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Faculty of Mathematics and Natural SciencesProf. Dr. Axel Klawonn

 

Publications (refereed) 

  1. A. Klawonn, Block-Triangular Preconditioners for Saddle Point Problems with a Penalty Term , SIAM J. Sci. Comput., 19(1), January 1998, pp. 172-184, http://dx.doi.org/10.1137/S1064827596303624 .

  2. A. Klawonn, An optimal Preconditioner for a Class of Saddle Point Problems with a Penalty Term , SIAM J. Sci. Comput., 19(2), March 1998, pp. 540-552, http://dx.doi.org/10.1137/S1064827595279575.

  3. A. Klawonn and L.F. Pavarino, Overlapping Schwarz methods for mixed linear elasticity and Stokes problems , Comp. Meth. Appl. Mech. Engrg., Vol. 165, pp. 233-245, 1998, http://dx.doi.org/10.1016/S0045-7825(98)00059-0 .

  4. A. Klawonn, Additive Domain Decomposition Algorithms for a class of mixed finite elements , AMS Contemporary Mathematics, 218, 1998, pp. 296-303, Article .

  5. A. Klawonn, Two Preconditioners for Saddle Point Problems with Penalty Term , Proceedings of the Ninth International Conference on Domain Decomposition Methods, Bergen, Norway, June 3-8, 1996, pp. 147-154, 1998, DD9.ps .

  6. A. Klawonn and L.F. Pavarino, An Overlapping Additive Schwarz Method for a Saddle Point Problem from Linear Elasticity, In: Iterative Methods in Scientific Computation , IMACS Series in Computational and Applied Mathematics, Volume 4, 1998, pp. 219-224.

  7. A. Klawonn and G. Starke, Block Triangular Preconditioners for Nonsymmetric Saddle Point Problems: Field-of-Values Analysis , Numer. Math. (1999) 81:577-594,

  8. A. Klawonn and O.B. Widlund, A domain decomposition method with Lagrange multipliers for linear elasticity , 1999, Proceedings of the Eleventh International Conference on Domain Decomposition Methods, Greenwich, UK, July 20-24, 1998, pp. 49-56, DD11proc.ps .

  9. D. Stefanica and A. Klawonn , The FETI method for Mortar Finite Elements , 1999, Proceedings of the Eleventh International Conference on Domain Decomposition Methods, Greenwich, UK, July 20-24, 1998, pp. 121-129, DD11proc.ps . Note: See also the extended technical report below.

  10. A. Klawonn and L.F. Pavarino, A Comparison of Overlapping Schwarz Methods and Block Preconditioners for Saddle Point Problems , Numer. Linear Algebra Appl. 2000, 7:1-25, Abstract and Article .

  11. A. Klawonn and O.B. Widlund, A domain decomposition method with Lagrange multipliers and inexact solvers for linear elasticity , SIAM J. Sci. Comput., 2000, Vol. 22, No. 4, pp.1199-1219. http://dx.doi.org/10.1137/S1064827599352495 .

  12. A. Klawonn, An iterative substructuring method with Lagrange multipliers for elasticity problems using approximate Neumann subdomain solvers , In: Multifield Problems: State of the Art, Editors: A.-M. Saendig, W. Schielen, W.L. Wendland, Springer-Verlag, Berlin, 2000, pp. 193-200.

  13. A. Klawonn and O.B. Widlund, New Results on FETI methods for Elliptic Problems with Discontinuous Coefficients , Numerical Analysis 1999, Editors D.F. Griffiths and G.A. Watson, CRC Press/Chapman & Hall, 2000, pp. 191- 209.

  14. A. Klawonn and O.B. Widlund, FETI and Neumann-Neumann Iterative Substructuring Methods: Connections and New Results , Comm. Pure Appl. Math., January 2001, Vol. 54, pp.57-90. http://dx.doi.org/10.1002/1097-0312(200101)54:1<57::AID-CPA3>3.0.CO;2-D

  15. A. Toselli and A. Klawonn, A FETI domain decomposition method for Edge Element Approximations in Two Dimensions with Discontinuous Coefficients , SIAM J. Numer. Anal., 2001, Vol. 39, No. 3, pp. 932-956, http://dx.doi.org/10.1137/S0036142999361372 .

