Martin Arnold

Selected publications

• T. Mudrić, N. Čeh, S. Hante, M. Arnold: Free rocking of a rigid block on a flexible structure with non-smooth contact dynamics. - Applied Sciences 14:6483. - 2024. - DOI: 10.3390/app14156483
• D. Tumiotto, M. Arnold: Local coordinates on Lie groups for half-explicit time integration of Cosserat rod models with constraints. - Multibody System Dynamics. - 2024, published online. - DOI: 10.1007/s11044-024-10002-8
• S. Holzinger, M. Arnold, J. Gerstmayr: Evaluation and implementation of Lie group integration methods for rigid multibody systems. - Multibody System Dynamics. - 2024, published online. - DOI: 10.1007/s11044-024-09970-8
• M. Arnold, E. Celledoni, E. Çokaj, B. Owren, D. Tumiotto: B-stability of numerical integrators on Riemannian manifolds. - Journal of Computational Dynamics 11:92-107. - 2024. DOI: 10.3934/jcd.2024002
• A. Abdi, M. Arnold, H. Podhaisky: The barycentric rational numerical differentiation formulas for stiff ODEs and DAEs. - Numerical Algorithms 97:431-451. - 2024. - DOI: 10.1007/s11075-023-01709-4

• D. Manfredo, V. Dörlich, J. Linn, M. Arnold: Data based constitutive modelling of rate independent inelastic effects in composite cables using Preisach hysteresis operators. - Multibody System Dynamics. - 2023, published online. - DOI: 10.1007/s11044-023-09910-y
• M. Arnold, M. Hantke, R. Kruse, H. Podhaisky, E. Celledoni, J. Frank, J. Lang (eds.): Selected papers from NUMDIFF-16. Special issue of Journal of Computational and Applied Mathematics, Volume 430, 2023. - DOI: 10.1016/j.cam.2023.115233

• M. Arnold: Modular time integration of coupled problems in system dynamics. In: M. Günther, W. Schilders (eds.): Novel Mathematics Inspired by Industrial Challenges, pp. 57-72. Springer International Publishing, Cham. - 2022. - DOI: 10.1007/978-3-030-96173-2_3
• S. Hante, D. Tumiotto, M. Arnold: A Lie group variational integration approach to the full discretization of a constrained geometrically exact Cosserat beam model. - Multibody System Dynamics 54:97-123. - 2022. - DOI: 10.1007/s11044-021-09807-8

• V. Wieloch, M. Arnold: BDF integrators for constrained mechanical systems on Lie groups. - Journal of Computational and Applied Mathematics 387:112517 (17 pages). - 2021. - DOI: 10.1016/j.cam.2019.112517
• S. Hante, M. Arnold: RATTLie: A variational Lie group integration scheme for constrained mechanical systems. - Journal of Computational and Applied Mathematics 387:112492 (14 pages). - 2021. - DOI: 10.1016/j.cam.2019.112492
• M. Arnold, H. Podhaisky, R. Weiner, E. Celledoni, J. Frank, J. Lang (eds.): Selected papers from NUMDIFF-15. Special volume of Journal of Computational and Applied Mathematics, Volume 387, 2021. - DOI: 10.1016/j.cam.2019.112611

• S. Hante, M. Arnold, M. Köbis: The SNiMoWrapper: An FMI-compatible testbed for numerical algorithms in co-simulation. In B. Schweizer (ed.): Proceedings of the IUTAM Symposium on Solver-Coupling and Co-Simulation, Darmstadt, Germany, September 18-20, 2017, pp. 99-116. - Springer International Publishing, Cham, 2019. DOI: 10.1007/978-3-030-14883-6_6

• I. Romero, M. Arnold: Computing with rotations: Algorithms and applications. In: E. Stein, R. de Borst, T.J.R. Hughes (eds.): Encyclopedia of Computational Mechanics Second Edition (27 pages). John Wiley & Sons, Ltd, Chichester, UK. - 2018. - DOI: 10.1002/9781119176817.ecm2119

