Ben Leimkuhler's Research Page

My research group is based in the School of Mathematics at the University of Edinburgh. We combine expertise in modelling, (stochastic) dynamics, numerical analysis and advanced scientific computing to develop forefront simulation methodology for applications including molecular simulation and data science.
On these pages you will find links to preprints and articles in journals, as well as some general information about the group. People interested in possibly joining the group, whether for upper division undergraduate, MSc, doctoral, or postdoctoral study are encouraged to use the email address below to find out about opportunities.

Contact Info:

email: b dot leimkuhler at-sign ed.ac.uk

mail: Ben Leimkuhler, School of Mathematics, James Clerk Maxwell Building, King's Buildings, University of Edinburgh, Edinburgh EH9 3JZ

We are part of the ExTASY (Extensible Tools for Adanced Sampling and analYsis) NSF-EPSRC software consortium which is designing forefront software systems for molecular modelling. As part of ExTASY we have established the MIST (Molecular Integrator Software Tools) to enable the convenient implementation of novel molecular integration algorithms within standard packages such as GROMACS and Amber. Learn about ExTASY and MIST here.

We are currently working with NAMD (http://www.ks.uiuc.edu/Research/namd/) to incorporate new algorithms into their state of the art molecular modelling package.

We have developed and freely distribute the MD.M MATLAB-based software suite for studying molecular dynamics algorithms and (small) model problems. The software and its documentation are provided via the website: www.moleculardynamics.info

MD.M is an easy to use and modify MATLAB-based toolkit for learning about molecular dynamics. Snapshots from simulations performed using the MD.M software package:

** Benedict Leimkuhler**

** Studies**

PhD 1988, MS 1986, University of Illinois

BS 1983, Purdue University

** Career History**

2006 -- Chair of Applied Mathematics, University of Edinburgh

2000 -- 2006 Professor of Applied Mathematics, University of Leicester

1996 -- 1999 Associate Professor of Mathematics, University of Kansas

1990 -- 1996 Assistant Professor of Mathematics, University of Kansas

1988 -- 1990 Researcher, Helsinki University of Technology

1986 Researcher, Lawrence Livermore National Laboratory

1983 -- 1988 Research Assistant, University of Illinois

**Research Interests **

My research is in the broad area of the computational modelling of dynamical systems, such systems ranging in scale from computer simulation of the motion of atoms and molecules to the modelling of celestial mechanics. This involves the development of appropriate numerical methods to solve the system of equations driving the dynamics. It is desirable to develop approximation schemes that preserve important qualitative features, so-called geometric integrators, and this has been the focus of much of my work. Of particular importance in this regard are the symplectic integrators for Hamiltonian systems which preserve the symplectic structure of phase space and have superior stability properties, particularly for long time computations.

While many of my articles are related to Hamiltonian systems and the development of geometry-preserving integration methods, I have lately been more focussed on stochastic differential equations. Results in this direction have been obtained on both formulation and numerical solution of SDE models for thermodynamic modelling, including proving the ergodicity of degenerate diffusion techniques and studying the perturbation of dynamics by stochastic methods. Most recently, I have focused on the design of Langevin dynamics integration strategies, including the construction of superconvergent Langevin dynamics methods for invariant measures relevant for molecular dynamics.

From 2009 to present I have been heavily involved with the EPSRC (Science and Innovation) Centre for Numerical Algorithms and Intelligent Software (NAIS) which links Edinburgh, Heriot-Watt and Strathclyde Universities.

In addition to NAIS, I have an ERC-funded collaboration in Biological Modelling with V. Danos in Informatics, and I am part of the ExTASY Project (Extensible Toolkit for Advanced Sampling and analYsis) which is cofunded by the UK’s EPSRC and the US NSF to develop advanced methods for the study of biological molecular energy surfaces.