  16. D.J. Rixen, P. Le Tallec, and A. Klawonn , A Matrix Description for the Domain Decomposition Methods of the FETI family , September 2000, Proceedings of the First MIT Conference on Computational Fluid and Solid Mechanics, MIT, Cambridge, USA, June 12-14, 2001, Elsevier, pp. 1636-1639.

  17. A. Klawonn and O.B. Widlund, Dual and Dual-Primal FETI Methods for Elliptic Problems with Discontinuous Coefficients in Three Dimensions , 2001, Proceedings of the 12th International Conference on Domain Decomposition Methods, Chiba, Japan, October 25-29, 1999, pp. 29-40. DD12proc.ps .

  18. A. Klawonn and O.B. Widlund, FETI-DP Methods for Elliptic Problems with Discontinuous Coefficients in Three Dimensions, Proceedings of the 13th International Conference on Domain Decomposition Methods, Lyon, France, October, 2000, Editors: N. Debit, M. Garbey, R. Hoppe, D. Keyes, Y. Kuznetsov, J. Periaus, CIMNE Barcelona (A Series of Handbooks on Theory and Engineering Applications of Computational Methods), pp.405-411. April 2002.

  19. A. Klawonn, O.B. Widlund, and M. Dryja, Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients , SIAM J. Numer. Anal., April 2002, Vol. 40, No. 1, pp. 159-179, http://dx.doi.org/10.1137/S0036142901388081 .

  20. A. Klawonn, O.B. Widlund, and M. Dryja, Dual-Primal FETI Methods with Face Constraints , Proceedings of a workshop on domain decomposition methods held at ETH Zürich June 7/8, 2001. Editors: Luca Pavarino and Andrea Toselli. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 23, 27-40 (2002).

  21. A. Klawonn and G. Starke, A Preconditioner for the Equations of Linear Elasticity Discretized by the PEERS Element , Numer. Linear Algebra Appl., Vol. 11, No. 5/6, pp. 493-510, June-August 2004, http://dx.doi.org/10.1002/nla.357 .

  22. A. Klawonn, O. Rheinbach, and O.B. Widlund, Some Computational Results for Dual-Primal FETI Methods for Three Dimensional Elliptic Problems. In: Domain Decomposition Methods in Science and Engineering, Editors: R. Kornhuber, R.H.W. Hoppe, D.E. Keyes, J. Periaux, O. Pironneau, and J. Xu. Berlin: Springer. Lect. Notes Comput. Sci. Eng., Vol. 40, pp. 361-368, 2005, http://dx.doi.org/10.1007/3-540-26825-1_36 .

  23. A. Klawonn and O.B. Widlund, Selecting Constraints in Dual-Primal FETI Methods for Elasticity in Three Dimensions, In: Domain Decomposition Methods in Science and Engineering, Editors: R. Kornhuber, R.H.W. Hoppe, D.E. Keyes, J. Periaux, O. Pironneau, and J. Xu. Berlin: Springer. Lect. Notes Comput. Sci. Eng., Vol. 40, pp. 67-81, 2005.

  24. S. Vanis, O. Rheinbach, A. Klawonn, O. Prymak, M. Epple , Numerical computation of the porosity of bone substitution materials from synchrotron micro computer tomographic data, Mat.-wiss. u. Werkstofftechn., Vol. 37, No. 6, 2006, http://dx.doi.org/10.1002/mawe.200600021 .

  25. A. Klawonn , FETI Domain Decomposition Methods for Second Order Partial Differential Equations , GAMM Mitteilungen, Vol. 29, No. 2, pp. 319-341, 2006.

  26. A. Klawonn and O.B. Widlund, Dual-Primal FETI Methods for Linear Elasticity Comm. Pure Appl. Math., Vol. 59, No. 11, pp.1523-1572, November 2006, http://dx.doi.org/10.1002/cpa.20156 .

  27. A. Klawonn and O. Rheinbach, A Parallel Implementation of Dual-Primal FETI Methods for Three Dimensional Linear Elasticity Using a Transformation of Basis, SIAM J. Sci. Comput., Vol. 28, No. 5, pp. 1886-1906, November 2006, http://dx.doi.org/10.1137/050624364 .