• F. Schneider, M. Burger, M. Arnold, B. Simeon: A new approach for force-displacement co-simulation using kinematic coupling constraints. - Z. Angew. Math. Mech. 97:1147-1166. - 2017. - DOI: 10.1002/zamm.201500129
• M. Arnold: DAE aspects of multibody system dynamics. In: A. Ilchmann, T. Reis (eds.): Surveys in Differential-Algebraic Equations IV, Differential-Algebraic Equations Forum, pp. 41-106. Springer International Publishing, Cham. - 2017. - DOI: 10.1007/978-3-319-46618-7_2
• M. Arnold, H. Podhaisky, R. Weiner, J. Frank, W. Hundsdorfer (eds.): Selected papers from NUMDIFF-14. Special volume of Journal of Computational and Applied Mathematics, Volume 316, pp. 1-392, 2017. - DOI: 10.1016/j.cam.2016.11.007

• M. Arnold, S. Hante: Implementation details of a generalized-α DAE Lie group method. - Journal of Computational and Nonlinear Dynamics 12:021002 (8 pages). - 2016. - DOI: 10.1115/1.4033441
• M. Arnold, A. Cardona, O. Brüls: A Lie algebra approach to Lie group time integration of constrained systems. In: P. Betsch (ed.): Structure-Preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics, vol. 565 of CISM Courses and Lectures, pp. 91-158. Springer International Publishing, Cham. - 2016. - DOI: 10.1007/978-3-319-31879-0_3
• M.A. Köbis, M. Arnold: Convergence of generalized-α time integration for nonlinear systems with stiff potential forces. - Multibody System Dynamics 37:107-125. - 2016. - DOI: 10.1007/s11044-015-9495-2
• S. Thomas, C. Matyssek, W. Hergert, M. Arnold, L. Kiewidt, M. Karamehmedović, T. Wriedt: Application of generalized Mie theory to EELS calculations as a tool for optimization of plasmonic structures. - Plasmonics 11:865-874, 2016. - DOI: 10.1007/s11468-015-0120-2

• R. Geilhufe, S. Achilles, M.A. Köbis, M. Arnold, I. Mertig, W. Hergert, A. Ernst: Numerical solution of the relativistic single-site scattering problem for the Coulomb and the Mathieu potential. - Journal of Physics: Condensed Matter 27:435202 (10 pages). - 2015. - DOI: 10.1088/0953-8984/27/43/435202 - A preliminary version of this material is available at arXiv:1506.07743 [cond-mat.mtrl-sci].
• M. Arnold, A. Cardona, O. Brüls: Order reduction in time integration caused by velocity projection. - Journal of Mechanical Science and Technology 29:2579-2585. - 2015. - DOI: 10.1007/s12206-015-0501-7. - This is a shortened and revised version of: M. Arnold, A. Cardona, O. Brüls: Order reduction in time integration caused by velocity projection. - In: Proceedings of The 3rd Joint International Conference on Multibody System Dynamics and the 7th Asian Conference on Multibody Dynamics, BEXCO, Busan, Korea, June 30 - July 3, 2014. - The full material is available online as Technical Report 02-2015, Martin Luther University Halle-Wittenberg, Institute of Mathematics, 2015. [.pdf].
• M. Arnold, O. Brüls, A. Cardona: Error analysis of generalized-α Lie group time integration methods for constrained mechanical systems. - Numerische Mathematik 129:149-179. - 2015. - DOI: 10.1007/s00211-014-0633-1

• M. Arnold, H. Podhaisky, R. Weiner, J. Frank, W. Hundsdorfer (eds.): Selected papers from NUMDIFF-13. Special volume of Journal of Computational and Applied Mathematics, Volume 262, pp. 1-398, 2014. - DOI: 10.1016/j.cam.2013.10.032
• S. Weber, M. Arnold: Semi-analytical methods for singularly perturbed multibody system models. - Journal of Computational and Applied Mathematics 262:322-332. - 2014. - DOI: 10.1016/j.cam.2013.07.040
• M. Köbis, M. Arnold: Numerical solution of penalty formulations for constrained mechanical systems using heterogeneous multiscale methods. - Journal of Computational and Applied Mathematics 262:193-204. - 2014. - DOI: 10.1016/j.cam.2013.07.029
• M. Schulze, S. Dietz, B. Burgermeister, A. Tuganov, H. Lang, J. Linn, M. Arnold: Integration of nonlinear models of flexible body deformation in multibody system dynamics. - Journal of Computational and Nonlinear Dynamics 9:011012. - 2014. - DOI: 10.1115/1.4025279
• M. Arnold: Simulation algorithms and software tools. In G. Mastinu, M. Plöchl (eds.): Road and Off-Road Vehicle System Dynamics Handbook, pp. 45-68. - CRC Press. - 2014. - DOI: 10.1201/b15560

