Publication List

General
Transition Paths, Free Energies
Sampling
Integrators
Fast Force Evaluation
Parallelism and Software
General Numerical Analysis

 
 

General

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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Transition Paths, Free Energies

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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Sampling

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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Integrators

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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Fast Force Evaluation

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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Parallelism and Software

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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General Numerical Analysis

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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Last updated 2013-3-11