Books/Book-contributions

  1. A. Zisowsky, A. Arnold, M. Ehrhardt, T. Koprucki: Transient Simulation of \(k p\) - Schrödinger Systems using discrete transparent Boundary Conditions, Multi-Band Effective Mass Approximations, Advanced Mathematical Models and Numerical Techniques (2014) 247-272, M. Ehrhardt, T. Koprucki (Eds.), Springer (2014). [pdf] [www]

  2. A. Arnold, M. Ehrhardt, M. Schulte: Numerical Simulation of Quantum wave guides, VLSI and Computer Architecture (2009). ISBN: 978-1-60692-075-6, K. Watanabe (Ed.), Nova Publishers (2009). [pdf] [www]

  3. G. Allaire, A. Arnold, P. Degond, T. Y. Hou: Quantum Transport - Modelling, Analysis and Asymptotics, Lecture Notes in Mathematics 1946 (2008). ISBN: 978-3-540-79573-5, Springer (2008), Berlin. [pdf] [www]

  4. A. Arnold, A. Jüngel: Multi-scale modeling of quantum semiconductor devices, Analysis, Modeling and Simulation of Multiscale Problems (2006) 331-363, A. Mielke (Ed.), Springer (2006), Berlin-Heidelberg. [pdf] [www]

  5. N. Ben Abdallah, A. Arnold, P. Degond, I. M. Gamba, R. T. Glassey, C. D. Levermore, C. Ringhofer (eds.): Dispersive Transport Equations and Multiscale Models, IMA Volumes in Mathematics and its Applications 136 (2003), Springer (2003), New York. [pdf] [www]

  6. N. Ben Abdallah, A. Arnold, P. Degond, I. M. Gamba, R. T. Glassey, C. D. Levermore, C. Ringhofer (eds.): Transport in Transition Regimes, IMA Volumes in Mathematics and its Applications 135 (2003), Springer (2003), New York. [pdf] [www]

Publications in refereed journals

  1. A. Arnold, G. Toshpulatov: Exponential stability and hypoelliptic regularization for the kinetic Fokker-Planck equation with confining potential, Submitted (2023). [pdf]

  2. A. Arnold, A. Einav, T. Wöhrer: Sharp Decay of the Fisher Information for Degenerate Fokker—Planck Equations, Submitted (2023). [pdf]

  3. F. Achleitner, A. Arnold, V. Mehrmann, E. A. Nigsch: Hypocoercivity in Hilbert spaces, Submitted (2023). [pdf]

  4. A. Arnold, A. Einav, T. Wöhrer: Generalised Fisher Information Approach to Defective Fokker-Planck Equations, Submitted (2022). [pdf]

  5. A. Arnold, S. Geevers, I. Perugia, D. Ponomarev: On the limiting amplitude principle for the wave equation with variable coefficients, Submitted (2022). [pdf]

  6. A. Arnold, J. Erb: Sharp entropy decay for hypocoercive and non-symmetric Fokker-Planck equations with linear drift, Submitted (2020). [pdf]

  7. F. Achleitner, A. Arnold, V. Mehrmann: Hypocoercivity in algebraically constrained partial differential equations with application to Oseen equations, J. Dynam. Differential Equations (2023). [pdf]

  8. F. Achleitner, A. Arnold, V. Mehrmann: Hypocoercivity and controllability in linear semi-dissipative Hamiltonian ordinary differential equations and differential-algebraic equations, ZAMM 103 (2023). e202100171; 30pp. [pdf] [www]

  9. F. Achleitner, A. Arnold, E. A. Carlen: The Hypocoercivity Index for the short time behavior of linear time-invariant ODE systems, Journal of Differential Equations 371 (2023) 83-115. [pdf] [www]

  10. F. Achleitner, A. Arnold, V. Mehrmann: Hypocoercivity and hypocontractivity concepts for linear dynamical systems, Electron. J. Linear Algebra 39 (2023) 33-61. [pdf] [www]

  11. A. Arnold, B. Signorello: Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium, Kinetic and Related Models 15, No. 5 (2022) 753-773. [pdf] [www]

