Prof. Dr. Arnold Reusken

Books

Buch Dahmen Reusken W. Dahmen, A. Reusken, Numerik für Ingenieure und Naturwissenschaftler,
First edition 2006, Second edition 2008.
Springer-Lehrbuch, ISBN 978-3-540-76492-2
Buch Gross Reusken S. Gross, A. Reusken, Numerical Methods for Two-phase Incompressible Flows,
First edition 2011,
Springer Series in Computational Mathematics, Vol. 40, ISBN 978-3-642-19685-0
Buch Bothe Reusken D. Bothe, A. Reusken Transport Processes at Fluidic Interfaces
Springer, ISBN 978-3-319-56602-3

Papers

  1. T. Ludescher, S. Groß, A. Reusken : A multigrid method for unfitted finite element discretizations of elliptic interface problems , IGPM report 481, RWTH Aachen (2018)
  2. I. Voulis, A. Reusken : A Time Dependent Stokes Interface Problem: Well-Posedness and Space-Time Finite Element Discretization , IGPM report 479, RWTH Aachen (2018)
  3. A. Reusken : Stream Function Formulation of Surface Stokes Equations , IGPM report 478, RWTH Aachen (2018)
  4. M. A. Olshanskii, A. Quaini, A. Reusken, V. Yushutin : A Finite Element Method for the Surface Stokes Problem , IGPM report 475, RWTH Aachen (2018)
    also available on arXiv.org
    Accepted for publication in SIAM J. Scientific Computing
  5. I. Voulis, A. Reusken: Discontinuous Galerkin Time Discretization Methods for Parabolic Problems with Constraints , IGPM report 474, RWTH Aachen (2018)
    Accepted for publication in Journal of Numerical Mathematics
  6. P. Bandi, S. Groß, Y. Heng, W. Marquardt, A. Mhamdi, M. Modigell, A. Reusken, L. Zhang: Mass transport in wavy falling films: reduced modeling and experiment ,
    Accepted for publication in AIChE journal
  7. S. Groß, T. Jankuhn, M.A. Olshanskii, A. Reusken: A Trace Finite Element Method for Vector-Laplacians on Surfaces , IGPM report 469, RWTH Aachen (2017)
  8. T. Jahnkuhn, M. A. Olshanskii , A. Reusken: Incompressible Fluid Problems on Embedded Surfaces: Modeling and Variational Formulations , IGPM report 462, RWTH Aachen (2017),
    Accepted for publication in Interfaces and Free Boundaries.
  9. M. A. Olshanskii , A. Reusken: Trace Finite Element Methods for PDEs on Surfaces , IGPM report 460, RWTH Aachen (2016)
    In: Geometrically Unfitted Finite Element Methods and Applications (P.A. Bordas, E. Burman, M. Larson, M. Olshanskii, eds.) Lecture Notes in Computational Engineering and Science Vol. 121, 211-248.
  10. C. Lehrenfeld, A. Reusken: High order unfitted finite element methods for interface problems and PDEs on surfaces, In: Transport Processes at Fluidic Interfaces (D. Bothe, A. Reusken, eds.). Advances in Mathematical Fluid Mechanics (Birkhäuser 2017), pp. 33-64 , IGPM report 459, RWTH Aachen (2016)
  11. J. Grande, C. Lehrenfeld, A. Reusken: Analysis of a high order trace finite element method for PDEs on level set surfaces, Submitted to SIAM J. Numer. Anal. (2017), IGPM report 457, RWTH Aachen (2016)
  12. C. Lehrenfeld, A. Reusken: L2-Error Analysis of an Isoparametric Unfitted Finite Element Method for Elliptic Interface Problems, IGPM report 450, RWTH Aachen (2016)
  13. C. Lehrenfeld, A. Reusken: Analysis of a high order unfitted finite element method for elliptic interface problems , IMA J. Numer. Anal. (2017), DOI: 10.1093/imanum/drx041 , IGPM report 445, RWTH Aachen (2016)
  14. C.J. Falconi, C. Lehrenfeld, H. Marschall, C. Meyer, R. Abiev, D. Bothe, A. Reusken, M. Schlüter, M. Wörner : Numerical and experimental analysis of local flow phenomena in laminar Taylor flow in a square mini-channel, Physics of Fluids (2016), 28, 012109, DOI: 10.1063/1.4939498
  15. A. Reusken, X. Xu, L. Zhang : Finite element methods for a class of continuum models for immiscible flows with moving contact lines , Int. J. Numer. Meth. Fluids (2016), DOI: 10.1002/fld.4349 , IGPM report 432, RWTH Aachen (2015)
  16. S. Groß, T. Ludescher, M. Olshanskii, A. Reusken: Robust Preconditioning for XFEM Applied to Time-Dependent Stokes Problems, SIAM J. Sci. Comput. 38, A3492-A3514 (2016), DOI: 10.1137/15M1024007, IGPM report 424, RWTH Aachen (2015)
  17. M. Kirchhart, S. Gross, A. Reusken : Analysis of an XFEM Discretization for Stokes Interface Problems , SIAM J. Sci. Comput. 38, A1019-A1043 (2016), DOI: 10.1137/15m1011779 , IGPM report 420, RWTH Aachen (2015).
