Publications

Books, Proceedings Volumes

• Computational Molecular Dynamics: Challenges, Methods, Ideas -- Proceedings of the 2nd International Symposium on Algorithms for Macromolecular Modelling, Berlin, May 21-24, 1997. P. Deuflhard, J. Hermans, B. Leimkuhler, A.E. Mark, S. Reich, R.D. Skeel (eds.), Lecture Notes in Computational Science and Engineering Vol. 4, Springer-Verlag, 1998.

• B. Leimkuhler and S. Reich, Simulating Hamiltonian Dynamics. The book will appear in January 2005, ISBN-0521772907.
And here is a preview:

Thesis

• S. Reich, Beitrag zur Theorie der Algebrodifferentialgleichungen. Ph.D. thesis, TU Dresden, 1990.

• S. Reich, Dynamical systems, numerical integration, and exponentially small estimates. Habilitationsschrift, Freie Universitat Berlin, 1998. (ps.gz-file available here)

Papers

• S. Reich, Algebrodifferentialgleichungen und Vektorfelder auf Mannigfaltigkeiten. Wissenschaftliche Zeitschrift der TU Dresden 38, 217-220, 1989.

• S. Reich, On a geometric interpretation of DAEs. Circ. Syst., Sig. Processing 9, 367-382, 1990.

• S. Reich, On a geometric characterization of DAEs. Mathematical Research Vol. 59, Akademie-Verlag, 105-113, 1990.

• S. Reich, New results on the numerical and analytical treatment of DAEs. in: Tagungsbericht des ITG-Seminars: Neue Anwendungen theoretischer Konzepten in der Elektrotechnik, Hannover, 79-90, 1990.

• E. Eich, C. Fuhrer, B. Leimkuhler, S. Reich, Stabilization and projection methods for multibody dynamics Report A281, Helsinki Univ. of Technology, 1990.

• S. Reich, On an existence and uniqueness theory for nonlinear DAEs. Circ. Syst., Sig. Processing 10, 344-359, 1991.

• S. Reich, DAEs and applications in circuit theory. Archiv für Elektronik and Übertragungstechnik (AEÜ)46, 298-304, 1992.

• U. Ascher, H. Chin, S. Reich, Stabilization of DAEs and invariant manifolds. Numerische Mathematik 67, 131-149, 1994. (ps.gz-file available here)

• B. Leimkuhler, S. Reich, Symplectic integration of constrained Hamiltonian systems. Math. Comp. 63, 598-605, 1994. (ps.gz-file available here)

• S. Reich, Momentum conserving symplectic integrators. Physica D 76, 375-383, 1994.

• S. Reich, On the local qualitative behavior of DAEs. Circ. Syst., Sig. Processing 14, 427-443, 1994.

• U. Ascher, H. Chin, L. Petzold, S. Reich, Stabilization of constrained mechanical systems with DAEs and invariant manifolds. Mech. Struct. & Mach. 23, 135-157, 1995. (ps.gz-file available here)

• S. Reich, Smoothed dynamics of highly oscillatory Hamiltonian systems. Physica D 89, 28-42, 1995. (ps.gz-file available here)

• S. Reich, Enhanced energy conserving methods. BIT 36, 122-134, 1996. (ps.gz-file available here)

• S. Reich, Symplectic integration of conservative multibody systems. Fields Institute Communications 10, 181-191, 1996. (ps.gz-file available here)

• B. Leimkuhler, S. Reich, R.D. Skeel, Integration methods for molecular dynamics. IMA Volumes in Mathematics and its Applications Vol. 82, Springer Verlag, 161-186, 1996. (ps.gz-file available here)

• S. Reich, Torsion dynamics of molecular systems. Phys. Rev. E 53, 4176-4181, 1996. (ps.gz-file available here and Fig. 1 , Fig. 2, Fig. 3)

• S. Reich, Symplectic integration of constrained Hamiltonian systems by composition methods. SIAM J. Numer. Anal. 33, 475-491, 1996. (ps.gz-file available here)

• S. Reich, On higher-order semi-explicit symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems. Numerische Mathematik 76, 231-247, 1997. (ps.gz-file available here)

• S. Reich, Smoothed Langevin dynamics of highly oscillatory systems. Physica D 138, 210-224, 2000. (ps.gz-file available here)

• S. Reich, Transmission line equations as Hamiltonian partial differential equations: theory and implications for circuit simulations. Kleinheubacher Berichte 40, 304-312, 1996. (ps.gz-file available here and Fig. 1)

• E. Barth, B. Leimkuhler, S. Reich, A time-reversible variable stepsize integrator for constrained dynamics. SIAM J. Sci. Comput. 21, 1027-1044, 1999. (ps.gz-file available here)

• U. Ascher, S. Reich, The midpoint scheme and variants for Hamiltonian systems: advantages and pitfalls. SIAM J. Sci. Comput. 21, 1045-1065, 1999. (ps.gz-file available here)

• S. Reich, Preservation of adiabatic invariants under symplectic discretization. Applied Numerical Mathematics 29, 45-56, 1999. (ps.gz-file available here)

• U. Ascher, S. Reich, On some difficulties in integrating highly oscillatory Hamiltonian systems. Lecture Notes in Computational Science and Engineering, Vol. 4, 281-296, 1998. (ps.gz-file available here)