• M. Arnold: A recursive multibody formalism for systems with small mass and inertia terms. - Mech. Sci. 4:221-231. - 2013. - DOI: 10.5194/ms-4-221-2013
• M. Arnold, C. Clauß, T. Schierz: Error analysis and error estimates for co-simulation in FMI for Model Exchange and Co-Simulation v2.0. - Archive of Mechanical Engineering LX:75-94. - 2013. - DOI: 10.2478/meceng-2013-0005. - This is the extended and revised version of M. Arnold, C. Clauß, T. Schierz: Numerical aspects of FMI for Model Exchange and Co-Simulation v2.0. - In: P. Eberhard, P. Ziegler (eds.): Proc. of The 2nd Joint International Conference on Multibody System Dynamics, Stuttgart, Germany, May 29 - June 1, 2012. - ISBN 978-3-927618-32-9.

• M. Schlegel, O. Knoth, M. Arnold, R. Wolke: Implementation of multirate time integration methods for air pollution modelling. - Geoscientific Model Development. 5:1395-1405. - 2012. - DOI: 10.5194/gmd-5-1395-2012. - This is the revised version of M. Schlegel, O. Knoth, M. Arnold, R. Wolke: Implementation of splitting methods for air pollution modeling. - Geoscientific Model Development Discussions. 4:2937-2972. - 2011. - DOI: 10.5194/gmdd-4-2937-2011
• J. Verwer, W. Hundsdorfer, M. Arnold, R. Weiner, (eds.): Numerical Solution of Differential and Differential-Algebraic Equations. Selected papers from NUMDIFF-12. Special issue of Applied Numerical Mathematics, Volume 62, Issue 10, pp. 1257-1604, 2012. - DOI: 10.1016/j.apnum.2012.06.001
• H. Schiller, M. Arnold: Convergence of continuous approximations for discontinuous ODEs. - Applied Numerical Mathematics 62:1503-1514. - 2012. - DOI: 10.1016/j.apnum.2012.06.021
• T. Schierz, M. Arnold: Stabilized overlapping modular time integration of coupled differential-algebraic equations. - Applied Numerical Mathematics 62:1491-1502. - 2012. - DOI: 10.1016/j.apnum.2012.06.020
• S. Weber, M. Arnold, M. Valášek: Quasistatic approximations for stiff second-order differential equations. - Applied Numerical Mathematics 62:1579-1590. - 2012. - DOI: 10.1016/j.apnum.2012.06.030
• H. Lang, M. Arnold: Numerical aspects in the dynamic simulation of geometrically exact rods. - Applied Numerical Mathematics 62:1411-1427. - 2012. - DOI: 10.1016/j.apnum.2012.06.011
• M. Schlegel, O. Knoth, M. Arnold, R. Wolke: Numerical solution of multiscale problems in atmospheric modeling. - Applied Numerical Mathematics 62:1531-1543. - 2012. - DOI: 10.1016/j.apnum.2012.06.023
• O. Brüls, A. Cardona, M. Arnold: Lie group generalized-α time integration of constrained flexible multibody systems. - Mechanism and Machine Theory 48:121-137. - 2012. - DOI: 10.1016/j.mechmachtheory.2011.07.017

• M. Arnold, B. Burgermeister, C. Führer, G. Hippmann, G. Rill: Numerical methods in vehicle system dynamics: State of the art and current developments. - Vehicle System Dynamics. 49:1159-1207. - 2011. - DOI: 10.1080/00423114.2011.582953
• B. Burgermeister, M. Arnold, A. Eichberger: Smooth velocity approximation for constrained systems in real-time simulation. Multibody System Dynamics 26:1-14. - 2011. - DOI: 10.1007/s11044-011-9243-1
• H. Lang, J. Linn, M. Arnold: Multibody dynamics simulation of geometrically exact Cosserat rods. Multibody System Dynamics 25:285-312. - 2011. - DOI: 10.1007/s11044-010-9223-x

