Geometry, compatibility and structure preservation in computational differential equations
GCS
3 July 2019 to 19 December 2019
Programme theme
Computations of differential equations are a fundamental activity in applied mathematics. While historically the main quest was to derive all-purpose algorithms such as finite difference, finite volume and finite element methods for space discretization, Runge–Kutta and linear multistep methods for time integration, in the last 25 years the focus has shifted to special classes of differential equations and purpose-built algorithms that are tailored to preserve special features of each class. This has given rise to the new fields of geometric numerical integration and of structure preserving discretization. In addition to being quantitatively accurate, these novel methods have the advantage of also being qualitatively accurate as they inherit the key structural properties of their continuum counterparts. This has meant a large-scale introduction of geometric and topological thinking into modern numerical mathematics.
During this scientific programme at the Isaac Newton Institute for Mathematical Sciences, we will address fundamental questions in the field of structure preserving discretizations of differential equations on manifolds in space and time. We will bring together two communities that have been pursuing their science along parallel tracks to endeavour breakthroughs in some major scientific applications, which call for advanced numerical simulation techniques. This will lead to the development of a new generation of space-time discretizations for evolutionary equations.
During the programme we intend to organise three workshops and two focused study periods lasting two weeks on selected application areas.
The core themes of the programme are:
- Compatible discretizations.
- Geometric numerical integration.
- Structure preservation and numerical relativity.
- Applications to computations in quantum mechanics.
Click here to download the programme's final scientific report
GCS programme: interview with organisers Arieh Iserles, Elena Celledoni and Elizabeth Mansfield
Preprints
| Title | Year | Programme | |
|---|---|---|---|
Numerical preservation of multiple local conservation lawsAuthors: Gianluca Frasca-Caccia, Peter E. Hydon |
2019 | GCS | 20 October 2022 |
Locally conservative finite difference schemes for the modified KdV equationAuthors: Gianluca Frasca-Caccia, Peter E. Hydon |
2019 | GCS | 20 October 2022 |
Discrete conservation laws for finite element discretisations of multisymplectic PDEsAuthors: James Jackaman, Elena Celledoni |
2019 | GCS | 20 October 2022 |
Conservative Galerkin methods for dispersive Hamiltonian problemsAuthors: James Jackaman, Tristan Pryer |
2019 | GCS | 20 October 2022 |
A surface nite element method for computational modelling of cell blebbingAuthors: Adam Nixon, Andreas Dedner, Bjorn Stinner |
2019 | GCS | 17 March 2020 |
DISCRETE VARIATIONAL METHODS AND SYMPLECTIC GENERALIZED ADDITIVE RUNGE-KUTTA METHODSAuthors: Antonella Zanna |
2019 | GCS | 23 January 2020 |
SYMPLECTIC P-STABLE ADDITIVE RUNGE-KUTTA METHODSAuthors: Antonella Zanna |
2019 | GCS | 23 January 2020 |
Symmetry and invariant bases in finite element exterior calculusAuthors: Martin Licht |
2019 | GCS | 24 December 2019 |
ON BASIS CONSTRUCTIONS IN FINITE ELEMENT EXTERIOR CALCULUSAuthors: Martin Licht |
2019 | GCS | 27 November 2019 |
A converging nite element scheme for motion by curvature of a network with a triple junctionAuthors: Bjorn Stinner, Paola Pozzi |
2019 | GCS | 22 November 2019 |
NEWEST VERTEX BISECTION OVER GENERAL TRIANGULATIONSAuthors: Martin Licht, Zhao Lyu, Michael Holst |
2019 | GCS | 6 November 2019 |
Workshops
Tutorial workshop
8 July 2019 to 12 July 2019
Structure preservation and general relativity
