General
Sampling
Integrators
Fast Force Evaluation
Parallelism and Software
KSSM05
L.V. Kale, K. Schulten, R.D. Skeel, G. Martyna, M. Tuckerman,
J.C. Phillips, S. Kumar, and G. Zheng,
Biomolecular modeling using parallel supercomputers,
In S. Aluru, editor,
Handbook of Computational Molecular Biology
pages 34-1 to 34-43, Chapman & Hall/CRC Press, 2005.
SkTu05
R. D. Skeel, P. Tupper, et al,
Mathematical Issues in Molecular Dynamics,
BIRS report, 2005.
PDF
SSBK99
T. Schlick, R. D. Skeel, A. T. Brunger, L. V. Kale, J. A. Board, Jr.,
J. Hermans and K. Schulten,
Algorithmic Challenges in Computational Molecular Biophysics,
J. Comput. Phys., 151:9-48, 1999.
DHLM98
P. Deuflhard, J. Hermans, B. Leimkuhler, A. Mark, S. Reich, R. D.
Skeel, editors,
Computational Molecular Dynamics: Challenges, Methods, Ideas,
Volume 4 of Lecture Notes in Computational Science and Engineering,
Springer-Verlag, November 1998.
BKSS94
J. A. Board Jr., L. V. Kale, K. Schulten, R. D. Skeel and T. Schlick,
Modeling Biomolecules: Larger Scales, Longer Durations,
IEEE Computational Science & Engineering, 1:19-30, 1994.
Back to Top
SHSI0y
C. R. Sweet, S. S. Hampton, R. D. Skeel, and J. A. Izaguirre,
Separable Shadow Hamiltonian Hybrid Monte Carlo Method,
preprint, 2009.
PDF
ZoSk03
G. Zou and R. D. Skeel,
Robust Biased Brownian Dynamics for Rate Constant Calculation,
Biophys. J., 85(4), 2147-2157, 2003.
PDF
ZoSk04
G. Zou and R. D. Skeel,
Robust Variance Reduction for Random Walk Methods,
SIAM J. Sci. Comput., 25(6), 1964-1981, 2004.
PDF
ZoSS00
G. Zou, R. D. Skeel and S. Subramaniam,
Biased Brownian Dynamics for Rate Constant Calculation,
Biophys. J. 79(2), 638-645, 2000.
PDF
Back to Top
BoSk08
S. D. Bond and R. D. Skeel,
Bias in Molecular Dynamics Averages due to Finite Step Size,
section of BIRS report, 2008.
PDF
Skee08
R. D. Skeel,
Supplement to "What Makes Molecular Dynamics Work?",
manuscript, Sep 6, 2008.
PDF
Skee09
R. D. Skeel,
What Makes Molecular Dynamics Work?,
SIAM J. Sci. Comput., 31, 1363-1378, 2009.
PDF
HaMS0x
E. Hairer, R. McLachlan, and R. D. Skeel,
On Energy Conservation of the Simplified Takahashi-Imada Method,
Math. Modelling Numer. Anal., in press.
PDF (3 Mb)
SkHP07
R. D. Skeel, D. J. Hardy, and J. C. Phillips,
Correcting Mesh-Based Force Calculations to
Conserve Both Energy and Momentum in Molecular Dynamics Simulations,
J. Comput. Phys., 225(1), 1-5, 2007.
PDF
EnSD05
R. D. Engle, R. D. Skeel, and M. Drees,
Monitoring Energy Drift with Shadow Hamiltonians,
J. Comput. Phys., 206(2), 432-452, 2005.
PDF
WaSk04
W. Wang and R. D. Skeel,
Comment on the Accuracy of
Numerical Integration Methods for the Langevin Equation,
manuscript, 2004.
Postscript
Engl03
R. D. Engle,
Interpolated Modified Hamiltonians,
M.S. thesis, Department of Computer Science, University of Illinois at
Urbana-Champaign, 2003.
Postscript (5 Mb)
MaIS03
Q. Ma, J. Izaguirre, and R. D. Skeel,
Verlet-I/r-RESPA Is Limited by Nonlinear Instability,
SIAM J. Sci. Comput., 24(6), 1951-1973, 2003.
PDF
SkIz02
R. D. Skeel and J. Izaguirre,
An Impulse Integrator for Langevin Dynamics,
Mol. Phys.,
100, 3885-3891, 2002.
PDF
WaSk03
W. Wang and R. D. Skeel,
Analysis of
a Few Numerical Integration Methods for the Langevin Equation,
Mol. Phys., 101(14), 2149-2156, 2003.
