General
Transition Paths, Free Energies
Sampling
Integrators
Fast Force Evaluation
Parallelism and Software
General Numerical Analysis
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.
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Skee09b
R. D. Skeel,
Two-Point Boundary Value Problems for Curves:
The Case of Minimum Free Energy Paths
in T. E. Simos, G. Psihoyios, and C. Tsitouras, editors,
Numerical Analysis and Applied Mathematics:
International Conference on Numerical Analysis and Applied Mathematics 2009
,
volume 1168/1, pages 29-31, 2009.
corrected PDF
ZhSS10
R. Zhao, J. Shen, and R. D. Skeel,
Maximum flux transition paths of conformational change,
J. Chem. Theory Comput., 6(8), 2411-2423, 2010.
PubMed
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DFBC14
N. Ding, Y. Fang, R. Babbush, C. Chen, R.D. Skeel, and H. Neven,
Bayesian sampling using stochastic gradient thermostats,
Advances in Neural Information Processing Systems 27:
Annual Conference on Neural Information Processing Systems 2014,
3203-3211, 2014.
FaSS14
Y. Fang, J.M. Sanz-Serna, and R.D. Skeel,
Compressible generalized hybrid Monte Carlo,
J. Chem. Phys., 140, 174108 (10 pages)., 2014.
Skee10
R. D. Skeel,
Towards a Definition of Equilibration for Markov Chains,
J. Numer. Anal. Ind. Appl. Math., 15(1-2), 102-111, 2010.
PDF preprint
The following article appeared in The Journal of Chemical Physics
and may be found
here.
SHSI09
C. R. Sweet, S. S. Hampton, R. D. Skeel, and J. A. Izaguirre,
A Separable Shadow Hamiltonian Hybrid Monte Carlo Method,
J. Chem. Phys., 131(17), 174106 (7 pages), 2009.
PDF
Copyright 2009 American Institute of Physics.
This article may be downloaded for personal use only.
Any other use
requires prior permission of the author and the American Institute of Physics.
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
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HaMS09
E. Hairer, R. McLachlan, and R. D. Skeel,
On Energy Conservation of the Simplified Takahashi-Imada Method,
Math. Modelling Numer. Anal., 43(4), 631--644, 2009.
PDF
Skee09
R. D. Skeel,
What Makes Molecular Dynamics Work?,
SIAM J. Sci. Comput., 31, 1363-1378, 2009.
PDF
Skee08
R. D. Skeel,
Supplement to "What Makes Molecular Dynamics Work?",
manuscript, Sep 6, 2008.
PDF
BoSk08
S. D. Bond and R. D. Skeel,
Bias in Molecular Dynamics Averages due to Finite Step Size,
section of BIRS report, 2008.
PDF
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)
MaIS03b
Q. Ma, J.A. Izaguirre, and R. D. Skeel,
Nonlinear Instability in Multiple Time-stepping Molecular Dynamics,
Proceedings of the 18th ACM Symposium on Applied Computing (SAC'03),
167-171, 2003.
PDF
MaIS03a
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.
PDF
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
OkSk94a
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.
PDF
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.
PDF preprint
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,
Physica 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)
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Skee16
R. D. Skeel,
An alternative construction of the Ewald sum,
Molec. Phys., , (5 pages), 2016.
eprint link
The following article appeared in The Journal of Chemical Physics
and may be found
here.
HWXS16
D.J. Hardy, M.A. Wolff, J. Xia, K. Schulten and R.D. Skeel,
Multilevel Summation with B-spline Interpolation
for Pairwise Interactions in Molecular Dynamics Simulations,
J. Chem. Phys., 144, 114112 (16 pages), 2016.
PDF
Copyright 2016 American Institute of Physics.
This article may be downloaded for personal use only.
Any other use
requires prior permission of the author and the American Institute of Physics.
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
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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.
PDF
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.
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SkTa92
R. D. Skeel and H.-W. Tam,
Limits of parallelism in explicit ODE methods,
Numer. Algorithms 2:337-350, 1992.
PDF
SkBe90
R. D. Skeel and M. Berzins,
A method for the spatial discretization of parabolic equations
in one space variable
,
SIAM J. Sci. Stat. Comput. 11:1-32, 1990.
PDF
Skee89
R. D. Skeel,
The second order backward differentiation formula
is unconditionally zero-stable,
Appl. Numer. Math. 5:145-149, 1989.
PDF
Skee86
R. D. Skeel,
Thirteen ways to estimate global error,
Numer. Math. 48:1-20, 1986.
PDF
Skee82
R. D. Skeel,
A theoretical framework for proving accuracy results for deferred corrections
,
SIAM J. Numer. Anal. 19:171-196, 1982.
PDF
Skee79
R. D. Skeel,
Scaling for numerical stability in Gaussian elimination
,
J. ACM. 26:494-526, 1979.
PDF
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