30 September 2019 to 4 October 2019
The future of structure-preserving algorithms
14 October 2019 to 18 October 2019
Seminars
| Wednesday 17th July 2019 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Christian Offen Massey University |
Room 1 | 
|
| Monday 22nd July 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Ralf Hiptmair ETH Zürich |
Room 2 |
|
| Tuesday 23rd July 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Annalisa Buffa EPFL - Ecole Polytechnique Fédérale de Lausanne; Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI) |
Room 1 | |
| Wednesday 24th July 2019 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Onno Bokhove University of Leeds |
Room 1 |
|
| Tuesday 30th July 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Melvin Leok University of California, San Diego |
Room 2 |
|
| 15:00 to 16:00 |
Benjamin Tapley Norwegian University of Science and Technology |
Room 2 |
|
| Wednesday 31st July 2019 | |||
|---|---|---|---|
| 15:00 to 16:00 |
Anthony Bloch University of Michigan |
Room 2 |
|
| Wednesday 7th August 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Arieh Iserles University of Cambridge |
Room 2 |
|
| 15:00 to 16:00 |
Robert McLachlan Massey University |
Room 2 | |
| Wednesday 14th August 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
David Garfinkle Oakland University |
Room 2 |
|
| 15:00 to 16:00 |
Ari Stern Washington University in St. Louis |
Room 2 |
|
| Wednesday 21st August 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Fernando Casas Universitat Jaume I |
Room 2 |
|
| 15:00 to 16:00 |
Yajuan Sun Chinese Academy of Sciences |
Room 2 | |
| Wednesday 28th August 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Gerard Awanou University of Illinois at Chicago |
Room 2 |
|
| 15:00 to 16:00 |
Milo Viviani Chalmers University of Technology |
Room 2 | |
| Wednesday 4th September 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Sina Ober-Blöbaum University of Oxford |
Room 2 |
|
| 15:00 to 16:00 |
Sigrid Leyendecker Friedrich-Alexander-Universität Erlangen-Nürnberg |
Room 2 |
|
| Thursday 5th September 2019 | |||
|---|---|---|---|
| 14:15 to 15:15 |
Chus Sanz-Serna Universidad Carlos III de Madrid |
Room 2 |
|
| Wednesday 11th September 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Peter Hydon University of Kent |
Room 2 |
|
| 15:00 to 16:00 |
Gianluca Frasca-Caccia University of Kent |
Room 2 |
|
| Wednesday 18th September 2019 | |||
|---|---|---|---|
| 14:05 to 14:50 |
Blanca Ayuso De Dios Università degli Studi di Milano - Bicocca; Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI) |
Room 2 | |
| 15:05 to 15:50 |
Linyu Peng Waseda University |
Room 2 | |
| Thursday 19th September 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Marcus Webb University of Manchester |
Room 2 | |
| Wednesday 25th September 2019 | |||
|---|---|---|---|
| 14:05 to 14:50 |
Martin Licht UC San Diego |
Room 2 |
|
| Wednesday 9th October 2019 | |||
|---|---|---|---|
| 14:05 to 14:50 |
Richard Falk Rutgers, The State University of New Jersey |
Room 2 |
|
| 15:05 to 15:50 |
Daniele Boffi Università degli Studi di Pavia |
Room 2 |
|
| Monday 21st October 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Donatella Marini Università degli Studi di Pavia; Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI) |
Room 1 |
|
| Tuesday 22nd October 2019 | |||
|---|---|---|---|
| 09:05 to 09:50 |
Franco Brezzi Institute for applied mathematics and information technologies (IMATI) |
Room 1 |
|
| 09:55 to 10:40 |
Andrea Cangiani |
Room 1 | |
| 11:10 to 11:55 |
Emmanuil Georgoulis University of Leicester; National Technical University of Athens |
Room 1 | |
| 13:05 to 13:50 |
Paul Houston University of Nottingham |
Room 1 | |
| 13:55 to 14:40 |
Jinchao Xu Pennsylvania State University |