  28. Axel Klawonn, Oliver Rheinbach, and Barbara Wohlmuth , Dual-primal iterative substructuring for almost incompressible elasticity , Springer Lect. Notes Comput. Sci. Eng., Vol. 55, pp. 399- 406, January 2007, http://dx.doi.org/10.1007/978-3-540-34469-8_49 .

  29. Axel Klawonn and Oliver Rheinbach, Some computational results for robust FETI-DP methods applied to heterogeneous elasticity problems in 3D , Springer Lect. Notes Comput. Sci. Eng., Vol. 55, pp. 391-398, January 2007, http://dx.doi.org/10.1007/978-3-540-34469-8_48 .

  30. A. Klawonn and O. Rheinbach, Robust FETI-DP methods for heterogeneous three dimensional elasticity problems , Comput. Meth. Appl. Mech. Engrg., Vol. 196, pp. 1400-1414, January 2007, http://dx.doi.org/10.1016/j.cma.2006.03.023 .

  31. A. Klawonn and O. Rheinbach , Inexact FETI-DP Methods , Inter. J. Numer. Methods Engrg., Vol. 69, pp. 284-307, January 2007, published electronically June 2006, http://dx.doi.org/10.1002/nme.1758 .

  32. C. Dohrmann, A. Klawonn, and O. Widlund, Extending theory for domain decomposition algorithms to irregular subdomains January 2008, Springer Lect. Notes Comput. Sci. Eng. Vol. 60, Editors U. Langer, M. Discacciati, O. Widlund, W. Zulehner.

  33. A. Klawonn, L. Pavarino, and O. Rheinbach, Exact and inexact FETI-DP methods for spectral elements in two dimensions, January 2008, Springer Lect. Notes Comput. Sci. Eng. Vol. 60, Editors U. Langer, M. Discacciati, O. Widlund, W. Zulehner, http://dx.doi.org/10.1007/978-3-540-75199-1_32 .

  34. C. Dohrmann, A. Klawonn, and O. Widlund, A family of energy minimizing coarse spaces for overlapping Schwarz preconditioners, January 2008, Springer Lect. Notes Comput. Sci. Eng. Vol. 60, Editors U. Langer, M. Discacciati, O. Widlund, W. Zulehner.

  35. C. Dohrmann, A. Klawonn, and O. Widlund, Domain decomposition for less regular subdomains: Overlapping Schwarz in two dimensions, published online May 2, 2008, SIAM J. Numer. Anal., Vol. 46, No. 4, pp. 2153-2168.

  36. A. Klawonn, O. Rheinbach and O. Widlund, An analysis of a FETI-DP algorithm on irregular subdomains in the plane, published online June 11, 2008, SIAM J. Numer. Anal., Vol. 46, No. 5, pp. 2484-2504, http://dx.doi.org/10.1137/070688675 .

