Applying geometric integrators

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Workshop theme

Satellite Workshop held at ICMS, 14 India Street, Edinburgh

Organisers: 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, 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.

Timetable

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	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
Celledoni, Elena	NTNU
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	Heinrich-Heine-Universität
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

Workshop theme

Satellite Workshop held at ICMS, 14 India Street, Edinburgh

Short Report

Timetable

Participants

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