Room 1 |
|
| Monday 28th October 2019 | |||
|---|---|---|---|
| 10:00 to 10:45 |
Erwan Faou INRIA Rennes - Bretagne Atlantique |
Room 2 |
|
| 10:45 to 11:30 |
Katharina Kormann Technische Universität München |
Room 2 |
|
| 12:00 to 12:45 |
Ernst Hairer Université de Genève |
Room 2 | |
| 14:00 to 14:45 |
Wayne Arter Culham Centre for Fusion Energy |
Room 2 | |
| 15:15 to 16:00 |
Jitse Niesen University of Leeds |
Room 2 |
|
| Wednesday 30th October 2019 | |||
|---|---|---|---|
| 14:05 to 15:05 |
Jinchao Xu Pennsylvania State University |
Room 2 |
|
| Thursday 31st October 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Patrick Farrell University of Oxford |
Room 2 |
|
| Monday 11th November 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Shi Jin Shanghai Jiao Tong University |
Room 2 |
|
| 16:00 to 17:00 |
Sergio Blanes Universidad Politécnica de Valencia |
Room 2 |
|
| Tuesday 12th November 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Erwan Faou INRIA Rennes - Bretagne Atlantique |
Room 2 |
|
| Wednesday 13th November 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Caroline Lasser Technische Universität München |
Room 2 |
|
| 16:00 to 17:00 |
Alexander Ostermann Leopold-Franzens Universtät Innsbruck |
Room 2 |
|
| Wednesday 20th November 2019 | |||
|---|---|---|---|
| 13:05 to 13:45 | Room 2 | ||
| 13:50 to 14:30 |
Tony Lelievre ENPC - École des Ponts ParisTech |
Room 2 |
|
| 15:05 to 15:35 |
Jonathan Goodman |
Room 2 | |
| 15:40 to 16:10 |
Miranda Holmes-Cefron |
Room 2 |
|
| Thursday 21st November 2019 | |||
|---|---|---|---|
| 13:05 to 13:45 |
Alessandro Barp Imperial College London |
Room 2 |
|
| 13:50 to 14:30 |
Benedict Leimkuhler University of Edinburgh |
Room 2 |
|
| 15:05 to 15:45 |
Elena Celledoni Norwegian University of Science and Technology |
Room 2 |
|
| 16:00 to 17:00 |
Peter Clarkson University of Kent |
Room 2 | |
| Tuesday 26th November 2019 | |||
|---|---|---|---|
| 14:05 to 14:50 |
Evelyne Hubert INRIA Sophia Antipolis |
Room 1 |
|
| 15:05 to 16:05 |
Anders Hansen University of Cambridge |
Room 1 |
|
| Thursday 28th November 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Elizabeth Mansfield University of Kent |
Room 1 |
|
| Wednesday 4th December 2019 | |||
|---|---|---|---|
| 14:05 to 14:50 |
Balázs Kovács Universität Tübingen |
Room 2 |
|
| Thursday 5th December 2019 | |||
|---|---|---|---|
| 13:30 to 14:15 |
Vanessa Styles University of Sussex |
Room 2 |
|
| 14:15 to 15:00 |
Bjorn Stinner University of Warwick |
Room 2 |
|
| 15:15 to 16:00 |
Bertram Düring University of Sussex |
Room 2 | |
| Friday 6th December 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Chus Sanz-Serna Universidad Carlos III de Madrid |
Room 1 |
|
| Wednesday 11th December 2019 | |||
|---|---|---|---|
| 14:05 to 14:50 |
Antonella Zanna Universitetet i Bergen |
Room 2 |
|
| 15:05 to 15:50 |
Brynjulf Owren Norwegian University of Science and Technology |
Room 2 |
|
Organisers
- Douglas Arnold University of Minnesota
- Franco Brezzi Institute for applied mathematics and information technologies (IMATI)
- Elena Celledoni Norwegian University of Science and Technology
- Arieh Iserles University of Cambridge
- Elizabeth Mansfield University of Kent
- Reinout Quispel La Trobe University
Speakers
- Wayne Arter Culham Centre for Fusion Energy
- Gerard Awanou University of Illinois at Chicago
- Blanca Ayuso De Dios Università degli Studi di Milano - Bicocca; Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI)
- Alessandro Barp Imperial College London
- Sergio Blanes Universidad Politécnica de Valencia
- Anthony Bloch University of Michigan
- Daniele Boffi Università degli Studi di Pavia
- Onno Bokhove University of Leeds
- Franco Brezzi Institute for applied mathematics and information technologies (IMATI)