  12. A. Arnold, S. Geevers, I. Perugia, D. Ponomarev: On the exponential time-decay for the one-dimensional wave equation with variable coefficients, Comm. on Pure and Applied Analysis 21, No. 10 (2022) 3389-3405. [pdf] [www]

  13. A. Arnold, C. Schmeiser, B. Signorello: Propagator norm and sharp decay estimates for Fokker-Planck equations with linear drift, Comm. Math. Sc. 20, No. 4 (2022) 1047-1080. [pdf] [www]

  14. A. Arnold, C. Klein, B. Ujvari: WKB-method for the 1D Schrödinger equation in the semi-classical limit: enhanced phase treatment, BIT Numerical Mathematics 62 (2022) 1-22. [pdf] [www]

  15. A. Arnold, S. Geevers, I. Perugia, D. Ponomarev: An adaptive finite element method for high-frequency scattering problems with variable coefficients, Computers Math. Applic. 109 (2022) 1-14. [pdf] [www]

  16. J. Körner, A. Arnold, K. Döpfner: WKB-based scheme with adaptive step size control for the Schrödinger equation in the highly oscillatory regime, J. Comput. Appl. Math. 404 (2022) 113905, 18 pp. [pdf] [www]

  17. P. Amodio, A. Arnold, T. Levitina, G. Settanni, E. Weinmüller: On the Abramov approach for the numerical simulation of the whispering gallery modes in prolate spheroids, Appl. Math. Comput. 409, No. 125599 (2021) 1-14. [pdf] [www]

  18. A. Arnold, A. Einav, B. Signorello, T. Wöhrer: Large Time Convergence of the Non-homogeneous Goldstein-Taylor Equation, J. Stat. Phys. 182 (2021) 41. [pdf] [www]

  19. A. Arnold, K. Döpfner: Stationary Schrödinger equation in the semi-classical limit: WKB-based scheme coupled to a turning point, Calcolo 57, No. 1, Paper no. 3 (2020) 44 pp. [pdf] [www]

  20. A. Arnold, S. Jin, T. Wöhrer: Sharp Decay Estimates in Local Sensitivity Analysis for Evolution Equations with Uncertainties: from ODEs to Linear Kinetic Equations, Journal of Differential Equations 268, No. 3 (2020) 1156-1204. [pdf] [www]

  21. D. Stürzer, A. Arnold, A. Kugi: Closed-loop Stability Analysis of a Gantry Crane with Heavy Chain, International Journal of Control 91, No. 8 (2018) 1931-1943. [pdf] [www]

  22. F. Achleitner, A. Arnold, E. A. Carlen: On multi-dimensional hypocoercive BGK models, Kinetic and Related Models 11, No. 4 (2018) 953-1009. [pdf] [www]

  23. A. Arnold, C. Negulescu: Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions, Numerische Mathematik 138, No. 2 (2018) 501-536. [pdf] [www]

  24. A. Arnold, A. Einav, T. Wöhrer: On The Rates of Decay to Equilibrium in Degenerate and Defective Fokker-Planck Equations, Journal of Differential Equations 264, No. 11 (2018) 6843-6872. [pdf] [www]

  25. L. Bian, G. Pang, S. Tang, A. Arnold: ALmost EXact boundary conditions for transient Schrödinger-Poisson system, J. Comput. Phys. 313 (2016) 233-246. [pdf] [www]

  26. M. Miletić, D. Stürzer, A. Arnold, A. Kugi: Stability of an Euler-Bernoulli beam with a nonlinear dynamic feedback system, IEEE Trans. Autom. Control 61, No. 10 (2016) 2782-2795. [pdf] [www]

  27. M. Miletić, A. Arnold: A piezoelectric Euler-Bernoulli beam with dynamic boundary control: Stability and dissipative FEM, Acta Applicandae Mathematicae 138, No. 1 (2015) 241-277. [pdf] [www]

  28. F. Achleitner, A. Arnold, D. Stürzer: Large-time behavior in non-symmetric Fokker-Planck equations, Rivista di Matematica della Università di Parma 6 (2015) 1-68. [pdf]