  37. D.Brands, A.Klawonn, O.Rheinbach, and J.Schröder, Modeling and convergence in arterial wall simulations using a parallel FETI solution strategy, Computer Methods in Biomechanics and Biomedical Engineering, Vol. 11, No. 5, October 2008, pp. 569-583, http://dx.doi.org/10.1080/10255840801949801 .
  38. A. Klawonn, L. Pavarino, and O. Rheinbach, Spectral element FETI-DP and BDDC preconditioners with multi-element subdomains, October 2007, revised August 2008. Comput. Meth. Appl. Mech. Engrg, Vol. 198 (3-4), pp. 511-523, 2008, http://dx.doi.org/10.1016/j.cma.2008.08.017 .
  39. D. Balzani, D. Brands, A. Klawonn, O. Rheinbach, J. Schröder On the mechanical modeling of anisotropic biological soft tissue an iterative parallel solution strategies, Archive of Applied Mechanics, Special Issue, November 2009 http://dx.doi.org/10.1007/s00419-009-0379-x
  40. Axel Klawonn and Oliver Rheinbach, Highly scalable parallel domain decomposition methods with an application to biomechanics, Z.Angew. Math. Mech. (ZAMM), 90, No. 1, pp.5-32, 2010, http://dx.doi.org/10.1002/zamm.200900329
  41. Axel Klawonn, Patrizio Neff, Oliver Rheinbach and Stefanie Vanis, Solving geometrically exact micromorphic elastcity with a staggered algorithm, GAMM-Mitteilungen, 33, No. 1, 57-72 (2010) DOI, http://dx.doi.org/10.1002/gamm.201010005
  42. Axel Klawonn, Patrizio Neff, Oliver Rheinbach and Stefanie Vanis, FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity, ESAIM Math. Model. Numer. Anal. (formerly M2AN Math. Model. Numer. Anal.), 2011, 45: 563-602, http://dx.doi.org/10.1051/m2an/2010067 .
  43. Axel Klawonn, Oliver Rheinbach, "Deflation, Projector Preconditioning, and Balancing in Iterative Substructuring Methods: Connections and New Results", SIAM J. Sci. Comput. 34(1) (2012), pp. A459-A484 (26 pages), http://dx.doi.org/10.1137/100811118.
  44. Marta Jarosova, Axel Klawonn and Oliver Rheinbach, Projector preconditioning and transformation of basis in FETI-DP algorithms for contact problems, Math. Comp. Simulation, Volume 82, Issue 10, June 2012, Pages 1894–1907, http://dx.doi.org/10.1016/j.matcom.2010.10.031
  45. Sabrina Gippert, Axel Klawonn, Oliver Rheinbach, "Analysis of FETI-DP and BDDC Algorithms for linear elasticity problems in 3D with almost incompressible components and varying coefficients inside subdomains", SIAM J. Numer. Anal. 50-5 (2012), pp. 2208-2236 http://dx.doi.org/10.1137/110838315
  46. Daniel Balzani, Dirk Böse, Dominik Brands, Raimund Erbel, Axel Klawonn, Oliver Rheinbach, Jörg Schröder, "Parallel Simulation of Patient-specific Atherosclerotic Arteries for the Enhancement of Intravascular Ultrasound Diagnistics". Engineering Computations, Vol. 29 No. 8, pp. 888-906 (2012) http://dx.doi.org/10.1137/130920563
  47. Dirk Böse, Sarah Brinkhues, Raimund Erbel, Axel Klawonn, Oliver Rheinbach, Jörg Schröder, "A Simultaneous Augmented Lagrange Approach for the Simulation of Soft Biological Tissue", Lecture Notes in Computational Science and Engineering, Springer-Verlag, Vol. 91, pp. 369-376 (2013).
  48. Sabrina Gippert, Axel Klawonn, Oliver Rheinbach, "FETI-DP for elasticity with almost incompressible material components". May 2011, Lecture Notes in Computational Science and Engineering, Springer-Verlag, Vol. 91, pp 353-360 (2013).
  49. Sarah Brinkhues, Axel Klawonn, Oliver Rheinbach, Jörg Schröder, "Augmented Lagrange Methods for quasi-incompressible materials - Applications to Soft Biological Tissue", Int. J. Numer. Methods Biomed. Eng (IJNMBE), Vol 29, No. 3, pp. 332-350 (2013)http://dx.doi.org/10.1002/cnm.2504
  50. Axel Klawonn, Martin Lanser, and Oliver Rheinbach, "Nonlinear FETI-DP and BDDC Methods", SIAM J. Sci. Comput., Vol. 36, No. 2, 2014, pp. 737-765, dowload pdf http://dx.doi.org/10.1137/130920563.