- Annalisa Buffa EPFL - Ecole Polytechnique Fédérale de Lausanne; Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI)
- Andrea Cangiani
- Fernando Casas Universitat Jaume I
- Elena Celledoni Norwegian University of Science and Technology
- Peter Clarkson University of Kent
- Bertram Düring University of Sussex
- Richard Falk Rutgers, The State University of New Jersey
- Erwan Faou INRIA Rennes - Bretagne Atlantique
- Patrick Farrell University of Oxford
- Gianluca Frasca-Caccia University of Kent
- David Garfinkle Oakland University
- Emmanuil Georgoulis University of Leicester; National Technical University of Athens
- Jonathan Goodman
- Ernst Hairer Université de Genève
- Anders Hansen University of Cambridge
- Ralf Hiptmair ETH Zürich
- Miranda Holmes-Cefron
- Paul Houston University of Nottingham
- Evelyne Hubert INRIA Sophia Antipolis
- Peter Hydon University of Kent
- Arieh Iserles University of Cambridge
- Shi Jin Shanghai Jiao Tong University
- Katharina Kormann Technische Universität München
- Balázs Kovács Universität Tübingen
- Caroline Lasser Technische Universität München
- Benedict Leimkuhler University of Edinburgh
- Tony Lelievre ENPC - École des Ponts ParisTech
- Melvin Leok University of California, San Diego
- Sigrid Leyendecker Friedrich-Alexander-Universität Erlangen-Nürnberg
- Martin Licht UC San Diego; University of California, San Diego
- Elizabeth Mansfield University of Kent
- Donatella Marini Università degli Studi di Pavia; Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI)
- Robert McLachlan Massey University
- Jitse Niesen University of Leeds
- Sina Ober-Blöbaum University of Oxford
- Christian Offen Massey University
- Alexander Ostermann Leopold-Franzens Universtät Innsbruck
- Brynjulf Owren Norwegian University of Science and Technology
- Linyu Peng Waseda University
- Chus Sanz-Serna Universidad Carlos III de Madrid
- Ari Stern Washington University in St. Louis
- Bjorn Stinner University of Warwick
- Vanessa Styles University of Sussex
- Yajuan Sun Chinese Academy of Sciences
- Benjamin Tapley Norwegian University of Science and Technology
- Milo Viviani Chalmers University of Technology
- Marcus Webb University of Manchester
- Jinchao Xu Pennsylvania State University
- Antonella Zanna Universitetet i Bergen
Participants
- Douglas Arnold University of Minnesota
- Wayne Arter Culham Centre for Fusion Energy
- Gerard Awanou University of Illinois at Chicago
- Blanca Ayuso De Dios Università degli Studi di Milano - Bicocca; Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI)
- Mary Barker Washington University in St. Louis
- Alessandro Barp Imperial College London
- Soeren Bartels Albert-Ludwigs-Universität Freiburg
- Lourenco Beirao da Veiga Università degli Studi di Milano - Bicocca
- Paul Bergold Technische Universität München
- Sergio Blanes Universidad Politécnica de Valencia
- Anthony Bloch University of Michigan
- Daniele Boffi Università degli Studi di Pavia
- Geir Bogfjellmo Norwegian University of Science and Technology
- Onno Bokhove University of Leeds
- Franco Brezzi Institute for applied mathematics and information technologies (IMATI)
- Maria Bruna University of Oxford
- Olivier Brüls Université de Liège
- Christopher Budd University of Bath
- Annalisa Buffa EPFL - Ecole Polytechnique Fédérale de Lausanne; Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI)
- Erik Burman University College London
- Andrea Cangiani
- Fernando Casas Universitat Jaume I
- Elena Celledoni Norwegian University of Science and Technology
- Quentin Chauleur Université de Rennes 1
- Snorre Christiansen University of Oslo
- Jan L. Cieśliński Uniwersytet w Bialymstoku
- Colin Cotter Imperial College London
- Charles Curry Norwegian University of Science and Technology
- Andreas Dedner University of Warwick
- Alan Demlow Texas A&M University