  29. M. Miletić, D. Stürzer, A. Arnold: An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip, Discrete Contin. Dyn. Sys. Ser. B 20, No. 9 (2015) 3029-3055. [pdf] [www]

  30. R. Hammer, W. Pötz, A. Arnold: Single-cone real-space finite difference scheme for the time-dependent Dirac equation, J. Comput. Phys. 265 (2014) 50-70. Erratum: Vol. 457 (2022), Paper No. 111118. [pdf] [www]

  31. D. Stürzer, A. Arnold: Spectral Analysis and Long-Time Behaviour of a Fokker-Planck Equation with a Non-Local Perturbation, Rendiconti Lincei Cl. Sci. Fis. Mat. Natur. 25, No. 1 (2014) 53-89. Erratum: Vol. 27 (2016) 147-149. [pdf] [www]

  32. R. Hammer, W. Pötz, A. Arnold: A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equations in (1+1)D, J. Comput. Phys. 256 (2014) 728-747. [pdf] [www]

  33. L. Neumann, A. Arnold, W. Hochhauser: Zur Stabilität von geklebten und geklotzten Glasscheiben: Beurteilung der Dunkerley'schen Geraden zur Beulwertbestimmung, Bauingenieur 1 (2013) 14-21. [pdf]

  34. A. Arnold, J. Kim, X. Yao: Estimates for a class of oscillatory integrals and decay rates for wave-type equations, J. Math. Anal. Appl. 394, No. 1 (2012) 139-151. [pdf] [www]

  35. A. Arnold, M. Ehrhardt, M. Schulte, I. Sofronov: Discrete transparent boundary conditions for the Schrödinger equation on circular domains, Comm. Math. Sc. 10, No. 3 (2012) 889-916. [pdf]

  36. J. Kim, A. Arnold, X. Yao: Global estimates of fundamental solutions for higher-order Schrödinger equations, Monatshefte für Mathematik 168, No. 2 (2012) 253-266. [pdf] [www]

  37. A. Arnold, L. Desvillettes, C. Prévost: Existence of nontrivial steady states for populations structured with respect to space and a continuous trait, Comm. on Pure and Applied Analysis 11, No. 1 (2012) 83-96. [pdf] [www]

  38. A. Arnold, I. M. Gamba, M. P. Gualdani, S. Mischler, C. Mouhot, C. Sparber: The Wigner-Fokker-Planck equation: stationary states and large time behavior, Math. Models and Meth. in the Appl. Sc. 22, No. 11-1250034 (31 pages) (2012). [pdf] [www]

  39. A. Arnold, N. Ben Abdallah, C. Negulescu: WKB-based schemes for the oscillatory 1D Schrödinger equation in the semi-classical limit, SIAM J. Numer. Anal. 49, No. 4 (2011) 1436-1460. [pdf] [www]

  40. A. Arnold, J. A. Carrillo, C. Manzini: Refined long-time asymptotics for some polymeric fluid flow models, Comm. Math. Sc. 8, No. 3 (2010) 763-782. [pdf] [www]

  41. X. Antoine, A. Arnold, C. Besse, M. Ehrhardt, A. Schädle: A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations, Commun. Comput. Phys. 4, No. 4 (2008) 729-796. [pdf] [www]

  42. A. Arnold, J. A. Carrillo, C. Klapproth: Improved entropy decay estimates for the heat equation, J. Math. Anal. Appl. 343, No. 1 (2008) 190-206. [pdf] [www]

  43. A. Arnold, E. A. Carlen, Q. Ju: Large-time behavior of non-symmetric Fokker-Planck type equations, Communications on Stochastic Analysis 2, No. 1 (2008) 153-175. [pdf] [www]

  44. M. Schulte, A. Arnold: Discrete transparent boundary conditions for the Schrödinger equation - a compact higher order scheme, Kinetic and Related Models 1, No. 1 (2008) 101-125. [pdf] [www]