PDF
Wang01
W. Wang,
Analysis of a Few Numerical Integration Methods for the Langevin Equation,
M.S. thesis, Department of Computer Science, University of Illinois at
Urbana-Champaign, 2001.
Postscript
SkHa01
R. D. Skeel and D. J. Hardy,
Practical Construction of Modified Hamiltonians,
SIAM J.Sci. Comput., 23(4):1172-1188, 2001.
PDF
ICWS00
J. A. Izaguirre, D. P. Catarello, J. M. Wozniak, and R. D. Skeel,
Langevin Stabilization of Molecular Dynamics,
J. Chem. Phys., 114(4), 2090-2098, 2000.
PDF
SkSr00
R. D. Skeel and K. Srinivas,
Nonlinear Stability Analysis of Area-Preserving Integrators,
SIAM J. Numer. Anal., 38(1):129-148, 2000.
IzRS99
J. Izaguirre, S. Reich and Robert D. Skeel,
Longer Time Steps for Molecular Dynamics,
J. Chem. Phys., 110(19):9853-9864, 1999.
PDF
Skee99b
R. D. Skeel,
Integration Schemes for Molecular Dynamics and Related Applications,
In M. Ainsworth and J. Levesley and M. Marletta editors,
The Graduate Student's Guide to Numerical Analysis, SSCM, pages
119-176, Springer-Verlag, 1999
PDF preprint
HaOS99
D. J. Hardy and D. I. Okunbor and R. D. Skeel,
Symplectic Variable Stepsize Integration for N-Body Problems,
Appl. Numer. Math. 29:19-30, 1999.
PDF
Skee99a
R. D. Skeel,
Symplectic Integration with Floating-Point Arithmetic and Other Approximations,
Appl. Numer. Math. 29:3-18, 1999.
PDF
Skee98
R. D. Skeel,
Comments on Numerical Instability due to Varying Time Steps in Explicit Wave
Propagation and Mechanics Calculations by Joseph P. Wright,
J. Comput. Phys., 145 (758-759), 1998.
GaSS98b
B. Garcia-Archilla and J. M. Sanz-Serna and R. D. Skeel,
Long-Time-Step Methods for Oscillatory Differential Equations,
SIAM J. Sci. Comput., 20(3):930-963, 1998.
PDF
SkIz98
R. D. Skeel and J. Izaguirre,
The Five Femtosecond Time Step Barrier, in P. Deuflhard, J. Hermans, B.
Leimkuhler, A. Mark, S. Reich, R. D. Skeel editors,
Computational Molecular Dynamics: Challenges, Methods, Ideas, Volume
4 of Lecture Notes in Computational Science and Engineering, Pages 303-318,
Springer-Verlag, Nov 1998.
SMSS98
T. Schlick, M. Mandziuk, R. D. Skeel and K. Srinivas,
Nonlinear Resonance Artifacts in Molecular Dynamics Simulations,
J. Comput. Phys., 139:1-29, 1998.
GaSS98a
B. Garcia-Archilla and J. M. Sanz-Serna and Robert D. Skeel,
The Mollified Impulse Method for Oscillatory Differential Equations, in D. F.
Griffiths and G. A. Watson editors,
Numerical Analysis 1997, pages 111-123, London, 1998.
ZhSk97
M. Zhang and R. D. Skeel,
Cheap Implicit Symplectic Integrators,
Appl. Num. Math., 25:297-302, 1997.
Postscript
BiSS97
T. Bishop and Robert D. Skeel and K. Schulten,
Difficulties with Multiple Timestepping and the Fast Multipole Algorithm in
Molecular Dynamics,
J. Comp. Chem., 18(14):1785-1791, 1997.
PDF
LiSZ97
T. R. Littell, R. D. Skeel and M. Zhang,
Error Analysis of Symplectic Multiple Time Stepping,
SIAM J. Numer. Anal., 34(5):1792-1807, 1997.
SkZS97
R. D. Skeel, G. Zhang and T. Schlick,
A family of symplectic integrators: stability, accuracy, and molecular dynamics
applications,
SIAM J. Sci. Comput., 18:203-222, 1997.
PDF
LoSS97
M. Lopez-Marcos, J. M. Sanz-Serna and R. D. Skeel,
Explicit Symplectic Integrators Using Hessian-Vector Products,
SIAM J. Sci. Comput., 18:223-238, 1997.
