intense research in mesh adaptation in the last decade.

The aim of this workshop was to bring together scientists from the fields of mathematics, scientific computing, physics, engineering, and meteorology to discuss the latest advances in adaptive moving and anisotropic meshes and their applications to real-life problems. Participants included both senior and young researchers to allow vigorous discussion and collaboration that will advance the state-of-the-art in these challenging and emerging areas.

The organisers intended for this workshop to bring a better theoretical understanding of the convergence and stability of moving mesh and anisotropic mesh adaptation methods, which will aid future work in their design. In addition there will be a clearer understanding of their computational complexity and effectiveness when solving very large problems (for example three dimensional problems in gas or fluid dynamics), particularly when using parallel methods. This will allow a better implementation of these methods for challenging practical problems and in new application areas.

Recorded Talks


MONDAY 09 MAY 2022
Lunch and Registration All times are British Summertime.
Welcome Housekeeping by Simon Kershaw, Conference Coordinator, ICMS
John MacKenzie, University of Strathclyde Adaptive moving mesh methods for computational cell biology
Vit Dolejsi, Charles University, Prague An anisotropic hp-mesh adaptation method for time-dependent problems based on the interpolation error control
Andrea Cangiani, SISSA Adaptive non-hierarchical Galerkin methods for parabolic problems: moving mesh and virtual element methods
Informal Welcome Reception Welcome Reception at ICMS until 18.00
Chris Budd, University of Bath Optimal transport methods for mesh adaption
Nicola Ferro, Politecnico di Milano Anisotropic mesh adaptation for topology optimization: from theory to practice
Refreshment Break
Charles Dapogny, CNRS & Laboratoire Jean Kuntzmann A level set based mesh evolution method for shape optimization
Thierry Coupez, CEMEF - Mines Paris Immersed method with metric based anisotropic meh adaptation for computational multiphase flow dynamics
Lunch Break Lunch served at ICMS
Ron Haynes, Memorial University (ONLINE) Towards Adaptive Parallel Solvers for PDEs on Surfaces
Weizhang Huang, University of Kansas (ONLINE) A surface moving mesh PDE method
Refreshment Break
Discussions Discussions will end around 17.30. Short break before Public Lecture
Chris Budd , University of Bath Computing: past, present and future' (Public Lecture)
Simone Appella, University of Bath r-adaptivity, deep learning and the deep Ritz method
Paul Zegeling, Utrecht University Adaptive moving grids for space-fractional PDEs
Refreshment Break
Andrew McRae, University of Oxford Optimal transport meshes on the sphere, and coupling moving meshes to fluid equations
Lunch Break Lunch served at ICMS
Visit to James Clerk Maxwell Foundation (India Street) Optional visit to birthplace of James Clerk Maxwell for workshop participants (finishing around 15.45)
Natalia Kopteva, University of Limerick Convergence behaviour and a posteriori error estimation for finite element approximations on anisotropic meshes
Kaloyan Kirilov, Imperial College London Mesh adaptation for high-order flow simulations
Refreshment Break
Joseph Wallwork, Imperial College London (ONLINE) Accelerating Mesh Adaptation using Neural Networks
Lunch Break Lunch served at ICMS
Jean-Francois Remacle, UC Louvain X-MESH : An eXtreme Mesh deformation method to follow sharp physical interfaces
Marco Picasso, EPFL Anisotropic, adaptive finite elements for academic and industrial problems
Refreshment Break
Panel discussion (HYBRID) Panel discussion on the big open problems (ending 16.45)
Workshop Dinner Workshop Dinner at ICMS until 20.30
FRIDAY 13 MAY 2022
Suzanne Shontz , University of Kansas Optimization-Based Approaches for High-Order Mesh Generation and Warping
Matthew Hubbard, University of Nottingham Adaptive Moving Meshes for Hyperbolic PDEs
Refreshment Break
End of Workshop Packed lunch available for participants to eat here, or take with them