Organisers: Leimkuhler, Ben (University of Edinburgh), McLachlan, Robert (Massey University)
Geometric integrators are numerical discretization methods for solving time-dependent differential equations which exactly conserve phase-flow structures such as time-reversibility, symplectic structure, phase space volume, or first integrals. In recent years there has been an extraordinary interest in geometric integration methods among physicists and mathematicians with chemists and engineers also employing geometric integrators for many calculations. In many cases the benefits of using a geometric integration approach are so great compared to alternatives that no other technique can be envisioned; for example the use of symplectic methods in molecular dynamics appears to offer such an overwhelming advantage. In other large scale applications, some of the available geometric structure of a given problem must be sacrificed due to the severe practical constraints of computational efficiency, or choices must be made between different types of structures which can be individually, but not simultaneously, preserved. While much research on geometric integrators is motivated by applications, there is often a gulf between the developers of mathematical methods and the large body of applications scientists who stand to benefit the most from that work. This 3-day workshop brought together experts in geometric integration, primarily from the mathematics and physics communities, with the goal of highlighting barriers to the implementation and use of geometric integration methods, clarifying the relative importance of different types of structures in the practical setting, and considering possible new types of geometric integration methodology which may have a strong impact on modern computational science.
This meeting was a satellite event of the Isaac Newton Institute programme on Highly Oscillatory Problems, held at the head-quarters of ICMS at 14 India Street. This house is the birthplace of James Clerk Maxwell and is situated in the historic New Town of Edinburgh, very near the centre.
|Tuesday 24 April|
|12.00-14.30||Registration and sandwich lunch|
|14.30-15.00||Hairer, Ernst (University of Geneva)
Modified differential equations
|15.00-15.30||Bond, Stephen (University of Illinois)
On the accuracy of numerically computed averages in molecular simulation
|16.00-16.30||Faou, Erwan (INRIA Rennes)
Molecular dynamics in a shaker
|16.30-17.00||Legoll, Frederic (École Nationale des Ponts et Chaussées)
Derivation of symplectic numerical schemes for highly oscillatory Hamiltonian systems: a new approach?
|17.10-17.40||Melnik, Roderick (WLU/Waterloo, Canada)
Conservative numerical approximations and the Cayley transform technique in applications to PDEs
|19.30||Group meal at Nargile, Hanover Street|
|Wednesday 25 April|
|09:00-09:30||Skeel, Bob (Purdue University)
What makes molecular dynamics work
|09:30-10:00||Sanz-Serna, Jesus (University of Valladolid)
Mollified impulse methods revisited
|10.30-11.00||Tuckerman, Mark (New York University)
Statistical mechanical concepts and measure-preserving integrators for non-Hamiltonian systems
|11.10-11.40||Izaguirre, Jesus (University of Notre Dame)
Longer time step integrator using normal-mode constraints
|11.40-12.10||Cohen, David (Norwegian University of Science & Technology)
Highly oscillatory Hamiltonian systems with non-constant mass matrix
|14.00-14.30||Quispel, Reinout (La Trobe University)
Integral-preserving integrators and linearization-preserving integrators
|14.30-15.00||Budd, Chris (University of Bath)
Geometric integration and 2D mesh generation
|15.00-15.30||Blanes Sergio (Universidad Politécnica de Valencia)
Adaptive splitting integrators
|15.30||Go to King's Buildings for Wanner's colloquium|
|Thursday 26 April|
|09.00-09.30||Laskar, Jacques (IMCCE, Observatory of Paris)
Long time integrations of the Solar System
|09.30-10.00||Lubich, Christian (University of Tübingen)
Symplectic integrators for numerical general relativity
|10.30-11.00||Mikkola, Seppo (Turku Observatory)
|11.10-11.40||Stadel, Joachim (University of Zurich)
Multi-stepping integrators in astrophysical N-body system
|11.40-12.10||Kennedy, Anthony (University of Edinburgh)
|14.00-14.30||Grimm, Volker (Heinrich-Heine-Universität)
On the computation of cosine of operators in second order abstract differential equations
|14.30-15.00||McLachlan, Robert (Massey University)
|15.30-16.00||Celledoni, Elena (NTNU)
Simulation of rigid body dynamics using Jacobi elliptic functions and integrals
|16.00-16.30||Wulff, Caudia (University of Surrey)
Approximate energy conservation for symplectic time-semidiscretizations of semilinear wave equations
|16.40-17.10||Dixon, Matthew (Imperial College London)
Moser-Veselov integrators for continuum dynamics
|17.10-17.40||Zanna, Antonella (University of Bergen)
On the exact integration of Rigid Body equations
|19.30||Workshop Dinner at Howies, Waterloo Place|
|Friday 27 April|
|09.00-09.30||Frank, Jason (CWI Amsterdam)
Statistical mechanics of Arakawa's Jacobian: numerical experiments
|09.30-10.00||Owren, Brynjulf (NTNU Trondheim)
Geometric integrators for the Camassa-Holm equations
|10.30-11.00||Fasso, Francesco (University of Padua)
The conjugate locus for the Euler top