PDF
LoSS96b
M. Lopez-Marcos, J. M. Sanz-Serna and R. D. Skeel,
Explicit Symplectic Integrators with Maximal Stability Intervals, In D. F.
Griffiths and G. A. Watson editors,
Numerical Analysis, A. R. Mitchell 75th Birthday Volume, pages 163-176,
World Scientific, Singapore, 1996.
LoSS96a
M. Lopez-Marcos and J. M. Sanz-Serna and R. D. Skeel,
Cheap Enhancement of Symplectic Integrators, in D. F. Griffiths and G. A.
Watson editors,
Numerical Analysis 1995, pages 107-122, London, 1996, Longman Group.
Reic96
S. Reich,
Enhancing Energy Conserving Methods,
BIT Numer.Math., 36:122-134, 1996.
LeRS96
B. J. Leimkuhler and S. Reich and R. D. Skeel,
Integration methods for molecular dynamics, in Jill P. Mesirov, Klaus Schulten,
De Witt Sumners, editors,
Mathematical Approaches to Biomolecular Structure and Dynamics,
Vol. 82 of IMA Volumes in Mathematics and its Applications, pages
161-185, Springer-Verlag , 1996.
ZhSk95
M. Q. Zhang and R. D. Skeel,
Symplectic Integrators and the Conservation of Angular Momentum,
J. Comput. Chem., 16:365-369, 1995.
Zhan95
M. Q. Zhang,
Stabilization of the Stormer/Verlet Method,
Manuscript, July 28, 1995.
Skee95
R. D. Skeel,
Numerical Hamiltonian Problems (J. M. Sanz-Serna and M. P. Calvo),
SIAM Review, 37(2), 1995.
Reic95
S. Reich,
Smoothed Dynamics of Highly Oscillatory Hamiltonian Systems,
Physica D, 89(1 and 2): 28-42, 1995.
BKLS95
E. Barth, K. Kuczera, B. Leimkuhler and R. D. Skeel,
Algorithms for Constrained Molecular Dynamics,
J. Comput. Chem. , 16:1192-1209, 1995.
SkBi94
R. D. Skeel and J. J. Biesiadecki,
Symplectic integration with variable stepsize,
Annals of Numer. Math. , 1:191-198, 1994.
Postscript
OkSk94b
D. Okunbor and R. D. Skeel,
Canonical Runge-Kutta-Nystrom methods of orders 5 and 6,
J. Comp. Appl. Math., 51:375-382, 1994.
PDF without figure
OkKs94a
D. Okunbor and R. D. Skeel,
Canonical numerical methods for molecular dynamics simulations,
J. Comput. Chem., 15:72-79, 1994.
LeSk94
B. Leimkuhler and R. D. Skeel,
Symplectic numerical integrators in constrained Hamiltonian systems,
J. Comput. Phys., 112:117-125, 1994.
SkBO93
R. D. Skeel and J. Biesiadecki and D. Okunbor,
Symplectic integration for macromolecular dynamics, in Kang Feng and Zhong-Ci
Shi, editors,
Proceedings of the International Conference on Computation of Differential
Equations and Dynamical Systems, World Scientific Publishing Co., page
49-61, 1993.
Skee93
R. D. Skeel,
Variable Step Size Destabilizes the Stormer/Leapfrog/Verlet Method,
BIT 33:172-175, 1993.
Okun93
D. Okunbor,
Variable step size does not harm second-order integrators for Hamiltonian
systems,
J. Comput. Appl. Math., 47:273-279, 1993.
BiSk93
J. J. Biesiadecki and R. D. Skeel,
Dangers of Multiple-Time-Step Methods,
J. Comput. Phys.,109:318-328, 1993.
SkGe92
R. D. Skeel and C. W. Gear,
Does variable step size ruin a symplectic integrator?,
Physica D, 60:311-313, 1992.
OkSk92b
D. Okunbor and R. D. Skeel,
Explicit canonical methods for Hamiltonian systems,
Math. Comput., 59: 439-455, 1992.
OkSk92a
D. Okunbor and R. D. Skeel,
An explicit Runge-Kutta-Nystrom method is canonical if and only if its adjoint
is explicit,
SIAM J. Numer. Anal., 29:521-527, 1992.
Okun92b
D. Okunbor,
Canonical Methods for Hamiltonian Systems: Numerical Experiments,
Physics D, 60:314-322, 1992.