  18. C. Lehrenfeld, A. Reusken : Finite Element Techniques for the Numerical Simulation of Two-Phase Flows with Mass Transport, In Computational Methods for Complex Liquid-Fluid Interfaces, Eds. M.T. Rahni, M. Karbaschi, R. Miller (2015),
    pp. 353-372, ISBN 9781498722087. IGPM report 413, RWTH Aachen (2014)
  19. C. Lehrenfeld, A. Reusken : Optimal preconditioners for Nitsche-XFEM discretizations of interface problems, Numerische Mathematik (2016), DOI: 10.1007/s00211-016-0801-6 IGPM report 406, RWTH Aachen (2014).
  20. J. Grande, A. Reusken : A higher order Finite Element Method for partial differential equations on surfaces, SIAM J. Numer. Anal., 54(1), 388–414. (2016), DOI: 10.1137/14097820X IGPM report 403, RWTH Aachen (2014)
  21. S. Gross, M.A. Olshanskii, A. Reusken : A trace Finite Element Method for a class of coupled bulk-interface transport problems, ESAIM: M2AM, Vol. 49 (5), 1303 - 1330 (2015), DOI: 10.1051/m2an/2015013 IGPM report 398, RWTH Aachen (2014)
  22. A. Reusken : Analysis of trace Finite Element Methods for surface partial differential equations, IMA Journal of Numerical Analysis, (2015), 35 (4), 1568-1590, doi:10.1093/imanum/dru047 IGPM report 387, RWTH Aachen (2014)
  23. J. Grande, M.A. Olshanskii, A. Reusken : A space-time FEM for PDEs on evolving surfaces, IGPM report 386, RWTH Aachen (2014). In Proceedings of the 11th World Congress on Computational Mechanics, 2014, E. Onate, J. Oliver and A. Huerta (Eds).
  24. M.A. Olshanskii, A. Reusken : Error analysis of a space-time finite element method for solving PDEs on evolving surfaces, SIAM J. Numer. Anal. 52 (4), 2092-2120 (2014), DOI: 10.1137/130936877 IGPM report 376, RWTH Aachen (2013)
  25. H. Marschall, S. Boden, C. Lehrenfeld, C.J. Falconi, U. Hampel, A. Reusken, M. Wörner, D. Bothe : Validation of interface capturing and tracking techniques with different surface tension treatments against a Taylor bubble benchmark problem, Computers & Fluids 102, 336-352 (2014), DOI: 10.1016/j.compfluid.2014.06.030
  26. M.A. Olshanskii, A. Reusken, X. Xu : An Eulerian space-time finite element method for diffusion problems on evolving surfaces, SIAM J. Numer. Anal. 52 (3), 1354-1377 (2014), DOI: 10.1137/130918149 IGPM report 362, RWTH Aachen (2013)
  27. M.A. Olshanskii, A. Reusken, X. Xu : On surface meshes induced by level set functions, Comp. Vis. Science 15, 53-60 (2012), DOI: 10.1007/s00791-013-0200-9 IGPM report 347, RWTH Aachen (2012)
  28. A. Reusken: A finite element level set redistancing method based on gradient recovery, SIAM J. Numer. Analysis 51, 2723-2745 (2013), DOI: 10.1137/120895433 IGPM report 346, RWTH Aachen (2012)
  29. S. Gross, A. Reusken: Numerical simulation of continuum models for fluid-fluid interface dynamics, Eur. Phys. J. Special Topics 222, 211-239 (2013), DOI: 10.1140/epjst/e2013-01836-9
  30. A. Reusken, Y. Zhang: Numerical simulation of incompressible two-phase flows with a Boussinesq-Scriven surface stress tensor, Numerical Methods in Fluids 73 (12), 1042-1058 (2013), DOI: 10.1002/fld.3835 IGPM report 345, RWTH Aachen (2012)