  45. A. Arnold, E. Dhamo, C. Manzini: The Wigner-Poisson-Fokker-Planck system: global-in-time solutions and dispersive effects, Ann. Inst. H. Poincaré C, Anal. Non Linéaire 24, No. 4 (2007) 645-676. [pdf] [www]

  46. A. Arnold, J.-P. Bartier, J. Dolbeault: Interpolation between Logarithmic Sobolev and Poincaré Inequalities, Comm. Math. Sc. 5, No. 4 (2007) 971-979. [pdf] [www]

  47. A. Arnold, E. Dhamo, C. Manzini: Dispersive effects in quantum kinetic equations, Indiana Univ. Math. J. 56, No. 3 (2007) 1299-1331. [pdf] [www]

  48. A. Zisowsky, A. Arnold, M. Ehrhardt, T. Koprucki: Discrete Transparent Boundary Conditions for transient kp-Schrödinger Equations with Application to Quantum-Heterostructures, ZAMM 85, No. 11 (2005) 793-805. [pdf] [www]

  49. A. Arnold, J. Dolbeault: Refined Convex Sobolev Inequalities, J. Funct. Anal. 225, No. 2 (2005) 337-351. [pdf] [www]

  50. A. Arnold, J. A. Carrillo, L. Desvillettes, J. Dolbeault, A. Jüngel, C. Lederman, P. A. Markowich, G. Toscani, C. Villani: Entropies and Equilibria of Many-Particle Systems: An Essay on Recent Research, Monatshefte für Mathematik 142, No. 1-2 (2004) 35-43. [pdf] [www]

  51. A. Arnold, C. Sparber: Quantum dynamical semigroups for diffusion models with Hartree interaction, Comm. Math. Phys. 251, No. 1 (2004) 179-207. [pdf] [www]

  52. A. Arnold, R. Bosi: Global existence of the von Neumann equation for Hartree-Fock systems with Relaxation-Time, Submitted (2004). [pdf]

  53. A. Arnold, J. L. López, P. A. Markowich, J. Soler: An Analysis of Quantum Fokker-Planck Models: A Wigner Function Approach, Rev. Mat. Iberoam. 20, No. 3 (2004) 771-814. [pdf] [www]

  54. A. Arnold, M. Ehrhardt, I. Sofronov: Discrete transparent boundary conditions for the Schrödinger equation: Fast calculation, approximation, and stability, Comm. Math. Sc. 1, No. 3 (2003) 501-556. [pdf] [www]

  55. A. Arnold, A. Unterreiter: Entropy Decay of Discretized Fokker-Planck Equations I - Temporal Semi-Discretization, Computers Math. Applic. 46, No. 10-11 (2003) 1683-1690. [pdf] [www]

  56. A. Arnold, J. A. Carrillo, E. Dhamo: On the periodic Wigner-Poisson-Fokker-Planck system, J. Math. Anal. Appl. 275 (2002) 263-276. [pdf] [www]

  57. A. Arnold, J. A. Carrillo, M. D. Tidriri: Large-time behavior of discrete kinetic equations with non-symmetric interactions, Math. Models and Meth. in the Appl. Sc. 12, No. 11 (2002) 1555-1564. [pdf] [www]

  58. A. Arnold: Mathematical concepts of open quantum boundary conditions, Transp. Theo. Stat. Phys. 30, No. 4-6 (2001) 561-584. [pdf] [www]

  59. M. Ehrhardt, A. Arnold: Discrete Transparent Boundary Conditions for the Schrödinger Equation, Rivista di Matematica della Università di Parma 6, No. 4 (2001) 57-108. [pdf]

  60. A. Arnold, J. A. Carrillo, I. M. Gamba, C.-W. Shu: Low and High Field Scaling Limits for the Vlasov- and Wigner-Poisson-Fokker-Planck Systems, Transp. Theo. Stat. Phys. 30, No. 2-3 (2001) 121-153. [pdf] [www]

  61. A. Arnold, P. A. Markowich, G. Toscani, A. Unterreiter: On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations, Comm. PDE 26, No. 1-2 (2001) 43-100. [pdf] [www]