  51. Ulrich Hetmaniuk and Axel Klawonn, "Error Estimates for a Two-Dimensional Special Finite Element Method Based on Component Mode Synthesis", Electronic Transactions on Numerical Analysis (ETNA), Vol. 41, 2014, pp. 109-132, Link.
  52. Axel Klawonn, Martin Lanser, Patrick Radtke, and Oliver Rheinbach, "On an Adaptive Coarse Space and on Nonlinear Domain Decomposition", In: Domain Decomposition Methods in Science and Engineering XXI, Editors: Erhel, J., Gander, M.,Halpern, L., Pichot, G., Sassi, T., Widlund, O.B. Springer Lecture Notes on Computational Science and Engineering, Vol. 98, 2014, pp. 71-83. Proceedings of the 21st International Conference on Domain Decomposition Methods in Science and Engineering, Rennes, France, June 25-29, 2012. pdf http://dx.doi.org/10.1007/978-3-319-05789-7_6
  53. Sabrina Gippert, Axel Klawonn, and Oliver Rheinbach, "A Deflation Based Coarse Space in Dual-Primal FETI Methods for Almost Incompressible Elasticity", Proceedings of the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Lausanne, August 26-30, 2013. Springer Lecture Notes on Computational Science and Engineering, Vol. 103, 2015, pp. 573-582. http://dx.doi.org/10.1007/978-3-319-10705-9_56
  54. Axel Klawonn, Patrick Radtke, and Oliver Rheinbach, "FETI-DP Methods with an Adaptive Coarse Space", SIAM Journal of Numerical Analyis (SINUM), Vol. 53, No. 1, pp. 297-320, January 2015. dowload pdf http://dx.doi.org/10.1137/130939675.
  55. Alexander Heinlein, Ulrich Hetmaniuk, Axel Klawonn, and Oliver Rheinbach, "The Approximate Component Mode Synthesis Special Finite Element Method in Two Dimensions: Parallel Implementation and Numerical Results", Journal of Computational and Applied Mathematics, Vol. 289, pp. 116-133, May 2015. http://dx.doi.org/10.1016/j.cam.2015.02.053.
  56. Axel Klawonn, Martin Lanser, Oliver Rheinbach, Holger Stengel and Gerhard Wellein, "Hybrid MPI/OpenMP parallelization in FETI-DP methods", Proceedings of "Recent Trends in Computational Engineering - CE2014", Springer Lecture Notes on Computational Science and Engineering, Vol. 105, pp. 67-84, 2015. Link and Preprint.
  57. Daniel Balzani, Simone Deparis, Simon Fausten, Davide Forti, Alexander Heinlein, Axel Klawonn, Alfio Quarteroni, Oliver Rheinbach, and Jörg Schröder, “Numerical Modeling of Fluid-Structure Interaction in Arteries with Anisotropic Polyconvex Hyperelastic and Anisotropic Viscoelastic Material Models at Finite Strains”, Int. J. Numer. Methods Biomed. Eng (IJNMBE), 2015. Published online December 7, 2015, http://dx.doi.org/10.1002/cnm.2756Preprint
  58. Axel Klawonn, Martin Lanser, and Oliver Rheinbach, "Towards Extremely Scalable Nonlinear Domain Decomposition Methods for Elliptic Partial Differential Equations", SIAM J. Sci. Comp., Vol. 37, No. 6, December 8, 2015, pp. C667-C696, http://dx.doi.org/10.1137/140997907 and pdf.
  59. Axel Klawonn, Patrick Radtke, and Oliver Rheinbach, "Adaptive Coarse Spaces for BDDC with a Transformation of Basis", Proceedings of the 22nd International Conference on Domain Decomposition Methods in Science and Engineering, Lugano, Switzerland, September 2013. Editors: Dickopf, T., Gander, M., Krause, R., Pavarino, L. Springer Lecture Notes on Computational Science and Engineering, 104, 2016, pp 301-309.  Preprint and Link. http://dx.doi.org/10.1007/978-3-319-18827-0_29
  60. Axel Klawonn, Patrick Radtke, and Oliver Rheinbach, "A Newton-Krylov-FETI-DP Method with an Adaptive Coarse Space Applied to Elastoplasticity", Proceedings of the 22nd International Conference on Domain Decomposition Methods in Science and Engineering, Lugano, Switzerland, September 2013. Editors: Dickopf, T., Gander, M., Krause, R., Pavarino, L. Springer Lecture Notes on Computational Science and Engineering, 104, 2016, pp. 293-300. Preprint and Link. http://dx.doi.org/10.1007/978-3-319-18827-0_28
