## Applying Geometric Integrators

*
Apr 24, 2007 - Apr 27, 2007 *

### ICMS, 14 India Street, Edinburgh

### Organisers

Name | Institution |
---|---|

Leimkuhler, Ben | University of Edinburgh |

McLachlan, Robert | Massey University |

### Short Report

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 (January -June, 2007).

Participants list and links to available presentations are further down this page.

Download the pdf file of the full report

### Arrangements

**Venue **

The Workshop will be 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. The seminar room is fully equipped with large whiteboards, overhead and data projectors. Other facilities include PCs, wireless network and rooms suitable for small discussion meetings.

The ICMS travel pages show the location of India St and have links to pages with advice on how to get to Edinburgh and travel around once here.

** Registration etc**

Registration will be from 12.00-14.00 on Tuesday 24, with a sandwich lunch provided. The talks will start at 14.00 and the workshop will end at 16.00 on Friday 27.

** Accommodation**

ICMS will arrange rooms in local guest houses for those who require it. Participants are also free to make their own arrangements and may claim back the cost, with receipts, up to a maximum of £45 per night for bed and breakfast. A list of Edinburgh accommodation of various sorts and prices is available here. Sections 1-3 are particularly relevant.

** Meals and Refreshments**

Morning and afternoon refreshments will be provided throughout the Workshop. A sandwich lunch will be supplied on Tuesday only. There will be an informal meal at a nearby restaurant on Tuesday evening and the Workshop Dinner will be on Thursday evening.

Further information will be provided in the next Invitation Letter.

### Programme

**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 |

15.30-16.00 | Coffee break |

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? |

17.00-17.10 | Short break |

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 |

10.00-10.30 | Coffee break |

10.30-11.00 | Tuckerman, Mark (New York University)Statistical mechanical concepts and measure-preserving integrators for non-Hamiltonian systems |

11.00-11.10 | Short break |

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 |

12.10-14.00 | Lunch break |

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 |

10.00-10.30 | Coffee break |

10.30-11.00 | Mikkola, Seppo (Turku Observatory)Algorithmic regularization |

11.00-11.10 | Short break |

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)tba |

12.10-14.00 | Lunch break |

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)Multisymplectic integrators |

15.00-15.30 | Coffee break |

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 |

16.30-16.40 | Short break |

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 |

10.00-10.30 | Coffee break |

10.30-11.00 | Fasso, Francesco (University of Padua)The conjugate locus for the Euler top |

11.00-11.10 | Short break |

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 |

12.10-14.00 | Lunch break |

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 |

### Participants

Name | Institution |
---|---|

Abdulle, Assyr | École Polytechnique Fédérale de Lausanne |

Blanes, Sergio | Universidad Politécnica de Valencia |

Bond, Stephen | Sandia National Laboratories |

Budd, Chris | University of Bath |

Casas Perez, Fernando | Universitat Jaume I |

Celledoni, Elena | Norwegian University of Science and Technology |

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 |

Grimm, Volker | Karlsruhe Institute of Technology |

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 | Norwegian University of Science and Technology |

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 |