** Associations, Positions, Roles**

2014-15 IMA Leslie Fox Prize Adjudication Committee

2014-- Fellow of the Royal Society of Edinburgh (FRSE)

2012-- Fellow of the Institute of Mathematics and its Applications (FIMA)

2012-- Co-Director, Maxwell Institute for Mathematical Sciences

2012 Senior Research Fellow, Netherlands Science Foundation

2011 JT Oden Fellowship, University of Texas

2009 - Member, Steering Committee of the Centre for Numerical Algorithms (NAIS)

2009 -11 Director, NAIS

2009 SIAM Dahlquist Prize Selection Committee

2008 -11 Deputy Director, Maxwell Institute for Mathematical Sciences

2007-- Member, Board of the International Centre for Mathematical Sciences (ICMS)

2007-- Member, Programme Committee, ICMS

2004-5 Leverhulme Trust Research Fellow

2004-5 Visiting Researcher, Institute for Mathematics and Its Applications, Minneapolis

1998 Member, Mathematical Sciences Research Insitute, Berkeley

1996-7 Visiting Researcher, Cambridge University

** Editorial Boards**

2014-- Proceedings of the Royal Society A

2012-- Journal of Computational Dynamics (AIMS)

2009-13 Nonlinearity

2009-13 SIAM Journal on Numerical Analysis

2008-- IMA Journal on Numerical Analysis

2001-7 SIAM Journal on Scientific Computing

**Major Grants and Projects **

2013 -- 2016 NSF-EPSRC SI2-CHE:ExTASY Extensible Tools for Advanced Sampling and analYsis

2013 -- 2018 ERC Advanced Grant in Ruled-Based Modelling for Biology

2009 -- 2014 EPSRC (S&I)/SFC Numerical Algorithms and Intelligent Software for the Evolving HPC Platform

2008 -- 2010 EPSRC Network (Bath, Bristol, Edinburgh, Warwick) “Mathematical Challenges of Molecular Dynamics”

2004 -- 2007 Australian RC Geometric Integration

2004 US NIH Algorithms for Macromolecular Modelling

2004 -- 2005 EPSRC Algorithms for Macromolecular Modelling

2004 -- 2007 EPSRC Developing an Efficient Method for Locating Periodic Orbits

2003 -- 2005 SRIF Advanced Computing Facility (HPC)

2002 -- 2004 Australian RC Geometric Numerical Integration

2001 -- 2004 EPSRC A Mixed Atomistic and Continuum Model for Crossing Multiple Length and Time Scales

2001 -- 2004 EPSRC Geometric Integrators for Switched and Multiple Time-scale Dynamics

2000 -- 2004 EU Research Training Network MASIE (Mechanics and Symmetry in Europe)

1994 -- 99 Multiple grants awarded whilst at the University of Kansas, mostly by US National Science Foundation

Conferences and Workshops* [examples]*

Principal Organiser of the inaugural conference in 1994 of the series on Algorithms for Macromolecular Modelling (AM3) in Lawrence, Kansas, followed by service on the Organising Committee for subsequent meetings in the series (Berlin, 1997; New York City, 2000; Leicester 2004 as Principal Organiser; Austin, 2009)

Organising Committee, LMS Durham Symposium, 2000

Co-Organiser, Advanced Integration Methods for Molecular Dynamics, CECAM, Lyon, 2000

Scientific Committee, Prestissimo/DFG Conference on Molecular Simulation, Inst. Henri Poincaré, Paris, 2004

Co-Organiser, Workshop on Astrophysical N-body Problems, Inst. for Pure and Applied Mathematics, UCLA, 2005

Co-Organiser, The Interplay between Mathematical Theory and Applications, Newton Institute, 2007

Co-Organiser, NSF-NAIS Workshop on Intelligent Software, Edinburgh 2009

Co-Organiser, Capstone Conference, EPSRC Conference on Challenges in Scientific Computing, Warwick 2009

Principal Organiser, Multiscale Molecular Modelling, Edinburgh, 2010

Principal Organiser, State-of-the-art Algorithms for Molecular Dynamics, Edinburgh 2012

Co-organiser, Complex Molecular Systems, Lorentz Center, Leiden, 2012

Organiser, Multiscale Computational Methods in Materials Modelling, Edinburgh 2014

** Books**

* Molecular Dynamics* (Springer, in press) one of the first mathematical books on the subject.