  62. A. Arnold, P. A. Markowich, G. Toscani: On large time asymptotics for drift-diffusion-Poisson systems, Transp. Theo. Stat. Phys. 29, No. 3-5 (2000) 571-581. [pdf] [www]

  63. A. Unterreiter, A. Arnold, P. A. Markowich, G. Toscani: On generalized Csiszár-Kullback inequalities, Monatshefte für Mathematik 131, No. 3 (2000) 235-253. [pdf] [www]

  64. A. Arnold, H. Lange, P. F. Zweifel: A discrete-velocity, stationary Wigner equation, J. Math. Phys. 41, No. 11 (2000) 7167-7180. [pdf] [www]

  65. A. Arnold: Numerically absorbing boundary conditions for quantum evolution equations, VLSI Design 6, No. 1-4 (1998) 313-319. [pdf] [www]

  66. A. Arnold, M. Ehrhardt: Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics, J. Comput. Phys. 145, No. 2 (1998) 611-638. [pdf] [www]

  67. A. Arnold, U. Giering: An Analysis of the Marshak Conditions for matching Boltzmann and Euler Equations, Math. Models and Meth. in the Appl. Sc. 7, No. 4 (1997) 557-577. [pdf] [www]

  68. A. Arnold, C. Ringhofer: An operator splitting method for the Wigner-Poisson problem, SIAM J. Numer. Anal. 33, No. 4 (1996) 1622-1643. [pdf] [www]

  69. A. Arnold, L. L. Bonilla, P. A. Markowich: Liapunov functionals and large-time asymptotics of mean-field nonlinear Fokker-Planck equations, Transp. Theo. Stat. Phys. 25, No. 7 (1996) 733-751. [pdf] [www]

  70. A. Arnold: Self-consistent relaxation-time models in quantum mechanics, Comm. PDE 21, No. 3&4 (1996) 473-506. [pdf] [www]

  71. A. Arnold, C. Ringhofer: Operator splitting methods applied to spectral discretizations of quantum transport equations, SIAM J. Numer. Anal. 32, No. 6 (1995) 1876-1894. [pdf] [www]

  72. A. Arnold: On absorbing boundary conditions for quantum transport equations, Math. Modell. Num. Anal. 28 (1994) 853-872. [pdf] [www]

  73. A. Arnold, F. Nier: Numerical analysis of the deterministic particle method applied to the Wigner equation, Math. of Comp. 58 (1992) 645-669. [pdf] [www]

  74. N. J. Mauser, A. Arnold, P. A. Markowich: The self-consistent Bloch-equation in one dimension, Computers Math. Applic. 21 (1991) 197-202. [pdf] [www]

  75. A. Arnold, F. Nier: The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case, Math. Meth. Appl. Sc. 14 (1991) 595-613. [pdf] [www]

  76. A. Arnold, P. A. Markowich, N. J. Mauser: The one-dimensional periodic Bloch-Poisson equation, Math. Models and Meth. in the Appl. Sc. 1 (1991) 83-112. [pdf] [www]

  77. A. Arnold, N. J. Mauser: An efficient method of bookkeeping next neighbours in molecular dynamics simulations, Comp. Phys. Comm. 59 (1990) 267-275. [pdf] [www]

  78. A. Arnold, P. A. Markowich: The periodic quantum Liouville-Poisson problem, Boll. U.M.I. 7 (1990) 449-484. [pdf]

  79. A. Arnold, N. J. Mauser, J. Hafner: A molecular dynamics study of the structure of liquid germanium, J. Phys., Cond. Matter 1 (1989) 965-980. [pdf] [www]

  80. A. Arnold, H. Steinrück: The 'electromagnetic' Wigner equation for an electron with spin, ZAMP 40, No. 6 (1989) 793-815. [pdf] [www]

  81. A. Arnold, P. Degond, P. A. Markowich, H. Steinrück: The Wigner-Poisson problem in a crystal, Appl. Math. Lett. 2, No. 2 (1989) 187-191. [pdf] [www]

Publications in conference proceedings

  1. A. Arnold, J. Körner: High-order WKB-based method for the 1D stationary Schrödinger equation in the semi-classical limit, To appear in ICNAAM 2022 (2022), T.E. Simos, AIP Publishing. [pdf]