• S. Reich, Modified potential energy functions for constrained molecular dynamics. Numerical Algorithms 19, 213-221, 1998. (ps.gz-file available here)

• P. Nettesheim and S. Reich, Symplectic multiple-time-stepping integrators for quantum-classical molecular dynamics. Lecture Notes in Computational Science and Engineering, Vol. 4, 412-420, 1998. (ps.gz-file available here)

• Th. Holder, B. Leimkuhler, and S. Reich, Explicit variable step-size and time-reversible integration. APNUM 39, 367-377, 2001. (ps.gz-file available here)

• J. Izaguirre, S. Reich, and R.D. Skeel, Longer time steps for molecular dynamics. J. Chem. Phys. 110 , 9853-9864, 1999. (ps.gz-file available here)

• S. Reich, Backward error analysis for numerical integrators. SIAM J. Numer. Anal. 36 , 1549-1570, 1999. (ps.gz-file available here)

• S. Reich, Multiple time-scales in classical and quantum-classical molecular dynamics. J. Comput. Phys. 151 , 49-73, 1999. (ps.gz-file available here)

• S. Reich, Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations. J. Comput. Phys. 157 , 473--499, 2000. (ps.gz-file available here)

• Th.J. Bridges and S. Reich, Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity. Physics Letters A 284 , 184-193, 2001. (ps.gz-file available here)

• J. Zhou, S. Reich and B.R Brooks, Elastic molecular dynamics with self-consistent flexible constraints. J. Chem. Phys. 112 , 7919--7929, 2000. (ps.gz-file available here)

• S. Reich, Finite volume methods for multi-symplectic PDEs. BIT 40 , 559--582, 2000. (ps.gz-file available here)

• S. Reich, The repulsive-particle method and the symplectic integration of the shallow-water equations. technical report. (ps.gz-file available here)

• Th.J. Bridges and S. Reich, Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations. Physica D 152 , 491-504, 2001. (ps.gz-file available here)

• Th.J. Bridges and S. Reich, Computing Lyapunov exponents on a Stiefel manifold. Physica D, 156, 219-238, 2001. (ps.gz-file available here)

• B. Leimkuhler and S. Reich, A reversible averaging integrator for multiple time-scale dynamics. J. Comput. Physics 171 , 95-114, 2001. (ps.gz-file available here)

• E. Barth, B. Leimkuhler and S. Reich, A test set for molecular dynamics. Lecture Notes in Computational Science and Engineering, Vol. 24, 73-103, 2002. (ps.gz-file available here)

• J. Frank and S. Reich, A Particle-Mesh Method for the Shallow Water Equations near Geostrophic Balance. J. Comput. Phys. 180, 407-426, 2002. (ps.gz-file available here)

• T. Bridges, P. Hydon and S. Reich, Vorticity and symplecticity in Lagrangian fluid dynamics. (submitted) (ps.gz-file available here)

• B. Moore and S. Reich, Backward error analysis for multi-symplectic integration methods. Numerische Mathematik 95, 625-652, 2003. (pdf-file available here)

• J. Frank and S. Reich, Conservation Properties of Smoothed Particle Hydrodynamics Applied to the Shallow Water Equations. BIT 43, 40-54, 2003. (ps.gz-file available here)

• J. Frank, G. Gottwald, and S. Reich, A Hamiltonian Particle-Mesh Method for the Rotating Shallow-Water Equations. Lecture Notes in Computational Science and Engineering, Vol. 26, 131-142, 2002. (ps.gz-file available here)

• B. Moore and S. Reich, Multi-symplectic Integration Methods for Hamiltonian PDEs. Future Generation Computer Systems 19, 395-402, 2003. (ps.gz-file available here)

• C. Cotter, J. Frank and S. Reich, Hamiltonian Particle-Mesh Method for Two-Layer Shallow-Water Equations Subject to the Rigid-Lid Approximation. SIAM J Applied Dynamical Systems 3, 69-83, 2004. (pdf-file available here)

• C.J. Cotter and S. Reich, Geometric Integration of a Wave-Vortex Model. APNUM 48, 293-305, 2004. (ps.gz-file available here)

• C.J. Cotter and S. Reich, An Extended Dissipative Particle Dynamics Model. Europhys. Lett. 64, 723-729, 2003. (pdf-file available here)

• C.J. Cotter and S. Reich, Adiabatic invariance and applications to MD and NWP. BIT, to appear. (pdf-file available here)

• J. Frank and S. Reich, The Hamiltonian Particle Mesh method for the spherical shallow-water equations. Atmospheric Science Letters 5, 89-95,2004. (pdf-file available here)

• C.J. Cotter and S. Reich, Time Stepping Algorithms for Classical Molecular Dynamics. Computational Nanotechnology (eds. M. Rieth and W. Schommers), to appear. (pdf-file available here -- version 27/03/2004)

• M. Dixon and S. Reich, Symplectic Time-Stepping for Particle Methods. , GAMM Mitteilungen 27, 9-24,2004. (pdf-file available here)

• J. Frank and S. Reich, On spurious reflections, nonuniform grids and finite difference discretizations of wave equations. submitted. (pdf-file available here)

• J. Frank, S. Reich, A. Staniforth, A. White, N. Wood, Analysis of a regularized, time-staggered discretization method and its link to the semi-implicit method., submitted. (pdf-file available here)