  61. Axel Klawonn, Martin Lanser, and Oliver Rheinbach, "A Nonlinear FETI-DP Method with an Inexact Coarse Problem", Proceedings of the 22nd International Conference on Domain Decomposition Methods in Science and Engineering, Lugano, Switzerland, September 2013. Editors: Dickopf, T., Gander, M., Krause, R., Pavarino, L. Springer Lecture Notes on Computational Science and Engineering, 104, 2016, pp. 41-52.  http://dx.doi.org/10.1007/978-3-319-18827-0_4
  62. Axel Klawonn, Patrick Radtke, Oliver Rheinbach, "A Comparison of Adaptive Coarse Spaces for Iterative Substructuring Methods in Two Dimensions", Electronic Transactions on Numerical Analysis (ETNA), Vol. 45, pp. 75–106, 2016. Preprint. Link
  63. Axel Klawonn, Martin Lanser, Oliver Rheinbach, "FE^2TI: Computational Scale Bridging for Dual-Phase Steels". Proceedings of ParCo 2015, pp. 797 - 806, IOS Series: Advances in Parallel Computing, Volume 27, Parallel Computing: On the Road to Exascale, 2016. Preprint.
  64. A. Klawonn, M. Kühn, O. Rheinbach, "Adaptive Coarse Spaces for FETI-DP in Three Dimensions", SIAM J. Sci. Comput., Vol. 38(5), pp. A2880–A2911. Preprint. Link.
  65. Allison H. Baker, Axel Klawonn, Tzanio Kolev, Martin Lanser, Oliver Rheinbach, Ulrike Meier Yang, "Scalability of Classical Algebraic Multigrid for Elasticity to Half a Million Parallel Tasks", Software for Exascale Computing - SPPEXA 2013-2015, vol. 113 Springer LNCSE, pages 113--140, 2016, Preprint.
  66. D. Balzani, A. Gandhi, A. Klawonn, M. Lanser, O. Rheinbach, J. Schröder, "One-way and fully-coupled FE^2 methods for heterogeneous elasticity and plasticity problems: Parallel scalability and an application to thermo-elastoplasticity of dual-phase steels", Software for Exascale Computing - SPPEXA 2013-2015, vol. 113
    Springer LNCSE, pages 91--112, 2016, Preprint.
  67. Axel Klawonn, Martin Lanser, Oliver Rheinbach, "A Highly Scalable Implementation of Inexact Nonlinear FETI-DP without Sparse Direct Solvers". Proceedings of the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Ankara, September, 2015. Springer Lecture Notes on Computational Science and Engineering, Vol. 112, 2016, pp. 255-264. Preprint.
  68. A. Heinlein, A. Klawonn, O. Rheinbach, "Parallel Two-Level Overlapping Schwarz Methods in Fluid-Structure Interaction", Proceedings of the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), Ankara, September, 2015. Springer Lecture Notes on Computational Science and Engineering, Vol. 112, 2016, pp. 521-530. Preprint.
  69. Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, "A Parallel Implementation of a Two-Level Overlapping Schwarz Method with an Energy-Minimizing Coarse Space based on Trilinos", SIAM J. Sci. Comp., Vol. 38, No. 6, December 6, 2016, pp. C713-C747. Preprint and http://dx.doi.org/10.1137/16M1062843.
  70. A. Heinlein, A. Klawonn, O. Rheinbach, "Parallel Overlapping Schwarz with an Energy-Minimizing Coarse Space", Proceedings of the International Conference on Domain Decomposition Methods 23. Springer Lecture Notes on Computational Science and Engineering, Vol. 116, March 2017, pp. 353-360. Preprint and http://dx.doi.org/10.1007/978-3-319-52389-7_36.
  71. A. Klawonn, M. Lanser, B. Niehoff, P. Radtke, O. Rheinbach, "Newton-Krylov-FETI-DP with Adaptive Coarse Spaces", Proceedings of the International Conference on Domain Decomposition Methods 23. Springer Lecture Notes on Computational Science and Engineering, Vol. 116, March 2017, pp. 197-205. https://doi.org/10.1007/978-3-319-52389-7_19.
  72. A. Klawonn, M. Lanser, O. Rheinbach, M. Uran, "New Nonlinear FETI-DP Methods Based on a Partial Nonlinear Elimination of Variables", Proceedings of the International Conference on Domain Decomposition Methods 23. Springer Lecture Notes on Computational Science and Engineering, Vol. 116, March 2017, pp. 207-215. https://doi.org/10.1007/978-3-319-52389-7_20
