Publications of Axel Klar

Journal Publications

1. T. Goetz, A. Klar, A. Unterreiter, R. Wegener Numerical evidence for the non-existence of solutions to the equations describing rotational fiber spinning,
   to appear in MMMAS

2. M. Grothaus, A. Klar Ergodicity of non-coercive diffusions in textile production processes
   to appear in SIAM Math. Anal.

3. G. Thoemmes, J. Becker, M. Junk,D. Kehrwald, A. Klar,K. Steiner, A. Wiegmann Lattice-Boltzmann / Level-Set Method for two-phase flow
   to appear in JCP

4. S. Hardt, S. Tiwari, A. Klar, Propulsion of Nanoobjects between Parallel Heated Plates
   Microfluidics and Nanofluidics, electronic version

5. A. Klar, M. Seaid, G. Thoemmes Lattice Boltzmann Simulation of Depth-Averaged Models in Flow Hydraulics,
   to appear in International Journal of Computational Fluid Dynamics

6. A. Klar, P. Reuterswaerd, M. Seaid, A Semi-Lagrangian method for a Fokker-Planck equation describing fibre dynamics
   to appear in J. Scientific Computing
   

7. A. Fuegenschuh, S. Goettlich, M. Herty, A. Klar, A. Martin, A discrete optimization approach to Large Scale Supply Networks based on Partial Differential Equations
   SIAM Scient. Computing 30, 3, 1490-1507 2008
   

8. L. Bonilla,T. Goetz, A. Klar, N. Marheineke, R. Wegener, Hydrodynamic limit of a Fokker--Planck equation describing fiber lay--down processes
   SIAM Appl. Math. 68, 3, 648-665, 2007
   

9. T. Goetz, A. Klar, N. Marheineke, R. Wegener, A Stochastic Model and Associated Fokker-Planck Equation for the Fiber Lay-down Process in Nonwoven Production Processes
   SIAM Appl. Math. 67, 6, 1704-1717, 2007
   

10. M. Frank, M. Frank, A. Klar, E. Larsen, S. Yasuda, Time -dependent Simplified PN Approximation to the Equations of radiative transfer
    JCP 226 (2), 2289-2305, 2007
    

11. M. Banda, A. Klar, M. Seaid, Lattice Boltzmann relaxation methods for coupled convection and radiation systems
    Journal of Computational Physics 226, 2, 2007, 1408-143
    

12. M. Banda, A. Klar, L. Pareschi, M. Seaid, Lattice Boltzmann type relaxation systems and relaxation schemes for the incompressible Navier Stokes equations
    Mathematics of Computation 77, 943-965, 2008
    

13. P. Degond, S. Goettlich, M. Herty, A. Klar, A network model for supply chains with multiple policies, SIAM Multiscale Modeling and Simulation 6, 3
    

14. E. Schneider, M. Seaid, J.Janicka, A. Klar Validation of simplified PN models for radiative transfer in combustion systems Comm. Num. Meth. Eng. 2007 (in press)
    

15. M. Herty, A. Klar, B. Piccolli, Existence of solutions for supply chain models based on partial differential equations, SIAM J. Math. Anal. 39 (1), 160-173, 2007
    

16. M. Frank. H. Hensel, A. Klar, A fast and accurate moment method for the Fokker-Planck equation and Applications to Electron Radiotherapy SIAM Appl. Math. 67 (2), 582-603, 2007
    

17. M. Gugat, M. Herty, A. Klar, G. Leugering, Conservation law constrained optimizaton based upon front-tracking
    MMAN 40 (5), 939-960, 2007
    

18. M. Herty, A. Klar, A.K. Singh, P. Spellucci Smoothed Penalty Algorithms for Optimization of Nonlinear Models
    COAP 37 (2), 2007 (online)
    

19. C. Kirchner, S. Goettlich, M. Herty, A. Klar Optimal control for continuous supply network models NHM 1 (4), 675-688, 2006
    

20. M. Herty, C. Kirchner, A. Klar Instantaneous Control For Traffic Flow MMAS 30 (2), 153-169, 2006
    

21. M. Frank, B. Dubroca, A. Klar Partial moment entropy approximation to radiative heat transfer
    JCP 218 (1), 1-18, 2006
    

22. M. Herty, R. Illner, A. Klar, V. Panferov Qualitative Properties of Solutions of Systems of Fokker-Planck Equations in Multilane Traffic Flow TTSP 35 (1-2), 31-54, 2006
    