  2. J. Körner, A. Arnold, C. Klein, J. M. Melenk: Optimally truncated WKB approximation for the highly oscillatory stationary 1D Schrödinger equation, Submitted (2023). [pdf]

  3. F. Achleitner, A. Arnold, A. Jüngel: Necessary and sufficient conditions for strong stability of explicit Runge-Kutta methods, Submitted (2023). [pdf]

  4. A. Arnold, J. Dolbeault, C. Schmeiser, T. Wöhrer: Sharpening of decay rates in Fourier based hypocoercivity methods, Recent Advances in Kinetic Equations and Applications, Proceedings of INdAM-workshop, Rome, Nov. 2019, No. 48 (2021) 1-50, F. Salvarani (ed.), Springer INdAM Series. [pdf] [www]

  5. K. Döpfner, A. Arnold: On the stationary Schrödinger equation in the semi-classical limit: Asymptotic blow-up at a turning point, PAMM 19, No. 1 (2019). 90th GAMM Annual Meeting, Wiley. [pdf] [www]

  6. F. Achleitner, A. Arnold, B. Signorello: On optimal decay estimates for ODEs and PDEs with modal decomposition, Stochastic Dynamics out of Equilibrium, Springer Proceedings in Mathematics & Statistics 282 (2019) 241-264, G. Giacomin et al. (eds.), Springer. [pdf] [www]

  7. F. Achleitner, A. Arnold, E. A. Carlen: On linear hypocoercive BGK models, Proceedings of "Particle Systems and PDE's - III", Braga, Portugal, Dec. 2014 126 (2016) 1-37. [pdf] [www]

  8. A. Arnold, M. Ehrhardt: A Transparent Boundary Condition for an Elastic Bottom in Underwater Acoustics, Proceedings of the "6th Conference on Finite Difference Methods: Theory and Applications," Lozenetz, Bulgaria, June 2014; in Lectures Notes in Computer Science 9045 "Finite Difference Methods, Theory and Applications" (2015) 15-24, I. Dimov, I. Faragó, L. Vulkov (eds.), Springer. [pdf] [www]

  9. A. Arnold, L. Neumann, W. Hochhauser: Stability of glued and embedded Glass Panes: Dunkerley straight Line as a conservative Estimate of superimposed buckling Coefficients, IFAC-PapersOnLine (2013) 124-129. Proceedings of the "7th Vienna International Conference on Mathematical Modelling" (I. Troch, F. Breitenecker, Ed.), Vienna 2012. [pdf] [www]

  10. J. Geier, A. Arnold: WKB-based schemes for two-band Schrödinger equations in the highly oscillatory regime, Nanosystems: Physics, Chemistry, Mathematics 2, No. 3 (2011) 7-28. [pdf]

  11. M. Miletić, A. Arnold: Euler-Bernoulli Beam with Boundary Control: Stability and FEM, PAMM 11, No. 1 (2011) 681-682. [pdf] [www]

  12. A. Arnold, J. Geier: Asymptotically correct finite difference schemes for highly oscillatory ODEs, AIP Conference Proceedings 1281 (2010) 206-209. International Conference of Numerical Analysis and Applied Mathematics 2010, T. E. Simos (ed.). [pdf] [www]

  13. X. Antoine, A. Arnold, C. Besse, M. Ehrhardt, A. Schädle: A Review of artificial boundary conditions for the Schrödinger equation, PAMM 7, No. 1 (2008) 1023201-1023202. [pdf] [www]

  14. A. Arnold, F. Fagnola, L. Neumann: Quantum Fokker-Planck models: the Lindblad and Wigner approaches, Quantum Probability and related Topics - Proceedings of the 28th Conference (Series: QP-PQ: Quantum Probability and White Noise Analysis - Vol. 23), J.C. García, R. Quezada, S.B. Sontz (Eds.), World Scientific (2008). [pdf] [www]