  73. A. Klawonn, M. Kühn, O. Rheinbach, "Adaptive Coarse Spaces for FETI-DP in Three Dimensions with Applications to Heterogeneous Diffusion Problems", Proceedings of the International Conference on Domain Decomposition Methods 23. Springer Lecture Notes on Computational Science and Engineering, Vol. 116, March 2017, pp 187-196. Link
  74. Axel Klawonn, Martin Lanser, Oliver Rheinbach, and Matthias Uran. "Nonlinear FETI-DP and BDDC Methods: A Unified Framework and Parallel Results", SIAM J. Sci. Comput. 39 (2017), no. 6, C417–C451. pdf version
  75. A. Klawonn, M. Kühn, O. Rheinbach,"Adaptive FETI-DP and BDDC methods with a Generalized Transformation of Basis for Heterogeneous Problems". Electronic Transactions on Numerical Analysis (ETNA), Vol. 49, pp. 1-27, 2018. Preprint. Link.
  76. Alexander Heinlein, Axel Klawonn, Jascha Knepper, and Oliver Rheinbach. "Multiscale Coarse Spaces for Overlapping Schwarz Methods Based on the ACMS Space in 2D", Electronic Transactions on Numerical Analysis (ETNA), Vol. 48, pp. 156-182, 2018. Preprint. Link.
  77. A. Klawonn, M. Lanser, O. Rheinbach, "Nonlinear BDDC Methods with Approximate Solvers". Electronic Transactions on Numerical Analysis (ETNA), Vol. 49, pp. 244-273, 2018. Preprint. https://doi.org/10.1553/etna_vol49s244
  78. Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, Olof Widlund, "Improving the Parallel Performance of Overlapping Schwarz Methods by Using a Smaller Energy Minimizing Coarse Space", Proceedings of the International Conference on Domain Decomposition Methods 24. Springer Lecture Notes on Computational Science and Engineering, Vol. 125, 2018, pp. 383-392. https://doi.org/10.1007/978-3-319-93873-8_36
  79. Alexander Heinlein, Axel Klawonn, Jascha Knepper, Oliver Rheinbach, "An Adaptive GDSW Coarse Space for Two-Level Overlapping Schwarz Methods in Two Dimensions", Proceedings of the International Conference on Domain Decomposition Methods 24. Springer Lecture Notes on Computational Science and Engineering, Vol. 125, 2018, pp. 373-382. https://doi.org/10.1007/978-3-319-93873-8_35
  80. A. Klawonn, M. Kühn, O. Rheinbach, "Preconditioning of Iterative Eigenvalue Problem Solvers in Adaptive FETI-DP". Proceedings of the International Conference on Domain Decomposition Methods 24. Springer Lecture Notes on Computational Science and Engineering, Vol. 125, 2018, pp. 415-423. https://doi.org/10.1007/978-3-319-93873-8_39
  81. Axel Klawonn, Martin Lanser, Oliver Rheinbach, "Using Algebraic Multigrid in Inexact BDDC Domain Decomposition Methods", Proceedings of the International Conference on Domain Decomposition Methods 24. Springer Lecture Notes on Computational Science and Engineering, Vol. 125, 2018, pp. 425-433, https://doi.org/10.1007/978-3-319-93873-8_40.
  82. Axel Klawonn, Martin Lanser, Oliver Rheinbach, Matthias Uran "On the Accuracy of the Inner Newton Iteration in Nonlinear Domain Decomposition", Proceedings of the International Conference on Domain Decomposition Methods 24. Springer Lecture Notes on Computational Science and Engineering, Vol. 125, 2018, pp. 435-443. https://doi.org/10.1007/978-3-319-93873-8_41
  83. M. Wittmann, G. Hager, R. Janalík, M. Lanser, A. Klawonn, O. Rheinbach, O. Schenk, and G. Wellein, Multicore Performance Engineering of Sparse Triangular Solves Using a Modified Roofline Model, Proceedings of the 30th IEEE International Symposium on Computer, Architecture and High Peformance Computing (SBAC-PAD) 2018, IEEE Xplore Proceedings, Article number 8645938, pp. 233-241, 2019.
  84. Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, and Friederike Röver. "A Three-Level Extension of the GDSW Overlapping Schwarz Preconditioner in Two Dimensions". Advanced Finite Element Methods with Applications: Selected Papers from the 30th Chemnitz Finite Element Symposium 2017, pp. 187-204, June 2019. Preprint and https://doi.org/10.1007/978-3-030-14244-5_10.