Okun92a
D. Okunbor,
Canonical Numerical Integrators for Hamiltonian Dynamical Systems,
Technical Report, UIUCDCS-R-92-1785, 1992. (Ph.D. thesis)
Back to Top
WaSk05
W. Wang and R. D. Skeel,
Fast Evaluation of Polarizable Forces,
J. Chem. Phys., 123, 164107 (12 pages), 2005.
PDF
SkTH02
R. D. Skeel , I. Tezcan, and D. J. Hardy,
Multiple Grid Methods for Classical Molecular Dynamics,
J. Comp. Chem., 23, 673-684, 2002.
PDF
Skee01
R. D. Skeel,
Multilevel Summation Methods for N-Body Interactions, In
Multiscale Computational Methods in Chemistry and Physics, pages 3-5,
IOS Press, Amsterdam, 2001.
Postscript
HKSS94b
M. Holst and R. Kozack and F. Saied and S. Subramaniam,
Treatment of electrostatic effects in proteins: Multigrid-based Newton
iterative method for solution of the full nonlinear Poisson-Boltzmann equation,
Proteins: Structure, Function, and Genetics, 18:231-245,
1994.
HKSS94a
M. Holst and R. E. Kozack and F. Saied and S. Subramaniam,
Protein Electrostatics: Rapid Multigrid-based Newton Algorithm for Solution of
the Full Nonlinear Poisson-Boltzmann Equation,
J. Biomol. Struct. Dyn. 11:1437-1445, 1994.
HoSa93
M. Holst and F. Saied,
J. Comp. Chem., 14:105-133, 1993.
Hols93
M. Holst,
Multigrid Solution of the Poisson-Boltzmann Equation,
Ph.D. thesis, Department of Computer Science, University of Illinois at
Urbana-Champaign, 1993.
HoSa92
M. Holst and F. Saied,
Technical Report,
UIUCDCS-R-92-1744, 1992.
Back to Top
PBWG05
J.C. Phillips, R. Braun, W. Wang, J. Gumbart, E. Tajkhorshid, E. Villa,
C. Chipot, R.D. Skeel, L. Kale, K. Schulten,
Scalable molecular dynamics with NAMD,
J. Comput. Chem., 26:1781-1802, 2005.
KSRB99
L. Kale, R. Skeel, R. Brunner, M. Bhandarkar, A. Gursoy, N. Krawetz,
J. Phillips, A. Shinozaki, K. Varadarajan and K. Schulten,
NAMD2: greater scalability for parallel
molecular dynamics,
J. Comput. Phys., 151(1):283-312, 1999.
PBSB98
J. C. Phillips, R. Brunner, A. Shinozaki, M. Bhandarkar, N. Krawetz,
A. Gursoy, L. Kale, R. D. Skeel and K. Schulten,
Avoiding Algorithmic Obfuscation in a Message-Driven Parallel MD Code, In P.
Deuflhard, J. Hermans, B. Leimkuhler, A. Mark, S. Reich, R. D. Skeel editors,
Computational Molecular Dynamics: Challenges, Methods, Ideas, Volume
4 of Lecture Notes in Computational Science and Engineering, pages 455-468,
Springer-Verlag, November 1998.
NHGD96
M. Nelson, W. Humphrey, A. Gursoy, A. Dalke, L. Kale, R. D. Skeel
and K. Schulten,
NAMD—a Parallel, Object-Oriented Molecular Dynamics Program,
Intl. J. Supercomput. Applics. High Performance Computing,
10(4):251-268, 1996.
PDF
NHGD95b
M. Nelson, W. Humphrey, A. Gursoy, A. Dalke and, L. Kale, R. D.
Skeel, K. Schulten and R. Kufrin,
MDScope—A Visual Computing Environment for Structural Biology, in S.N.
Atluri and G. Yagawa and T.A. Cruse, editors,
ICES '95 Conference Proceedings-Computational Mechanics 95, ,
volume 1, pages 476-481, 1995.
NHGD95a
M. Nelson, W. Humphrey, A. Gursoy, A. Dalke, L. Kale, R. D. Skeel,
K. Schulten and R. Kufrin,
MDScope—A Visual Computing Environment for Structural Biology,
Comput. Phys. Commun., 91 (1,2 and 3):111-134, 1995.
Skee89
R. D. Skeel,
Macromolecular dynamics on a shared-memory multiprocessor,
J. Comput. Chem. 12, 1991 also, Rpt. No. 929, Center for
Supercomputing Research and Development, Univ. of Illinois at Urbana-Champaign,
1989.
Back to Top
|