  15. A. Arnold, M. Schulte: Transparent boundary conditions for quantum-waveguide simulations, Proceedings of MATHMOD 2006, Vienna, Austria, Mathematics and Computers in Simulation 79 (2008) 898-905. [pdf] [www]

  16. A. Arnold, M. Schulte: Transparent boundary conditions for the 2D Schrödinger equation: efficient implementation, PAMM 7, No. 1 (2008) 1023203-1023204. [pdf] [www]

  17. A. Arnold, M. Ehrhardt, I. Sofronov: Approximation and fast calculation of non-local boundary conditions for the time-dependent Schrödinger equation, Domain Decomposition Methods in Science and Engineering (Series: Lecture Notes in Computational Science and Engineering) 40 (2004) 141-148, R. Kornhuber, R. Hoppe, J. Périaux, O. Pironneau, O. Widlund, J. Xu (eds.), Springer. [pdf] [www]

  18. M. Ehrhardt, A. Arnold: Discrete transparent boundary conditions for wide angle parabolic equations: Fast calculation and approximation, Proceedings of the "Seventh European Conference on Underwater Acoustics - ECUA 2004" - TU Delft, Netherlands, July 2004 (2004) 9-14, D. G. Simons (ed.). [pdf]

  19. A. Arnold, M. Ehrhardt, I. Sofronov: A Fast method to implement non-local discrete transparent boundary condition for the Schrödinger equation, PAMM 2, No. 1 (2003) 424-425. [pdf] [www]

  20. A. Arnold, E. A. Carlen: A generalized Bakry-Emery condition for non-symmetric diffusions, EQUADIFF 99, Proceedings of the "International Conference on Differential Equations", Berlin 1999, B. Fiedler, K. Gröger, J. Sprekels (eds.), World Scientific Publishing (2000) 732-734. [pdf] [www]

  21. A. Arnold, M. Ehrhardt: A new discrete transparent boundary condition for standard and wide angle "parabolic" equations in underwater acoustics, Theoretical and Computational Acoustics '97, Y.-C. Teng et al. (ed.), Proceedings of the 3rd ICTCA, Newark, USA (1997) 623-635. [pdf] [www]

  22. A. Arnold: The relaxation-time von Neumann-Poisson equation, Proceedings of ICIAM 95, Hamburg (1995), Oskar Mahrenholtz, Reinhard Mennicken (eds.); ZAMM 76, No. S2 (1996) 293-296. [pdf]

  23. A. Arnold: The relaxation-time Wigner equation, Mathematical Problems in Semiconductor Physics, Proceedings of workshop in Rome, Italy (1993); Pitman Research Notes in Mathematics Series, Longman-London 340 (1995) 105-117, Marcati, Markowich, Natalini (eds.). [pdf]

  24. A. Arnold: A mixed spectral-collocation and operator splitting method for the Wigner- Poisson equation, Mathematics of Computation 1943-1993, Proceedings of symposium in Vancouver, Canada 1993, American Mathematical Society (1994) 249-253, W. Gautschi (ed.). [pdf]

  25. A. Arnold, C. Ringhofer: Operator splitting methods for the Wigner-Poisson equation, Proceedings of the International Workshop on Computational Electronics, Urbana-Champaign, USA (1992). [pdf] [www]

  26. A. Arnold: Quantum transport in semiconductors: numerical methods, Proceedings of Numsim '91, Berlin, ZIB, Technical Report 91, No. 8 (1991) 51-56, Gajewski, Deuflhard, Markowich (eds.). [pdf]

  27. A. Arnold, P. A. Markowich: Quantum transport models for semiconductors, Applied and Industrial Mathematics (1991) 301-307, R. Spigler (ed.), Kluwer Acad. Publ. [pdf] [www]

Conference Posters

  1. R. Hammer, C. Ertler, W. Pötz, A. Arnold: Dynamics of Dirac Fermions in Topological Insulators, Internat. Symposium on Advanced Nanodevices and Nanotechnology 2011, Maui, USA (2011). [pdf]

Lecture Notes

  1. A. Arnold: Entropy method and the large-time behavior of parabolic equations, Summer School in Ravello, Italy (2002) 1-37. [pdf]