• S. Weber, M. Arnold: Model reduction via quasistatic approximations. Proc. Angew. Math. Mech. 10:655-656. - 2010. - DOI: 10.1002/pamm.201010320
• M. Arnold: Stability of sequential modular time integration methods for coupled multibody system models. - Journal of Computational and Nonlinear Dynamics 5:031003. - 2010. - DOI: 10.1115/1.4001389
• A. Pfeiffer, M. Arnold: Sensitivity analysis of discontinuous multidisciplinary models: Two examples. In P.G. Thomsen, H. True, (eds.): Non-smooth Problems in Vehicle Systems Dynamics. Proceedings of the Euromech 500 Colloquium. pp. 239-251. - Springer-Verlag Berlin Heidelberg, 2010. - DOI: 10.1007/978-3-642-01356-0_21
• M. Arnold: Towards improved error estimates for higher order time integration of ODEs with non-smooth right hand side. In P.G. Thomsen, H. True, (eds.): Non-smooth Problems in Vehicle Systems Dynamics. Proceedings of the Euromech 500 Colloquium. pp. 227-237. - Springer-Verlag Berlin Heidelberg, 2010. - DOI: 10.1007/978-3-642-01356-0_20

• M. Schlegel, O. Knoth, M. Arnold, R. Wolke: Multirate Runge-Kutta schemes for advection equations. - Journal of Computational and Applied Mathematics 226:345-357. - 2009. - doi:10.1016/j.cam.2008.08.009. Abstract.
• B. Sommeijer, J. Verwer, M. Arnold, R. Weiner, (eds.): Numerical Solution of Differential and Differential-Algebraic Equations. Selected papers from NUMDIFF-11. Special issue of Applied Numerical Mathematics, Volume 59, Issue 3-4, pp. 405-844, 2009. Preface.
• M. Arnold, W. Schiehlen (eds.): Simulation Techniques for Applied Dynamics CISM Courses and Lectures, vol. 507. - Springer, Wien New York, ISBN 978-3-211-89547-4, 384 pages, 2009. [ more ... ]
• M. Arnold: Numerical methods for simulation in applied dynamics. In M. Arnold, W. Schiehlen (eds.): Simulation Techniques for Applied Dynamics, vol. 507 of CISM Courses and Lectures, pp. 191-246. - Springer, Wien New York. - 2009. Abstract.

• S. Hartmann, K.J. Quint, M. Arnold: On plastic incompressibility within time-adaptive finite elements combined with projection techniques. - Computer Methods in Applied Mechanics and Engineering 198:178-193. - 2008. - doi:10.1016/j.cma.2008.06.011. Abstract.
• O. Brüls, M. Arnold: The generalized-α scheme as a linear multistep integrator: Towards a general mechatronic simulator. - Journal of Computational and Nonlinear Dynamics, 3:041007. - 2008. Abstract.

• B. Burgermeister, M. Arnold, A. Eichberger: A quasi-static approach for constrained systems in real-time simulation. - Proc. Angew. Math. Mech. 7:4010021-4010022. - 2007. Abstract.
• M. Arnold, O. Brüls: Convergence of the generalized-α scheme for constrained mechanical systems. - Multibody System Dynamics 18:185-202. - 2007. Abstract. - This is the revised version of Technical Report 09(2007), Martin Luther University Halle-Wittenberg, Institute of Mathematics [.pdf].
• M. Arnold: Multi-rate time integration for large scale multibody system models. In P. Eberhard (ed.): IUTAM Symposium on Multiscale Problems in Multibody System Contacts, pp. 1-10. - Springer-Verlag, Dordrecht, 2007. Abstract.
• M. Arnold, B. Burgermeister, A. Eichberger: Linearly implicit time integration methods in real-time applications: DAEs and stiff ODEs. - Multibody System Dynamics 17:99-117. - 2007. Abstract.
• M. Arnold, A. Heckmann: From Multibody Dynamics to Multidisciplinary Applications. In J.C. García Orden, J.M. Goicolea, J. Cuadrado (eds.): Multibody Dynamics. Computational Methods and Applications, pp. 273-294. - Springer-Verlag, Dordrecht, 2007. Abstract.