|11.10-11.40||Cotter, Colin (Imperial College London)
Particle-mesh methods for matching shapes
|11.40-12.10||Casas Perez, Fernando (Universitat Jaume I)
On the convergence of Magnus and related expansions
|14.00-14.30||Malham, Simon (Heriot-Watt University)
Lie group stochastic integrators
|14.30-15.00||Leimkuhler, Ben (University of Edinburgh)
A generalized molecular dynamics model
|15.00||End of workshop|
|Abdulle, Assyr||University of Edinburgh|
|Blanes, Sergio||Universidad Politécnica de Valencia|
|Bond, Stephen||University of Illinois|
|Budd, Chris||University of Bath|
|Casas Perez, Fernando||Universitat Jaume I|
|Cohen, David||Norwegian University of Science & Technology|
|Cotter, Colin||Imperial College London|
|Dehnen, Walter||University of Leicester|
|Dixon, Matthew||Imperial College London|
|Faou, Erwan||INRIA Rennes|
|Fasso, Francesco||University of Padua|
|Frank, Jason||CWI Amsterdam|
|Hairer, Ernst||University of Geneva|
|Heggie, Douglas||University of Edinburgh|
|Izaguirre, Jesus||University of Notre Dame|
|Kennedy, Anthony||University of Edinburgh|
|Laskar, Jacques||IMCCE, Observatory of Paris|
|Legoll, Frederic||École Nationale des Ponts et Chaussées|
|Leimkuhler, Ben||University of Edinburgh|
|Lubich, Christian||University of Tübingen|
|Malham, Simon||Heriot-Watt University|
|McLachlan, Robert||Massey University|
|Melnik, Roderick||WLU/Waterloo, Canada|
|Mikkola, Seppo||Turku Observatory|
|Noorizadeh, Emad||University of Edinburgh|
|Owren, Brynjulf||NTNU Trondheim|
|Quispel, Reinout||La Trobe University|
|Sanz-Serna, Jesus||University of Valladolid|
|Skeel, Bob||Purdue University|
|Stadel, Joachim||University of Zurich|
|Tuckerman, Mark||New York University|
|Vanneste, Jacques||University of Edinburgh|
|Wanner, Gerhard||University of Geneva|
|Wulff, Claudia||University of Surrey|
|Zanna, Antonella||University of Bergen|
Subscribe for the latest updates on events and news
INI is a creative collaborative space which is occupied by up to fifty-five mathematical scientists at any one time (and many more when there is a workshop). Some of them may not have met before and others may not realise the relevance of other research to their own work.
INI is especially important as a forum where early-career researchers meet senior colleagues and form networks that last a lifetime.
Here you can learn about all activities past, present and future, watch live seminars and submit your own proposals for research programmes.
Within this section of the website you should find all the information required to arrange and plan your visit to the Institute. If you have any further questions, or are unable to find the information you require, please get in touch with the relevant staff member or our Reception team via our contact pages.
INI and its programme participants produce a range of publications to communicate information about activities and events, publish research outcomes, and document case studies which are written for a non-technical audience. You will find access to them all in this section.
The Isaac Newton Institute aims to maximise the benefit of its scientific programmes to the UK mathematical science community in a variety of ways.
Whether spreading research opportunities through its network of correspondents, offering summer schools to early career researchers, or hosting public-facing lectures through events such as the Cambridge Festival, there is always a great deal of activity to catch up on.
Find out about all of these endeavours in this section of the site.
There are various ways to keep up-to-date with current events and happenings at the Isaac Newton Institute. As detailed via the menu links within this section, our output covers social media streams, news articles, a regular podcast series, an online newsletter, and more detailed documents produced throughout the year.
“A world famous place for research in the mathematical sciences with a reputation for efficient management and a warm welcome for visitors”
The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period.
INI has a vital national role, building on many strengths that already exist in UK universities, aiming to generate a new vitality through stimulating and nurturing research throughout the country.During each scientific programme new collaborations are made and ideas and expertise are exchanged and catalysed through lectures, seminars and informal interaction, which the INI building has been designed specifically to encourage.
For INI’s knowledge exchange arm, please see the Newton Gateway to Mathematics.
The Institute depends upon donations, as well as research grants, to support the world class research undertaken by participants in its programmes.
Fundraising activities are supported by a Development Board comprising leading figures in academia, industry and commerce.
Visit this section to learn more about how you could play a part in supporting INI’s groundbreaking research.
In this section you can find contact information, staff lists, maps and details of how to find INI’s main building in Cambridge.
Our administrative staff can help you with any queries regarding a prospective or planned visit. If you would like to discuss a proposed a research programme or other event, our senior management team will be happy to help.