* Simulating Hamiltonian Dynamics * (Cambridge University Press, 2005), co-authored with S. Reich (Potsdam) is an introduction to the subject of Geometric Integration for undergraduate and graduate students in mathematics and cognate disciplines.

** Selected Articles**

- Symplectic numerical integrators in contrained Hamiltonian systems (with R.D. Skeel), J. Comput. Phys. 112 (1994), 117-125.
- Integration methods for molecular dynamics (with S. Reich and R.D. Skeel), IMA Vol. Math. Appl. 82 (1996), 161-185.
- Symplectic methods for conservative multibody systems (with E. Barth), Fields Inst. Comm. 10 (1996), 25-43.
- The adaptive Verlet method (with W. Huang), SIAM J. Sci. Comput. 18 (1997), 239-256.
- Time-transformations for reversible variable stepsize integration (with S.D. Bond), Numer. Algorithms 19 (1998), 55-71.
- Comparison of geometric integrators for rigid body simulation, Lect. Notes Comput. Sci. Eng. 4 (1999), 349-362.
- The Nosé-Poincaré method for constant temperature molecular dynamics (with S.D.Bond and B.B. Laird), J. Comput. Phys 151 (1999), 114-134.
- Asymptotic error analysis of the adaptive Verlet method (with S. Cirilli and E. Hairer), BIT 39 (1999), 25-33.
- Explicit variable step-size and time-reversible integration (with T. Holder and S. Reich), Appl. Numer. Math 39 (2001), 367-377
- An efficient multiple time-scale reversible integrator for the gravitational N-body problem, Appl. Numer. Math. 43 (2002), 175-190.
- On the approximation of the Feynman-Kac path intergral (with B.B. Laird), J. Comput. Phys. 185 (2003), 472-483.
- The canonical ensemble via symplectic integration using Nosé and Nosé-Poincaré chains (with C. Sweet), J. Chem. Phys. 121 (2004), 108-116.
- Molecular dynamics and the accuracy of numerically computed averages (with. S.D. Bond), Acta Numer. 16 (2007), 1-65.
- Molecular simulation in the canonical ensemble and beyond (with Z. Jia), Math. Model. Numer. Anal. 41 (2007), 333-350.
- Stabilized integration of Hamiltonian systems with hard-sphere inequality constraints (with S.D. Bond), SIAM J. Sci. Comput. 30 (2007/2008), 134-147.
- Simplified modelling of a thermal bath, with applications to a fluid vortex system (with S. Dubinskina and J. Frank), Multiscale Model Simul. 8 (2010), 1182-1902.
- Comparing the efficiencies of stochastic isothermal molecular dynamics methods (with E. Noorizadeh and O. Penrose), J. Stat. Phys. 143 (2011), 921-942.1572-9613.
- Dimensional reductions for the computation of time-dependent quantum expectations (with G. Mazzi), SIAM J. Sci. Comput. 33 (2011), 2024-2038.
- Robust and efficient configurational molecular sampling via Langevin Dynamics (with C. Matthews), J. Chem. Phys., published online 1 May 2013 (Vol.138, Issue 17).
- Rational construction of stochastic numerical methods for molecular sampling (with C. Matthews), Applied Mathematics Research Express, 2013, (2013), 34-56.
- On the long-time integration of stochastic gradient systems (with C. Matthews and M. Tretyakov), Proceedings of the Royal Society A, 470 (2014) 20140120

My group's work is performed in collaboration with researchers in other areas of mathematics (numerical analysis, probability theory, analysis) and also with scientists and engineers. This broad-based approach combines model development with simulation and rigorous numerical analysis. Our goal is to use the flexibility of our toolset to expand understanding of algorithms without much regard to whether or not the approach taken fits a particular formalism or mathematical school. We always appreciate the elegance that only a full mathematical theory can provide, but at the same time we are pragmatic: there are many problems which cannot be resolved in complete rigor using current theories. In these cases the boundaries of knowledge can usually still be explored using computational experiments on carefully chosen model problems. We use painstaking numerical testing to formulate conjectures which can later be subjects of in-depth mathematical study.