- Bertram Düring University of Sussex
- Kurusch Ebrahimi-Fard Norwegian University of Science and Technology
- Solve Eidnes Norwegian University of Science and Technology
- Charlie Elliott University of Warwick
- Richard Falk Rutgers, The State University of New Jersey
- Erwan Faou INRIA Rennes - Bretagne Atlantique
- Patrick Farrell University of Oxford
- Jason Frank Universiteit Utrecht
- Gianluca Frasca-Caccia University of Kent
- Daisuke Furihata Osaka University
- David Garfinkle Oakland University
- Evan Gawlik University of Hawaii
- Emmanuil Georgoulis University of Leicester; National Technical University of Athens
- Håkon Gimse Universitetet i Bergen
- Volker Grimm Karlsruhe Institute of Technology (KIT)
- Johnny Guzma´n Brown University
- Ernst Hairer Université de Genève
- Ralf Hiptmair ETH Zürich
- Anil Hirani University of Illinois at Urbana-Champaign
- Michael Holst University of California, San Diego
- Jialin Hong Chinese Academy of Sciences
- Paul Houston University of Nottingham
- Kaibo Hu University of Minnesota
- Evelyne Hubert INRIA Sophia Antipolis
- Peter Hydon University of Kent
- Arieh Iserles University of Cambridge
- James Jackaman Memorial University of Newfoundland
- Shi Jin Shanghai Jiao Tong University
- Katharina Kormann Technische Universität München
- Balázs Kovács Universität Tübingen
- Lisa Maria Kreusser University of Cambridge
- Karolina Kropielnicka University of Gdansk
- Caroline Lasser Technische Universität München
- Luis Lehner Perimeter Institute for Theoretical Physics
- Benedict Leimkuhler University of Edinburgh
- Tony Lelievre ENPC - École des Ponts ParisTech
- Melvin Leok University of California, San Diego
- Sigrid Leyendecker Friedrich-Alexander-Universität Erlangen-Nürnberg
- Lu Li NTNU
- Martin Licht UC San Diego; University of California, San Diego
- Christian Lubich Eberhard Karls Universität Tübingen
- Pål Erik Lystad NTNU
- Elizabeth Mansfield University of Kent
- Gloria Mari-Beffa University of Wisconsin-Madison
- Donatella Marini Università degli Studi di Pavia; Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI)
- Robert McLachlan Massey University
- Hans Munthe-Kaas Universitetet i Bergen
- Jitse Niesen University of Leeds
- Nilima Nigam Simon Fraser University
- Sina Ober-Blöbaum University of Oxford
- Christian Offen Massey University
- Alexander Ostermann Leopold-Franzens Universtät Innsbruck
- Brynjulf Owren Norwegian University of Science and Technology
- Linyu Peng Waseda University
- Ilaria Perugia Universität Wien
- Timothee Pouchon University of Edinburgh
- Reinout Quispel La Trobe University
- Francesca Rapetti Université de Nice Sophia Antipolis
- Sebastian Reich Universität Potsdam; University of Reading
- Marcel Rød NTNU
- Giancarlo Sangalli Università degli Studi di Pavia
- Chus Sanz-Serna Universidad Carlos III de Madrid
- Alexander Schmeding Universitetet i Bergen
- Katharina Schratz Karlsruhe Institute of Technology (KIT)
- Carola-Bibiane Schönlieb University of Cambridge
- Pranav Singh University of Bath
- Ari Stern Washington University in St. Louis
- Bjorn Stinner University of Warwick
- Vanessa Styles University of Sussex
- Chunmei Su Technischen Universität München
- Yajuan Sun Chinese Academy of Sciences
- Endre Süli University of Oxford
- Nikolas Tapia Weierstraß-Institut für Angewandte Analysis und Stochastik; Technische Universität Berlin
- Benjamin Tapley Norwegian University of Science and Technology
- Milo Viviani Chalmers University of Technology
- Tiffany Vlaar University of Edinburgh
- Andy Wan University of Northern British Columbia
- Beth Wingate University of Exeter
- Ragnar Winther University of Oslo
- Jinchao Xu Pennsylvania State University
- Antonella Zanna Universitetet i Bergen
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