  31. C. Lehrenfeld. A. Reusken: Analysis of a Nitsche-XFEM-DG discretization for a class of two-phase mass transport problems, SIAM J. Numer. Anal. 51, No. 2, 958-983 (2013), DOI: 10.1137/120875260 IGPM report 340, RWTH Aachen (2012)
  32. M.A. Olshanskii, A. Reusken, X. Xu : A stabilized finite element method for advection-diffusion equations on surfaces, IMA J. Numer. Anal. 34 (2), 732-758 (2013), DOI: 10.1093/imanum/drt016 IGPM report 335, RWTH Aachen (2012)
  33. M.A. Olshanskii, A. Reusken, X. Xu : A volume mesh finite element method for PDEs on surfaces, IGPM report 342 , RWTH Aachen 2012. In: Proceedings of the ECCOMAS 2012 conference (2012)
  34. A. Reusken : Finite element techniques for the numerical simulation of two-phase incompressible flows, In: Proceedings of 6th International Berlin Workshop on Transport Phenomena with Moving Boundaries, VDI Fortschritt Bericht Nr. 929, 162-177 (2012)
  35. P. Bandi, S. Gross, M. Karalashvili, A. Mhamdi, H. Pirnay, L. Zhang, W. Marquardt, M. Modigell, A. Reusken : Experimental identification of effective mass transport models in falling films, In: Proceedings of 6th International Berlin Workshop on Transport Phenomena with Moving Boundaries, VDI Fortschritt Bericht Nr. 929, 276-297 (2012)
  36. C. Lehrenfeld. A. Reusken: Nitsche-XFEM with streamline diffusion stabilization for a two-phase mass transport problem, SIAM J. Sci. Comp. 34, 2740-2759 (2012), DOI: 10.1137/110855235 IGPM report 333, RWTH Aachen (2011)
  37. A. Reusken, E. Loch: On the accuracy of the level set SUPG method for approximating interfaces, IGPM report 319, RWTH Aachen (2011)
  38. A. Reusken, P.Esser: Analysis of time discretization methods for a Stokes equations with a nonsmooth forcing term, Numerische Mathematik (2013) DOI : 10.1007/s00211-013-0564-2 IGPM report 327, RWTH Aachen (2011)
  39. M. Karalashvili, S. Gross, W. Marquardt, A. Mhamdi, A. Reusken : Identification of transport coefficient models in convection-diffusion equations, SIAM J. Sci. Comp.Vol. 33, 303-327 (2011), DOI: 10.1137/09077360X
  40. B. Pollul, A. Reusken : Iterative solvers for discretized stationary Euler equations, In: Summary of Flow Modulation and Fluid-Structure Interaction Findings (W. Schröder, ed.), Notes on Numerical Fluid Mechanics and Multidisciplinary Design Vol. 109, 295-223 (2010), DOI: 10.1007/978-3-642-04088-7 IGPM report 297, RWTH Aachen (2009)
  41. A. Reusken, T.-H. Nguyen: Nitsche's method for a transport problem in two-phase incompressible flows, J. Fourier Analysis and Applications 15, 663-683 (2009), DOI: 10.1007/s00041-009-9092-y IGPM report 298, RWTH Aachen (2009)
  42. A. Reusken, T.-H. Nguyen: Nitsche-XFEM for a transport problem in two-phase incompressible flows, Proceedings of the ECCOMAS Thematic Conference on Extended Finite Element Methods (XFEM 2009), RWTH Aachen.