• B. Burgermeister, M. Arnold, B. Esterl: DAE time integration for real-time applications in multi-body dynamics. - Z. Angew. Math. Mech. 86:759-771. - 2006. Abstract. - This is the revised version of Technical Report 03(2006) of Martin-Luther-University Halle, Department of Mathematics and Computer Science [.pdf].
• M. Arnold, W. Schiehlen, (eds.): Advances in Simulation Techniques for Applied Dynamics. Special issue of Multibody System Dynamics, Volume 15, Number 1, pp. 1-106, 2006. Preface.
• M. Arnold, A. Fuchs, C. Führer: Efficient corrector iteration for DAE time integration in multibody dynamics. - Comp. Meth. Appl. Mech. Eng. 195:6958-6973. - 2006. Abstract. - This is the completely revised version of the earlier Technical Report 29(2004) of Martin-Luther-University Halle, Department of Mathematics and Computer Science.

• A. Heckmann, M. Arnold, O. Vaculín: A modal multifield approach for an extended flexible body description in multibody dynamics. Multibody System Dynamics 13:299-322. - 2005. Abstract.
• A. Pfeiffer, M. Arnold: Numerical analysis of structure preserving Nyström methods for Hamiltonian systems. - Applied Numerical Mathematics 53:391-408. - 2005. Abstract.

• M. Arnold, O. Vaculín, (eds.): Multibody System Simulation in Vehicle System Dynamics. To the memory of Willi Kortüm (1938 - 2002). Special issue of Vehicle System Dynamics, Volume 41, Number 5, pp. 335-429, 2004. Table of contents.
• M. Arnold: Numerical methods in the simulation of vehicle-guideway interaction [.pdf]. In A. Buikis, R. Čiegis, A.D. Fitt, (eds.): Progress in Industrial Mathematics at ECMI 2002. - Springer-Verlag, Berlin Heidelberg, pp. 115-120, 2004.

• M. Arnold, A. Carrarini, A. Heckmann, G. Hippmann: Simulation techniques for multidisciplinary problems in vehicle system dynamics. In M. Valášek, editor, Computational Mechanics in Vehicle System Dynamics, Supplement to Vehicle System Dynamics, Vol. 40, pages 17-36. Taylor & Francis, London, 2003. Abstract.
• M. Arnold, C. Führer, B. Simeon, (eds.): Numerical Methods in Multibody Dynamics. Proceedings of an ECMI-Workshop at Bad Herrenalb, Germany, October 2001. - Special issue of Z. Angew. Math. Mech., Volume 83, Issue 10, pp. 635-728, 2003. Preface.
• M. Arnold, A. Pfeiffer: Energy conservation in modified Nyström methods for separable Hamiltonian systems [.pdf]. - Proc. Angew. Math. Mech., 3:557-558, 2003.