A few links to collaborators (former and future), ex-students/postdocs, other research colleagues and friends:

Assyr Abdulle (EPFL, Lausanne)

Teijo Arponen (Aalto, Finland)

Eric Barth (Kalamazoo)

Noam Bernstein (Naval Research Lab)

Stephen Bond (Sandia, New Mexico)

Nawaf Bou-Rabee (Rutgers)

Chris Budd (Bath)

Giovanni Ciccotti (Dublin/Rome)

Gabor Csanyi (Cambridge)

Vincent Danos (Edinburgh/Paris)

Carl Dettmann (Bristol)

Ron Elber (Texas)

Jason Frank (CWI-Amsterdam)

Gero Friesecke (Munich)

Martin Hairer (Warwick)

Ernst Hairer (Geneva)

Arieh Iserles (Cambridge)

George Karniadakis (Brown)

Markos Katsoulakis (Amherst)

Claude Lebris (ENPC, Paris)

Frederic Legoll (ENPC, Paris)

Tony Lelievre (ENPC, Paris)

Mitch Luskin (Minnesota)

Charles Matthews (Chicago)

Houman Owhadi (Caltech)

Greg Pavliotis (Imperial)

Oliver Penrose (Heriot-Watt)

Petr Plechac (Delaware)

Sebastian Reich (Potsdam)

Christof Schuette (Berlin)

Robert Skeel (Purdue)

Gabriel Stoltz (ENPC, Paris)

Amos Storkey (Edinburgh)

Andrew Stuart (Warwick)

Chris Sweet (Notre Dame)

Florian Theil (Warwick)

Michael Tretyakov (Leicester)

Mark Tuckerman (NYU)

Eric Vanden-Eijnden (NYU)

Jonathan Weare (Chicago)

Jonannes Zimmer (Bath)

Teijo Arponen (Aalto, Finland)

Eric Barth (Kalamazoo)

Noam Bernstein (Naval Research Lab)

Stephen Bond (Sandia, New Mexico)

Nawaf Bou-Rabee (Rutgers)

Chris Budd (Bath)

Giovanni Ciccotti (Dublin/Rome)

Gabor Csanyi (Cambridge)

Vincent Danos (Edinburgh/Paris)

Carl Dettmann (Bristol)

Ron Elber (Texas)

Jason Frank (CWI-Amsterdam)

Gero Friesecke (Munich)

Martin Hairer (Warwick)

Ernst Hairer (Geneva)

Arieh Iserles (Cambridge)

George Karniadakis (Brown)

Markos Katsoulakis (Amherst)

Claude Lebris (ENPC, Paris)

Frederic Legoll (ENPC, Paris)

Tony Lelievre (ENPC, Paris)

Mitch Luskin (Minnesota)

Charles Matthews (Chicago)

Houman Owhadi (Caltech)

Greg Pavliotis (Imperial)

Oliver Penrose (Heriot-Watt)

Petr Plechac (Delaware)

Sebastian Reich (Potsdam)

Christof Schuette (Berlin)

Robert Skeel (Purdue)

Gabriel Stoltz (ENPC, Paris)

Amos Storkey (Edinburgh)

Andrew Stuart (Warwick)

Chris Sweet (Notre Dame)

Florian Theil (Warwick)

Michael Tretyakov (Leicester)

Mark Tuckerman (NYU)

Eric Vanden-Eijnden (NYU)

Jonathan Weare (Chicago)

Jonannes Zimmer (Bath)

*Books:*

Simulating Hamiltonian Dynamics, B. Leimkuhler and S. Reich, Cambridge University Press, 2005.