  43. E. Bertakis, S. Gross, J. Grande, O. Fortmeier, A. Reusken, A. Pfennig: Validated simulation of droplet sedimentation with finite-element and level-set methods,, Chem. Eng. Science 65, 2037-2051 (2010), DOI: 10.1016/j.ces.2009.11.043
  44. P. Esser, J. Grande, A. Reusken: An extended finite element method applied to levitated droplet problems, Int. J. for Numer. Meth. in Engineering 84, 757-773 (2010), DOI: 10.1002/nme.2913 IGPM report 291, RWTH Aachen (2008)
  45. A. Reusken: Introduction to multigrid methods for elliptic boundary value problems, In: Multiscale Simulation Methods in Molecular Sciences, eds. J. Grotendorst, S. Blugel, D. Marx, ISBN 978-3-9810843-8-2 (2009). pp. 467-506. IGPM report 290, RWTH Aachen (2008)
  46. M. A. Olshanskii, A. Reusken: A finite element method for surface PDEs: matrix properties, Numerische Mathematik 114, 491-520 (2009), DOI: 10.1007/s00211-009-0260-4 IGPM report 287, RWTH Aachen (2008)
  47. M. A. Olshanskii, A. Reusken, J. Grande: A finite element method for elliptic equations on surfaces, SIAM J. Numer. Anal. 47, 3339-3358 (2009), DOI: 10.1137/080717602 IGPM report 286, RWTH Aachen (2008)
  48. A. Reusken: Analysis of an extended pressure finite element space for two-phase incompressible flows, Comp. Visual. Sci. 11, 293-305, (2008), DOI: 10.1007/s00791-008-0099-8 IGPM report 281, RWTH Aachen (2007)
  49. M. Larin, A. Reusken: A comparative study of efficient iterative solvers for generalized Stokes equations, Numer. Lin. Algebra Appl. 15, 13-34, (2008), DOI: 10.1002/nla.561 IGPM report 272, RWTH Aachen (2007)
  50. M. F. M. Speetjens, A. Reusken, S. Maier-Paape, W. Marquardt: Stability analysis of two-dimensional pool-boiling systems, SIAM J. Appl. Dyn. Sys. 7, 933-961, (2008), DOI: 10.1137/070706823 IGPM report 275, RWTH Aachen (2007)
  51. M. F. M. Speetjens, A. Reusken, W. Marquardt: Steady-state solutions in a three-dimensional nonlinear pool-boiling heat-transfer model, Comm. Nonlin. Sci. Num. Sim. 13, 1518-1537, (2008), DOI: 10.1016/j.cnsns.2006.11.002 IGPM report 263, RWTH Aachen (2006)
  52. M. F. M. Speetjens, A. Reusken, W. Marquardt: Steady-state solutions in a nonlinear pool boiling model, Comm. Nonlin. Sci. Num. Sim. 13, 1475-1494, (2008), DOI: 10.1016/j.cnsns.2006.11.001 IGPM report 256, RWTH Aachen (2006)
  53. Y. Heng, A. Mhamdi, S. Gross, A. Reusken, M. Buchholz, H. Auracher, W. Marquardt: Reconstruction of local boundary heat fluxes in pool boiling experiments along the entire boiling curve from high resolution transient temperature measurements, Int. J. Heat Mass Trans. 51, 5072-5087, (2008), DOI: 10.1016/j.ijheatmasstransfer.2008.03.020
  54. M. Karalashvili, S. Gross, A. Mhamdi, A. Reusken, W. Marquardt: Incremental identification of transport phenomena in convection-diffusion systems, SIAM J. Sci. Comput. 30, 3249-3269, (2008), DOI: 10.1137/070692388 IGPM report 276, RWTH Aachen (2007)
  55. B. Pollul, A. Reusken: Numbering techniques for preconditioners in iterative solvers for compressible flows, Int. J. Numer. Meth. in Fluids 55, 241-261, (2007). IGPM report 255, RWTH Aachen (2006)
  56. A. Reusken, M. Soemers: On the robustness of a multigrid method for anisotropic reaction-diffusion problems, Computing 80, 299-317, (2007). IGPM report 266, RWTH Aachen (2006)
  57. S. Gross, A. Reusken: Finite element discretization error analysis of a surface tension force in two-phase incompressible flows, SIAM J. Numer. Anal. 45, 1679-1700, (2007). IGPM report 262, RWTH Aachen (2006)
  58. S. Gross, A. Reusken: An extended pressure finite element space for two-phase incompressible flows with surface tension, J. Comp. Phys. Volume 224,Issue 1, Pages 40-58, (2007). IGPM report 264, RWTH Aachen (2006)
  59. M. A. Olshanskii, J. Peters, A. Reusken: Uniform preconditioners for a parameter dependent saddle point problem with application to generalized Stokes interface equations, Numer. Math. 105, 159-191, (2006). IGPM report 252, RWTH Aachen (2005)
  60. M. A. Olshanskii, A. Reusken: Analysis of a Stokes interface problem, Numer. Math. 103, 159-149, (2006). IGPM report 237, RWTH Aachen (2004)
  61. S. Gross, V. Reichelt, A. Reusken: A finite element based level set method for two-phase incompressible flows, Comp. Visual. Sci. 9, 239-257, (2006). IGPM report 243, RWTH Aachen (2003)
  62. S. Gross, M. Soemers, A. Mhamdi, F. Al Sibai, A. Reusken, W. Marquardt, U. Renz: Identification of boundary heat fluxes in a falling film experiment using high resolution temperature measurements, Int. J. of Heat and Mass Transfer 48, 5549-5562, (2005).