• M. Arnold: Constraint partitioning in dynamic iteration methods [.ps]. - Z. Angew. Math. Mech., Supplement 3 to vol. 81:S735-S738, 2001.
• W. Kortüm, W.O. Schiehlen, M. Arnold: Software tools - from multibody system analysis to vehicle system dynamics. - In H. Aref, J.W. Phillips, (eds).: Mechanics for a New Millennium. - Kluwer Academic Publishers, Dordrecht, pp. 225-238, 2001. Abstract.
• M. Arnold, M. Günther: Preconditioned dynamic iteration for coupled differential-algebraic systems [.ps]. -  BIT Numerical Mathematics 41:1-25. - 2001.
• M. Arnold: A pre-conditioned method for the dynamical simulation of coupled mechanical multibody systems [.ps]. - Z. Angew. Math. Mech., Supplement 3 to vol. 80:S817-S818, 2000.
• M. Arnold, B. Simeon: Pantograph and catenary dynamics: a benchmark problem and its numerical solution. - Applied Numerical Mathematics 34:345-362. - 2000. Abstract.
• B. Simeon, M. Arnold: Coupling DAE's and PDE's for simulating the interaction of pantograph and catenary. - Mathematical and Computer Modelling of Dynamical Systems 6:129-144. - 2000. Abstract.
• M. Arnold: A note on the uniform perturbation index [.pdf]. - Rostocker Mathematisches Kolloquium, 52:33-46, 1998.
• M. Arnold: Singularities in differential-algebraic systems with unilateral constraints [.ps]. - Z. Angew. Math. Mech., Supplement 3 to vol. 78:S857-S860, 1998.
• M. Arnold: Zur Theorie und zur numerischen Lösung von Anfangswertproblemen für differentiell-algebraische Systeme von höherem Index [.pdf]. - Fortschrittberichte VDI, Reihe 20, Nr. 264. - VDI-Verlag Düsseldorf. - 1998.
• M. Arnold: Half-explicit Runge-Kutta methods with explicit stages for differential-algebraic systems of index 2 [.ps]. - BIT Numerical Mathematics 38:415-438, 1998.
• M. Arnold, A. Murua: Non-stiff integrators for differential-algebraic systems of index 2 [.ps]. - Numerical Algorithms 19:25-41, 1998.
• M. Arnold: The stabilization of linear multistep methods for constrained mechanical systems. - Applied Numerical Mathematics 28:143-159, 1998. Abstract.
• M. Arnold, H. Netter: Approximation of contact geometry in the dynamical simulation of wheel-rail systems [.ps]. - Mathematical and Computer Modelling of Dynamical Systems 4:162-184, 1998. Erratum.
• M. Arnold, K. Frischmuth: Solving problems with unilateral constraints by DAE methods [.ps]. - Mathematics and Computers in Simulation 47:47-67, 1998. - DOI: 10.1016/S0378-4754(98)00118-9
• M. Arnold, H. Netter: Wear profiles and the dynamical simulation of wheel-rail systems [.ps]. - In M. Brøns, M.P. Bendsøe, M.P. Sørensen, (eds.): Progress in Industrial Mathematics at ECMI 96, pp. 77-84. - Teubner, Stuttgart, 1997.
• K. Frischmuth, M. Arnold, M. Hänler, H. Netter: Differentialgleichungen und singuläre Mannigfaltigkeiten in der dynamischen Simulation von Rad-Schiene-Systemen. - In K.-H. Hoffmann, W. Jäger, Th. Lohmann, H. Schunck (eds.): Mathematik - Schlüsseltechnologie für die Zukunft, pp. 331-342. - Springer-Verlag, Berlin Heidelberg New York, 1997. Abstract.
• M. Arnold: Numerical problems in the dynamical simulation of wheel-rail systems [.ps]. - Z. Angew. Math. Mech., Proceedings ICIAM 95, Issue 3, pp. 151-154. - 1996.
• M. Arnold: Numerische Probleme in der dynamischen Simulation von Rad-Schiene-Systemen [.ps]. - Z. Angew. Math. Mech., Supplement to vol. 75:S677-S678, 1995.
• M. Arnold: A perturbation analysis for the dynamical simulation of mechanical multibody systems [.ps]. - Applied Numerical Mathematics 18:37-56, 1995. - DOI: 10.1016/0168-9274(95)00042-S
• M. Arnold: Implicit Runge-Kutta methods for transferable differential-algebraic equations. Volume 29 of Banach Center Publications, Polish Academy of Sciences, pp. 267-274, 1994.
• M. Arnold. Stability of numerical methods for differential-algebraic equations of higher index. Applied Numerical Mathematics 13:5-14, 1993.
• R. Weiner, M. Arnold, P. Rentrop, K. Strehmel: Partitioning strategies in Runge-Kutta type methods. IMA J. Numer. Anal., 13:303-319, 1993. - DOI: 10.1093/imanum/13.2.303
• M. Arnold, K. Strehmel, R. Weiner: Half-explicit Runge-Kutta methods for semi-explicit differential-algebraic equations of index 1. - Numer. Math. 64:409-431, 1993. - DOI: 10.1007/BF01388697
• M. Arnold: Linearly implicit Runge-Kutta methods for DAE's of index 1 - two approaches. In K. Strehmel, (ed.):Numerical Treatment of Differential Equations. Proceedings of the fifth seminar "NUMDIFF-5", Halle 1989, Teubner-Texte zur Mathematik, Teubner-Verlag Leipzig, pp. 9-15, 1991.