23. S. Goettlich, M. Herty, A. Klar, Modelling and Optimization of supply chains on complex networks
    CMS, 4(2), 315-330, 2006
    

24. M. Banda, M. Herty, A. Klar Coupling conditions for gas networks governed by the isothermal Euler equations
    NHM 1(2), 295-314, 2006
    

25. M. Banda, M. Herty, A. Klar Gas flow in pipeline networks
    NHM 1(1), 41-56, 2006
    

26. I. Teleaga, M. Seaid, I. Gasser, A. Klar, J. Struckmeier Radiation models for thermal flows at low Mach numbers
    JCP 215 (2), 506-525, 2006
    

27. M.K. Banda, Wen-An Yong, A. Klar A Stability Notion for Lattice Boltzmann Equations SISC 27,(6), 2098-2111, 2006
    

28. A. Fuegenschuh, M. Herty, A. Klar, A. Martin Combinatorial and Continuous Models for the Optimization of Traffic Flows on Networks SIOPT 16(4), 1155-1176, 2006
    

29. S. Goettlich, M. Herty, A. Klar Network models for supply chains
    CMS 3(4), 545-559, 2005
    

30. M. Herty, A. Klar, L. Pareschi General kinetic models for vehicular traffic flow and Monte Carlo methods Computational methods in applied mathematics 5(2), 155-169, 2005
    

31. M. Junk, A. Klar, L.S. Luo Asymptotic Analysis of the Lattice Boltzmann Equation JCP 210 (2), 676-704, 2005
    

32. M. Gugat, M. Herty, A. Klar, G. Leugering Optimal control for traffic flow networks JOTA 126 (3), 589-616, 2005
    

33. M. Seaid, M. Frank, A. Klar, R. Pinnau and G. Thoemmes Efficient numerical methods for radiation in gas turbines J. Comp. Applied Math. 170 (1), 217-239, 2004
    

34. R. Turpault, M. Frank, B. Dubroca, A. Klar Multigroup half space moment approximations to the radiative heat transfer equations JCP, 198 (1), 363-371, 2004
    

35. M. Herty, A. Klar Simplified dynamics and Optimization of Large Scale Traffic Flow Networks
    Math. Mod. Meth. Appl. Sci. 14 (4), 579-601, 2004

36. N. BenAbdallah, I. Gamba, A. Klar The Milne Problem for High Field Kinetic Equations
    SIAM Appl. Math. 64/5, 1709-1736, 2004

37. A. Klar, R. Wegener Traffic flow: models and numerics
    in Modeling and Computational Methods for Kinetic Equations, Editors: P. Degond, L. Pareschi, G. Russo, Birkhaeuser, 219-259, 2004

38. E. Larsen, G. Thoemmes, A. Klar New Frequency-Averaged Approximations to the Equations of Radiative Heat Transfer
    SIAM Appl. Math.64 (2), 565-582, 2003

39. M. Herty, A. Klar Modeling, Simulation and Optimization of Traffic Flow Networks
    SIAM Sci. Comp. 25 (3), 1066-1087, 2003

40. A. Klar, L. Pareschi, M. Seaid Uniformly accurate schemes for relaxation approximations to fluid dynamic equations
    Appl. Math. Let. 16 (7), 1123-1127, 2003

41. M. Guenther, A. Klar, T. Materne, R. Wegener Multivalued fundamental diagrams and stop and go waves for continuum traffic flow equations SIAM J. Appl. Math. 64 (2), 468-483, 2003
    

42. R. Illner, A. Klar, T. Materne Vlasov-Fokker-Planck models for multilane traffic flow
    Comm. Math. Sci. 1 (1), 1-12, 2003

43. M. Banda, M. Junk, A. Klar Kinetic derivation of a finite difference scheme for the incompressible Navier Stokes equation
    J. Comp. Appl. Math., 154 (2), 341-354 , 2003

44. J. Greenberg, A. Klar, M. Rascle Congestion on multilane highways
    SIAM J. Appl. Math. 63 (3), 818-833, 2003

45. B. Dubroca, M. Frank, A. Klar, G. Thoemmes A half space moment approximation to the radiative heat transfer equations
    Z. Angew. Math.Mech., 83 (12), 853-8582003

46. (with B. Dubroca) A half moment model to take into account strong kinetic non-equilibrium
    C.R.Acad.Sci.Paris, Ser. I 335 (8), 699-704, 2002