  63. J. Peters, V. Reichelt, A. Reusken: Fast iterative solvers for discrete Stokes equations, SIAM J. Sci. Comp. 27, 646-666, (2005). IGPM report 241, RWTH Aachen (2004)
  64. S. Gross, A. Reusken: Parallel multilevel tetrahedral grid refinement, SIAM J. Sci. Comp. 26, 1261-1288, (2005). IGPM report 227, RWTH Aachen (2003)
  65. M. A. Olshanskii, A. Reusken: Grad-div stabilization for Stokes equations, Math. Comp. 73, 1699-1718, (2004). IGPM report 208, RWTH Aachen (2001)
  66. M. A. Olshanskii, A. Reusken: A Stokes interface problem: stability, finite element analysis and a robust solver, In: P. Neittaanmki et al. (eds), Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004. IGPM report 239, RWTH Aachen (2004)
  67. M. A. Olshanskii, A. Reusken: Convergence analysis of a multigrid method for a convection-dominated model problem, SIAM J. Numer. Anal. 42, 1261-1291, (2004). IGPM report 231, RWTH Aachen (2003)
  68. A. Reusken: Convergence analysis of the Gauss-Seidel method for discretized one-dimensional Euler equations, SIAM J. Numer. Anal. 41, 1388-1405, (2003). IGPM report 213, RWTH Aachen (2002)
  69. A. Reusken: Convergence analysis of a multigrid method for convection-diffusion equations, Numer. Math. 91, 323-349, (2002). IGPM report 190, RWTH Aachen (2000)
  70. A. Reusken: Approximation of the determinant of large sparse symmetric positive definite matrices, SIAM J. Matrix Anal. 23, 799-818, (2002). IGPM report 187, RWTH Aachen (2000)
  71. M. A. Olshanskii, A. Reusken: Navier-Stokes equations in rotation form: A robust multigrid solver for the velocity problem, SIAM J. Scientific Comp. 23, 1683-1706, (2000). IGPM report 193, RWTH Aachen (2000)
  72. O. Bröker, M. Grote, C. Mayer, A. Reusken: Robust parallel smoothing for multigrid via sparse approximate inverses, SIAM J. Scientific Comp. 32, 1395-1416, (2001).
  73. V. Reichelt, A. Reusken: Mit Gittern auf der Spur von Tropfen, TerraTech, Zeitschrift für Altlasten und Bodenschutz V. 6, 35-37, (2001).