*Papers*

1 Efficient molecular dynamics using geodesic integration and solvent-solute splitting

B. Leimkuhler and C. Matthews,

Proceedings of the Royal Society A, 472: , 2016. JOURNAL WEB

2 A stochastic algorithm for the isobaric-isothermal ensemble with Ewald summations for all long range forces

M. Di Pierro, R. Elber,and B. Leimkuhler,

Journal of Chemical Theory and Compuitation, to appear: 5624-5637, 2015. JOURNAL WEB

3 Covariance-controlled adaptive Langevin thermostat for large-scale Bayesian sampling

X. Shang, Z. Zhu, B. Leimkuhler and A. Storkey,

Advances in Neural Information Processing Systems (NIPS 2015), 28: Preprint(2015) . WEB

4 Extended Hamiltonian approach to continuous tempering

G. Gobbo and B. Leimkuhler,

Phys Rev E, 91: 61301, 2015. JOURNAL WEB

5 Adaptive Thermostats for Noisy Gradient Systems

B. Leimkuhler and X. Shang,

SIAM Journal on Scientific Computing, 38: Preprint(2015) . WEB

6 Least-biased correction of extended dynamical systems using observational data

K. Myerscough, J. Frank, and B. Leimkuhler, Preprint(2014) . WEB

7 Direct control of the small-scale energy balance in 2D fluid dynamics

J. Frank, B. Leimkuhler and K. Myerscough,

Journal of Fluid Mechanics, 782: 240-259, 2015. JOURNAL WEB

8 The Adaptive Buffered Force QM/MM method in the CP2K and Amber software packages

L. Mones, A. Jones, A. Götz, T. Laino, R. Walker, B. Leimkuhler, G. Csànyi, and N. Bernstein,

Journal of Computational Chemistry, 36: 633-648, 2015. JOURNAL WEB

9 Numerical simulations of nonlinear modes in mica: past, present and future

J. Bajars, C. Eilbeck and B. Leimkuhler,

in Quodons in Mica:
Nonlinear Localized Travelling Excitations in Crystals; Springer Series in Materials Science Vol 221, 35-67, 2015. JOURNAL WEB