47. B. Dubroca, A. Klar Half Moment closure for radiative transfer equations
    J. Comp. Phys., 180 (2), 584-596, 2002

48. E. Larsen, G. Thoemmes,M. Seaid,T. Goetz, A. Klar Simplified PN approximations to the equations of radiative transfer and applicatons to glass manufacturing
    J. Comp. Phys., 183 (2), 652-675, 2002

49. R. Illner, C.Stoica, A. Klar, R. Wegener Kinetic equilibria in traffic flow models
    TTSP, 31 (7), 615-634, 2002

50. A. Klar, A. Unterreiter Uniform stability of a finite difference scheme for transport equations in diffusive regimes
    SIAM J. Num. Anal. 40 (3), 891-913, 2002

51. A. Aw, A. Klar, T. Materne, M. Rascle Derivation of continuum flow traffic models from microscopic Follow the leader models
    SIAM J. Appl. Math. 63 (1), 259-278, 2002

52. M. Guenther, A. Klar, T. Materne, R. Wegener An explicitly solvable kinetic model for vehicular traffic and associated macroscopic equations,
    Math. Comp. Modelling 35 (5-6), 591-606, 2002

53. P. Degond, A. Klar A relaxation approximation for transport equations in the diffusive limit
    Appl. Math. Lett. 15(2), 131--135, 2002

54. A. Klar, C. Schmeiser Numerical Passage from Radiative Heat Transfer to Nonlinear Diffusion Models
    Math. Meth. Mod. Appl. Sci. 11 (5), 749-767, 2001

55. M. Junk, A. Klar Discretization for the incompressible Navier Stokes equations based on the Lattice-Boltzmann method
    SIAM J. Sci. Comp., 22 (1), 1-19, 2000

56. A. Klar, R. Wegener Kinetic Derivation of Macroscopic Anticipation Models for Vehicular Traffic,
    SIAM J. Appl. Math. 60 (5), 1749-1766, 2000

57. S. Albeverio, A. Klar Longtime Behaviour of Stochastic Hamiltonian Systems
    Potential Analysis 12, 281-297, 2000

58. A. Klar, R. Wegener Kinetic Traffic Flow Models,
    in 'Modeling in Applied Sciences: A kinetic theory approach', Editors N. Bellomo, M. Pulvirenti, Birkhäuser,
    263-317, 2000

59. A. Klar, H. Neunzert, J. Struckmeier Transition from Kinetic Theory to Macroscopic Fluid Equations: A Problem for Domain Decomposition and a Source for New Algorithms, TTSP 29 (1-2), 93-106, 2000
    

60. A. Klar An Asymptotic Preserving Numerical Scheme for Kinetic Equations in the Low Mach Number Limit
    SIAM J. Num. Anal., 36 (5), 1507-1527, 1999

61. R. Illner, A. Klar, H. Lange, A. Unterreiter, R. Wegener A Kinetic Model for Vehicular Traffic: Existence of stationary solutions
    J. Math. Anal. Appl. 237 (2), 622-643, 1999

62. A. Klar Relaxation Scheme for a Lattice Boltzmann-type Discrete Velocity Model and Numerical Navier Stokes Limit
    J. Comp. Phys. 148 (2), 416-432, 1999

63. A. Klar, R. Wegener A Hierarchy of Models for Multilane Vehicular Traffic I: Modeling
    SIAM J. Appl. Math. 59 (3), 983-1001, 1999
    

64. A. Klar, R. Wegener A Hierarchy of Models for Multilane Vehicular Traffic II: Numerical Investigations
    SIAM J. Appl. Math. 59 (3), 1002-1011, 1999
    

65. A. Klar A Numerical Method for Kinetic Semiconductor Equations in the Drift Diffusion Limit
    SIAM J. Sci. Comp., 20 (5), 1696-1712, 1999
    

66. A. Klar An Asymptotic Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit
    SIAM J. Num. Anal. 35 (3), 1073-1094, 1998

67. A. Klar Asymptotic Induced Domain Decomposition Methods for Kinetic and Drift Diffusion Semiconductor Equations
    SIAM J. Sci. Comp. 19 (6), 2032-2050, 1998

68. (with N. Siedow) Boundary Layers and Domain Decomposition for Radiative Heat Transfer and diffusion Equations: Applications to Glass Manufacturing Processes
    Eur. J. Appl. Math. 9-4, 351-372, 1998
    

69. A. Klar, S. Tiwari An Adaptive Domain Decomposition Procedure for Boltzmann and Euler Equations
    J. Comp. Appl. Math. 90 (2), 223-237, 1998
    

70. A. Klar Asymptotic Analysis and Coupling Conditions for Kinetic and Hydrodynamic Equations
    Comp. Math. Appl., Vol. 35 (1-2), 127-137, 1998