  74. M. A. Olshanskii, A. Reusken: On the convergence of a multigrid method for linear reaction-diffusion problems, Computing 65, 193-202, (2000). IGPM report 192, RWTH Aachen (2000)
  75. A. Reusken: An algebraic multilevel preconditioner for symmetric positive definite and indefinite problems, In: Numerical Challenges in Lattice Quantum Chromodynamics (A. Frommer, T. Lippert, B. Medeke, K. Schilling, eds.) Lecture Notes in Computational Science and Engineering 15, 66-83, (2000). IGPM report 179, RWTH Aachen (1999)
  76. A. Reusken: On the Approximate Cyclic Reduction Preconditioner, SIAM J. Scientific Comp. 21, 565-590, (1999). IGPM report 144, RWTH Aachen (1997)
  77. J. Bey, A. Reusken: On the convergence of basic iterative methods for convection-diffusion equations, Numerical Linear Algebra with Appl. 6, 329-352, (1999). IGPM report 169, RWTH Aachen (1998)
  78. A. Reusken: Approximate cyclic reduction preconditioning, In: W. Hackbusch, G. Wittum (eds.), Multigrid Methods 5, Proceedings of the Fifth European Multigrid Conference. Lecture Notes in Computational Science and Engineering Vol. 3, 243-259, (1998).
  79. M. Anthonissen, B. van't Hof, A. Reusken: A finite volume scheme for solving elliptic boundary value problems on composite grids, Computing 61, 285-305, (1998). IGPM report 152, RWTH Aachen (1998)
  80. P. J. J. Ferket, A. Reusken: A finite difference discretization method on composite grids, Computing 56, 343-369, (1996).
  81. A. Reusken: A multigrid method based on incomplete Gaussian elimination, Numerical Linear Algebra with Appl. 3, 369-390, (1996).
  82. P. J. J. Ferket, A. Reusken: Further analysis of the Local Defect Correction Method, Computing 56, 117-139, (1996).
  83. A. Reusken: On a robust multigrid solver, Computing 56, 303-322, (1996).
  84. A. Reusken: Fourier analysis of a robust multigrid method for convection-diffusion problems, Numer. Math. 71, 365-397, (1995).
  85. A. Reusken: A new robust multigrid method for 2D convection-diffusion problems, In: Fast Solvers for Flow Problems, Proceedings of the Tenth GAMM-Seminar Kiel (eds. W. Hackbusch, G. Wittum). Notes on Numerical Fluid Mechanics Vol 49, 229-240, (1995).
  86. A. Reusken: Multigrid with matrix-dependent transfer operators for convection-diffusion problems, In: P. W. Hemker, P. Wesseling (eds.), Multigrid Methods 4, Proceedings of the fourth European Multigrid Conference. International series of Numerical Mathematics Vol. 116, 269-280, (1994).
  87. A. Reusken: On maximum norm convergence of multigrid methods for elliptic boundary value problems, SIAM J. Numer. Anal. 31, 378-392, (1994).
  88. A. Reusken: Multigrid with matrix-dependent transfer operators for a singular perturbation problem, Computing 50, 199-211, (1993).
  89. A. Reusken: The smoothing property for regular splittings, In: Incomplete Decompositions (ILU)-Algorithms, theory and applications (eds. W. Hackbusch, G. Wittum). Notes on Numerical Fluid Mechanics Vol. 41, 130-138, (1993).
  90. A. Reusken: Multigrid applied to two-dimensional exponential fitting for drift-diffusion models, In: Iterative Methods in Linear Algebra, Proceedings of the IMACS International Symposium on Iterative Methods in Linear Algebra, 505-514, (1992).
  91. A. Reusken: On maximum norm convergence of multigrid methods for two-point boundary value problems, SIAM J. Numer. Anal. 29, 1569-1578, (1992).
  92. A. Reusken: Multigrid applied to mixed finite element schemes for current continuity equations, In: Multigrid Methods 3. Proceedings of the third European conference on multigrid methods (eds. W. Hackbusch, U. Trottenberg), 325-338, Birkhäuser, Basel, (1991).
  93. A. Reusken: Steplength optimization and linear multigrid methods, Numer. Math. 58, 819-838, (1991).
  94. W. Hackbusch, A. Reusken: Analysis of a damped nonlinear multilevel method, Numer. Math. 55, 225-246, (1989).
  95. A. Reusken: Convergence of the multilevel full approximation scheme including the V-cycle, Numer. Math. 54, 663-686, (1988).
  96. W. Hackbusch, A. Reusken: On global multigrid convergence for nonlinear problems, In: Robust multigrid methods. Notes on Numerical Fluid Dynamics, 105-113, Vieweg, Braunschweig, (1988).
  97. A. Reusken: Convergence of the multigrid full approximation scheme for a class of elliptic mildly nonlinear boundary value problems, Numer. Math. 52, 251-277, (1988).