10 Nonlinear propagating localized modes in a 2D hexagonal crystal lattice

J. Bajars, C. Eilbeck and B. Leimkuhler,

Physica D, 301-302: 8-20, 2015. JOURNAL WEB

11 On the numerical treatment of dissipative particle dynamics and related systems

B. Leimkuhler and X. Shang,

Journal of Computational Physics, 280: 72-95, 2015. JOURNAL WEB

12 On the long-time integration of stochastic gradient systems

B. Leimkuhler, C. Matthews and M. Tretyakov,

Proceedings of the Royal Society A, 470: 20140120, 2014. JOURNAL WEB

13 The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics

B. Leimkuhler, C. Matthews and G. Stoltz,

IMA Journal on Numerical Analysis, , 2015. JOURNAL PDF WEB

14 Robust and efficient configurational molecular sampling via Langevin Dynamics

B. Leimkuhler and C. Matthews,

Journal of Chemical Physics, 138: 174102, 2013. JOURNAL PDF WEB

15 Stochastic resonance-free multiple time-step algorithm for molecular dynamics with very large time steps

B. Leimkuhler, D. Margul and M. Tuckerman,

Molecular Physics, 111: 3579-3594, 2013. JOURNAL PDF WEB

16 Weakly coupled heat bath models for Gibbs-like invariant states in nonlinear wave equations

J. Bajars, J. Frank and B. Leimkuhler,

Nonlinearity, 26: 1945-1973, 2013. JOURNAL PDF

17 Rational construction of stochastic numerical methods for molecular sampling

B. Leimkuhler and C. Matthews,

Applied Mathematics Research Express, 2013: 34-56, 2013. JOURNAL PDF WEB

18 Comparing the efficiencies of stochastic isothermal molecular dynamics methods

B. Leimkuhler, E. Noorizadeh and O. Penrose,

Journal of Statistical Physics, 143: 921-942, 2011. JOURNAL PDF

19 Adaptive stochastic methods for sampling driven molecular systems

A. Jones and B. Leimkuhler,

Journal of Chemical Physics, 135: 84125, 2011. JOURNAL

20 Dimensional reductions for the computation of time-dependent quantum expectations

B. Leimkuhler and G. Mazzi,

SIAM Journal on Scientific Computing, 33: 2024-2038, 2011. JOURNAL

21 Stochastic-dynamical thermostats for constraints and stiff restraints

J. Bajars, J. Frank and B. Leimkuhler,

The European Physical Journal, 200: 131-152, 2011. JOURNAL PDF

22 Simplified modelling of a thermal bath, with application to a fluid vortex system

S. Dubinkina, J. Frank, and B. Leimkuhler,

SIAM Multiscale Modelling and Simulation, 8: 1882-1901, 2010. JOURNAL PDF

23 Generalized Bulgac-Kusnezov methods for sampling of the Gibbs-Boltzmann measure

B. Leimkuhler,

Physical Review E, 81: 26703, 2010. JOURNAL PDF

24 A gentle stochastic thermostat for molecular dynamics

B. Leimkuhler, E. Noorizadeh and F. Theil,

Journal of Statistical Physics, 135: 261-277, 2009. JOURNAL PDF

25 A Metropolis-adjusted Nose-Hoover thermostat

B. Leimkuhler and S. Reich,

ESAIM:Mathematical modelling and numerical analysis, 43: 743-755, 2009. JOURNAL PDF

26 A temperature control technique for nonequilibrium molecular simulation

B. Leimkuhler, F. Legoll and E. Noorizadeh,

Journal of Chemical Physics, 128: 74105, 2008. JOURNAL PDF

27 Molecular dynamics and the accuracy of numerically computed averages

S. Bond and B. Leimkuhler,

Acta Numerica, 16: 1-65, 2007. JOURNAL PDF

28 Stabilized integration of Hamiltonian systems with hard-sphere inequality constraints

S. Bond and B. Leimkuhler,

SIAM Journal on Scientific Computing, 30: 134-147, 2007. JOURNAL PDF

29 Molecular simulation in the canonical ensemble and beyond

Z. Jia and B. Leimkuhler,

ESAIM:Mathematical modelling and numerical analysis, 41: 333-350, 2007. JOURNAL

30 Rapid thermal equilibration of coarse-grained molecular dynamics

S. Gill, Z. Jia, B. Leimkuhler and A. Cocks,

Physical Review B, 73: 184304, 2006. JOURNAL PDF

31 Geometric integrators for multiple timescale simulation

Z. Jia and B. Leimkuhler,

Journal of Physics A, 39: 5379-5403, 2006. JOURNAL

32 Approach to thermal equilibrium in biomolecular simulation

E. Barth, B. Leimkuhler, and C. Sweet,

New Algorithms for Macromolecular Simulation (Springer Lecture Notes in Computational Science and Engineering), 49: 125-140, 2006. JOURNAL PDF