71. A. Klar, R. Wegener Enskog-like Kinetic Models for Vehicular Traffic
    J. Stat. Phys., 87, (1-2), 91-114, 1997
    

72. (with Y.Arkipov, O. Mingalyov, V.Vedenyapin) A Class of Invariants for the Boltzmann Equation and the Broadwell Model
    Eur. J. Mech./B, 16, 3, 387-399, 1997
    

73. (with R. Kuehne, R. Wegener) Mathematical Models for Vehicular Traffic
    Surv. Math. Ind., 6, 215-239, 1996
    

74. A. Klar, R. Wegener A Kinetic Model for Vehicular Traffic Derived from a Stochastic Microscopic Model
    Transp. Theory Stat. Phys., 25(7), 785-798, 1996
    

75. A. Klar Domain Decomposition for Kinetic Problems with Noneqilibrium States
    Eur. J. Mech., B/Fluids, 15, 2, 203-216, 1996

76. A. Klar Computation of nonlinear functionals in Particle Methods
    Computing 55 (3), 207-221, 1995

77. F. Golse, A. Klar A Numerical Method for Computing Asymptotic States and Outgoing Distributions for a Kinetic Linear Half Space Problem
    J. Stat. Phys. 80 (5-6), 1033-1061, 1995
    

78. A. Klar Convergence of Alternating Domain Decomposition Schemes
    Math. Meth. Appl. Sci. 18 (8), 649-670, 1995

79. (with Y.Arkipov, V.Vedenyapin) On the Connection of Entropy and Stationary Distributions
    J. Stat. Phys. 77 (5-6), 1027-1037, 1994
    

80. S. Albeverio, A. Klar Longtime Behaviour of Nonlinear Stochastic Oscillators
    J. Math. Phys. 35(8), 4005-4027, 1994
    

    Refereed Proceedings

81. S Tiwari,C. Drumm. V.K. Sharma. J. Kuhnert, M.Attarakih, A. Klar, H-J Bart A meshfree CFD-population balance equation coupled model
    SINTEF/NTNU, Trondheim 2008

82. M. Herty, A. Klar and A.K. Singh An ODE traffic network model
    Journal of Computational and Applied Mathematics, 203 (2), 419-436, 2007

83. M. Seaid, A. Klar Asymptotic-Preserving Schemes for Unsteady Flow Simulations
    J. Computers and Fluids 35 (8-9), 872-878, 2006

84. M. Banda, M. Junk, A. Klar Kinetic-based numerical schemes for incompressible Navier- Stokes equations
    J. Computers and Fluids, 35 (8-9), 879-887, 2006

85. M. Seaid, A. Klar, R. Pinnau Numerical Solvers for Radiation and Conduction in High Temperature Gas Flows
    J. Flow Turbulence and Combustion, 75, 173-190, 2005

86. M. Seaid, A. Klar Multigrid Solution of Three-Dimensional Radiative Heat Transfer in Glass Manufacturing
    Progress in Industrial Mathematics at ECMI 2004, 8, 283-287, 2005

87. A. Klar, J. Lang, M. Seaid Adaptive solutions of SP_N-Approximations to radiative heat transfer in glass
    Int. J. Thermal Sciences, 44, 1013-1023, 2005

88. B. Dubroca, A. Klar and M. Seaid Flux Limiters in the Coupling of Radiation and Hydrodynamics Models
    J. Comp. Appl. Math. 168 (1-2), 425-435, 2004

89. M. Frank, A. Klar, M. Seaid, R.. Pinnau and G. Thoemmes A comparison of approximate models for radiation in gas turbines
    Progress in Computational Fluid Mechanics (PCFD) 4 (3-5), 191-197, 2004

90. M. Herty, A.K. Singh, A. Klar Flow optimization on traffic networks
    PAMM 4 (1), 624-625, 2004

91. M. Banda, M. Seaid A. Klar, L. Pareschi Compressible and Incompressible Limits for Hyperbolic Systems with Relaxation
    J. Comp. Appl. Math. 168 (1-2), 41-52, 2004

92. (with M.K. Banda, Wen-An Yong ) Stability Structure for Lattice Boltzmann Equations: Some Computational Results
    Proceedings in Applied Mathematics and Mechanics (PAMM), 3 (1),72-75, 2003

93. M. Seaid, A. Klar Efficient Preconditioning of Linear Systems Arising from the Discretization of Radiative Transfer Equation
    Challenges in Scientific Computing, Berlin 2002, Lecture Notes in Computational Science and Engineering, 35, 211-236, 2003

94. R. Illner, A. Klar, T. Materne On Vlasov-Fokker-Planck type kinetic models for multilane traffic Flow
    Rarefied Gas Dynamics: 23rd International Symposium, Whistler 2002, 283-290, 2003

95. M. Seaid Generalized numerical approximations for the radiative heat transfer problems in two space dimensions
    Eurotherm73 on Computational Thermal Radiation in Participating Media, Mons, Belgium, 419-429, 2003

96. A. Klar, G. Thoemmes Numerical methods for radiative heat transfer in diffusive regimes
    in IMA Volumes in Mathematics and its Applications 135: Transport in Transition Regimes Springer-Verlag, New York, 199-216, 2003

97. A. Klar, M. Herty Modelling of Traffic Flow Networks
    Modelisation du trafic: Actes du groupe de travail 2002, Actes No. 97, Les Collections des L'Inr ets, Editor M. Arion, F. Boillot, J.-P. Lebacque

98. G. Thoemmes, R. Pinnau, M. Seaid, T. Goetz, A. Klar Numerical Methods and Optimal Control for Glass Cooling Processes
    TTSP 31 (4-6), 513-529, 2002

99. M. Banda, M. Junk, A. Klar A limiter based on Kinetic theory
    TTSP, 31 (4-6), 491-512, 2002

100. (with M. Seaid) High-Order Relaxation Methods for Incompressible Navier-Stokes Equations
     Numerical Mathematics and Advanced Applications, 79-89, 2001

101. A. Klar, R. Wegener Vehicular Traffic: From Microscopic to Macroscopic Description
     Proceedings of the 5th MAFPD workshop, Maui, Hawaii 1998, TTSP 29 (3-5), 479-493, 2000
     

102. A. Klar A Numerical Method for Nonstationary Transport Equations in Diffusive Regimes
     Proceedings of the 15. International Conference on Transport Theory 1997 in Goeteborg, TTSP 27 (5-7), 653-666, 1998

103. A. Klar Asymptotic-Induced Domain Decomposition Methods for Kinetic Equations with the Diffusion Scaling
     Proceedings of GAMM 1997 in Regensburg, Germany, Z. Angew. Math. Mech. 78, Suppl. 3, 975-976, 1998

104. A. Klar, H.Neunzert, J. Struckmeier Particle Methods and Domain Decomposition
     Proceedings of the 20. International Symposium on Rarefied Gas Dynamics 1996 in Bejing, ed. by C. Shen, Peking University Press, 263-272, Beijing, 1997
     

105. A. Klar, H.Neunzert, J. Struckmeier Particle Methods: Theory and Applications
     ICIAM 95: proceedings of the Third International Congress on Industrial and Applied Mathematics held in Hamburg, Germany, 1995, ed. by K. Kirchgaessner, O. Mahrenholtz, R. Mennicken, Berlin: Akad. Verl., (Mathematical Research, Vol. 87) 281-306, 1996
     

106. Domain Decomposition for Kinetic and Aerodynamic Equation
     Proceedings of the Third International Congress on Industrial and Applied Mathematics, ICIAM, in Hamburg 1995, in Applied Sciences, especially Mechanics, ed. by E. Kreuzer, O. Mahrenholtz, Akademie Verlag, Berlin Z. Angew. Math. Mech. 76-5, 255-256, 1996

107. A. Klar Domain Decomposition and Coupling Conditions for Kinetic and Hydrodynamic Equations
     Numerical Treatment of Coupled Systems, ed. by W. Hackbusch, G. Wittum, Vieweg, Braunschweig, Notes Numer. Fluid Mech. 51, 128-138, 1995

108. (with S.Albeverio, J. Gaines) Longtime Behaviour of Nonlinear Hamiltonian Systems with a Stochastic Force
     Stochastic Processes, Physics and Geometry II, Proceedings Locarno, Switzerland, 24 - 29 June 1991, S. Albeverio, U.Cattaneo, D.Merlini (Edts), 14-28, World Scientific, Singapore 1995
     

     Further publications

109. Asymptotic Analysis and Numerical Methods for Transport Equations, Habilitationsschrift, Universität Kaiserslautern, 1997
     

110. Domain Decomposition for Kinetic and Aerodynamic Equations, Dissertation, Universität Kaiserslautern, 1994

111. Langzeitverhalten nichtlinearer stochastischer Oszillatoren, Diplomarbeit, Ruhr-Universität Bochum, 1991

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