33 A projective thermostatting technique

Z. Jia and B. Leimkuhler,

SIAM Multiscale Modelling and Simulation, 4: 563-583, 2005. JOURNAL PDF

34 A Hamiltonian formulation for recursive multiple thermostats in a common timescale

B. Leimkuhler and C. Sweet,

SIAM Journal on Applied Dynamical Systems, 4: 187-216, 2005. JOURNAL PDF

35 An efficient geometric integrator for thermostatted anti-/ferromagnetic Models

T. Arponen and B. Leimkuhler,

BIT Numerical Mathematics, 44: 403-424, 2004. JOURNAL PDF

36 The canonical ensemble via symplectic integration using Nose and Nose-Poincare chains

B. Leimkuhler and C. Sweet,

Journal of Chemical Physics, 121: 108-117, 2004. JOURNAL PDF

37 A parallel multiple time-scale reversible integrator for dynamics simulation

Z. Jia and B. Leimkuhler,

Future Generation Computer Systems, 19: 415-424, 2003. JOURNAL PDF

38 Generating generalized distributions from dynamical simulation

E. Barth, B. Laird and B. Leimkuhler,

Journal of Chemical Physics, 118: 5759-5769, 2003. JOURNAL PDF

39 Generalized dynamical thermostatting technique

B. Laird and B. Leimkuhler,

Physical Review E 68, 016704 (2003), 68: 16704, 2003. JOURNAL PDF

40 On the approximation of Feynman-Kac path integrals

S. Bond, B. Laird, and B. Leimkuhler,

Journal of Computational Physics, 185: 472-483, 2003. JOURNAL PDF

41 An efficient multiple time-scale reversible integrator for the gravitational N-body problem

B. Leimkuhler,

Applied Numerical Mathematics, 43: 175-190, 2002. JOURNAL PDF

42 A separated form of Nosé dynamics for constant temperature and pressure simulation

B. Leimkuhler,

Computer Physics Communications, 148: 206-213, 2002. JOURNAL PDF

43 A test set for molecular dynamics

E. Barth, B. Leimkuhler, and S. Reich,

Lecture Notes in Computational Science and Engineering, 24: 73-103, 2002. JOURNAL PDF

44 A reversible averaging integrator for multiple timescale dynamics

B. Leimkuhler and S. Reich,

Journal of Computational Physics, 171: 95-114, 2001. JOURNAL PDF

45 Explicit, time-reversible and variable stepsize integration

T. Holder, B. Leimkuhler, and S. Reich,

Applied Numerical Mathematics, 39: 367-377, 2001. JOURNAL PDF

46 Scaling invariance and adaptivity

C. Budd, B. Leimkuhler and M. Piggott,

Applied Numerical Mathematics, 39: 261-288, 2001. JOURNAL PDF

47 Molecular dynamics algorithms for mixed hard-core/continuous potentials

Y. Houndonougbo, B. Laird, and B. Leimkuhler,

Journal of Molecular Physics, 98: 309-316, 2000. JOURNAL PDF

48 A time-reversible, regularized, switching integrator for the N-body problem

A. Kvaerno and B. Leimkuhler,

SIAM Journal on Scientific Computing, 22: 1016-1035, 2000. JOURNAL PDF

49 Geometric integrators based on scaling and switching

B. Leimkuhler,

Proceedings of the Equadiff Conference (Berlin, 1999), World Scientific, Preprint(2000) . PDF

50 A Semi-explicit, variable-stepsize integrator for constrained dynamics

E. Barth, B. Leimkuhler, and S. Reich,

SIAM Journal on Scientific Computing, 21: 1027-1044, 1999. JOURNAL PDF

51 Reversible adaptive regularization: perturbed Kepler motion and classical atomic trajectories

B. Leimkuhler,

Philosophical Transactions of the Royal Society of London A, 357: 1101-1134, 1999. JOURNAL PDF

52 Reversible adaptive regularization methods for atomic N-body problems in applied fields

B. Leimkuhler,

Applied Numerical Mathematics, 29: 31-43, 1999. JOURNAL PDF

53 Asymptotic error analysis of the Adaptive Verlet method

S. Cirilli, E. Hairer and B. Leimkuhler,

BIT Numerical Mathematics, 39: 25-33, 1999. JOURNAL PDF

54 The Nose-Poincare method for constant temperature molecular dynamics

S. Bond, B. Leimkuhler and B. Laird,

Journal of Computational Physics, 151: 114-134, 1999. JOURNAL PDF

55 Timestep acceleration of waveform relaxation

B. Leimkuhler,

SIAM Journal on Numerical Analysis, 35: 31-50, 1998. JOURNAL PDF

56 Symplectic methods for rigid body dynamics

B. Leimkuhler,

in Computational Molecular Dynamics: Challenges, Methods, Ideas, Springer Lecture Notes in Computational Science and Engineering, 4: , 1998. JOURNAL

57 Time transformations for reversible variable stepsize integration

S. Bond and B. Leimkuhler,

Numerical Algorithms, 19: 55-71, 1998. JOURNAL

58 The Adaptive Verlet method

W. Huang and B. Leimkuhler,

SIAM Journal on Scientific Computing, 18: 239-256, 1997. JOURNAL PDF

59 Geometric integrators for classical spin systems

J. Frank, W. Huang and B. Leimkuhler,

Journal of Computational Physics, 133: 160-172, 1997. JOURNAL PDF

60 Split-Hamiltonian methods for rigid body molecular dynamics

A. Dullweber, B. Leimkuhler and R. McLachlan,

Journal of Chemical Physics, 107: 5840-5851, 1997. JOURNAL PDF

61 A symplectic method for rigid-body molecular simulation

A. Kol, B. Laird and B. Leimkuhler,

Journal of Chemical Physics
, 107: 2580–2588, 1997. JOURNAL

62 Integration Methods for Molecular Dynamics

B. Leimkuhler, S. Reich and R.D. Skeel,

in IMA Volumes in Mathematics and Its Applications, Springer-Verlag, 82: , 1997. JOURNAL

63 A symplectic integrator for Riemannian manifolds

B. Leimkuhler and G. Patrick,

Journal of Nonlinear Science, 6: 367-384, 1996. JOURNAL PDF

64 Orthosymplectic integration of linear Hamiltonian systems

B. Leimkuhler and E. Van Vleck,

Numerische Mathematik, 77: 269-282, 1996. JOURNAL PDF

65 Symplectic Methods for Conservative Multibody Systems

E. Barth and B. Leimkuhler,

Communications of the Fields Institute , 10: 25-43, 1996. JOURNAL

66 Algorithms for constrained molecular dynamics

E. Barth, K. Kuczera, B. Leimkuhler and R. Skeel,

Journal of Computational Chemistry, 16: 1192-1209, 1995. JOURNAL PDF

67 Symplectic integration of constrained Hamiltonian systems

B. Leimkuhler and S. Reich,

Mathematics of Computation, 63: 589-605, 1994. JOURNAL PDF

68 Symplectic numerical integrators in constrained Hamiltonian systems

B. Leimkuhler and R. Skeel,

Journal of Computational Physics, 112: 117-125, 1994. JOURNAL PDF

69 Estimating waveform relaxation convergence

B. Leimkuhler,

SIAM Journal on Scientific Computing, 14: 872-889, 1993. JOURNAL PDF

70 Relaxation Techniques in Multibody Dynamics

B. Leimkuhler,

Transactions of the Canadian Society of Mechanical Engineering, 17: 459-471, 1993. JOURNAL

71 Rapid Convergence of Waveform Relaxation

B. Leimkuhler and A. Ruehli,

Applied Numerical Mathematics, 11: 211-224, 1993. JOURNAL

72 Dynamic Iteration Schemes for Differential-Algebraic Equations in Large Scale Circuit Simulation

B. Leimkuhler,

Proceedings of the Conference on Computational Ordinary Differential Equations(London, 1990), IMA, 39: Preprint(1992) .

73 Waveform Relaxation for Linear RC-Circuits

B. Leimkuhler, U. Miekkala and O.Nevanlinna,

IMPACT of Computing in Science and Engineering, 3: 123-145, 1991. JOURNAL

74 Differentiation of Constraints in Differential-Algebraic Equations

S.L. Campbell and B. Leimkuhler,

Mechanics of Structures and Machines, 19: 19-39, 1991. JOURNAL

75 Numerical solution of differential-algebraic equations for constrained mechanical motion

C. Fuehrer and B. Leimkuhler,

Numerische Mathematik, 59: 55-69, 1991. JOURNAL PDF

76 Formulation and Numerical Solution of the Equations of Constrained Mechanical Motion

C. Fuehrer and B. Leimkuhler,

Proceedings of NUMDIFF-5 (Halle, 1989), Teubner- Texte in Mathematics, 121: , 1991. JOURNAL

77 Approximation Methods for the Consistent Initialization of Differential Algebraic Equations

B. Leimkuhler, L.R.Petzold and C.W. Gear,,

SIAM Journal on Numerical Analysis, 28: 205-226, 1991. JOURNAL

78 A New Class of Generalized Inverses for Discretized Euler-Lagrange Equations

C. Fuehrer and B. Leimkuhler,

in NATO Advanced Research Workshop on Real-Time Integration Methods for Mechanical System Simulation, Springer, , 1990. JOURNAL

79 Automatic integration of Euler-Lagrange equations with constraints

C.W. Gear, B. Leimkuhler, G.K. Gupta,

Journal of Computational and Applied Mathematics, 12-13: 77-90, 1985. JOURNAL PDF