  85. Alexander Heinlein, Christian Hochmuth, Axel Klawonn, "Monolithic Overlapping Schwarz Domain Decomposition Methods with GDSW Coarse Spaces for Incompressible Fluid Flow Problems". SIAM J. Sci. Comput. 41 (2019), no. 4, C291–C316. Preprint and https://doi.org/10.1137/18M1184047. PDF version.
  86. Alexander Heinlein, Axel Klawonn, Jascha Knepper, Oliver Rheinbach, "Adaptive GDSW Coarse Spaces for overlapping Schwarz methods in three dimensions". SIAM J. Sci. Comput. 41 (2019), no. 5, A3045–A3072. Preprint and https://doi.org/10.1137/18M1220613.
  87. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber, "Machine Learning in Adaptive Domain Decomposition Methods -Predicting the Geometric Location of Constraints". SIAM J. Sci. Comput. 41 (2019), no. 6, A3887-A3912. Preprint and https://doi.org/10.1137/18M1205364.
  88. Axel Klawonn, Martin Lanser, Oliver Rheinbach, Janine Weber. "Preconditioning the coarse problem of BDDC methods - Three-level, algebraic multigrid, and vertex-based preconditioners", Electronic Transaction on Numerical Analysis, Volume 51, pp. 432-450, 2019. Preprint and https://doi.org/10.1553/etna_vol51s432
  89. Axel Klawonn, Stephan Köhler, Martin Lanser, Oliver Rheinbach, "Computational Homogenization with Million-way Parallelism using Domain Decomposition Methods". Computational Mechanics, Springer Nature, 65, pp. 1-22, 2020. Published online in July 2019. Preprint, Shared Link, and https://doi.org/10.1007/s00466-019-01749-5.
  90. Axel Klawonn, Martin J. Kühn, Oliver Rheinbach, "Parallel adaptive FETI-DP using lightweight asynchronous dynamic load balancing". Int J Numer Methods Eng., Volume 121, no. 4, pp. 621 - 643, 2020. Preprint and https://doi.org/10.1002/nme.6237.
  91. Alexander Heinlein, Christian Hochmuth, Axel Klawonn. "Reduced dimension GDSW coarse spaces for monolithic Schwarz domain decomposition methods for incompressible fluid flow problems". Int J Numer Methods Eng.  2020; 121: 1101– 1119. Preprint and https://doi.org/10.1002/nme.6258.
  92. A. Klawonn, M. Kühn, O. Rheinbach, "Coarse spaces for FETI-DP and BDDC Methods for heterogeneous problems: Connections of Deflation and a Generalized Transformation-of-Basis Approach". Electronic Transactions on Numerical Analysis (ETNA), Vol. 52, pp. 43-76, 2020. Preprint and https://doi.org/10.1553/etna_vol52s43
  93. A. Klawonn, M. Lanser, M. Uran, O. Rheinbach, S. Köhler, J. Schröder, L. Scheunemann, D. Brands, D. Balzani, A. Gandhi, G. Wellein, M. Wittmann, O. Schenk, R. Janalìk, "EXASTEEL - Towards a virtual laboratory for the multiscale simulation of dual-phase steel using high-performance computing". In: Bungartz HJ., Reiz S., Uekermann B., Neumann P., Nagel W. (eds) Software for Exascale Computing - SPPEXA 2016-2019. Lecture Notes in Computational Science and Engineering, vol 136. Springer, Cham., 2020. PDF and https://doi.org/10.1007/978-3-030-47956-5_13
  94. A. Klawonn, M. Lanser, O. Rheinbach, G. Wellein, M. Wittmann, "Energy efficiency of nonlinear domain decomposition methods". The International Journal of High Performance Computing Applications, 2020. Preprint and https://doi.org/10.1177/1094342020953891
  95. Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, Friederike Röver, "A Three-Level Extension of the GDSW Overlapping Schwarz Preconditioner in Three Dimensions". Domain Decomposition Methods in Science and Engineering XXV. DD 2018. Lecture Notes in Computational Science and Engineering, vol 138. Springer, Cham, 2020. https://doi.org/10.1007/978-3-030-56750-7_20, Preprint.
  96. Alexander Heinlein, Axel Klawonn, Sivasankaran Rajamanickam, Oliver Rheinbach, "FROSch: A Fast And Robust Overlapping Schwarz Domain Decomposition Preconditioner Based on Xpetra in Trilinos". Domain Decomposition Methods in Science and Engineering XXV. DD 2018. Lecture Notes in Computational Science and Engineering, vol 138. Springer, Cham, 2020. https://doi.org/10.1007/978-3-030-56750-7_19, Preprint.
  97. Alexander Heinlein, Axel Klawonn, Martin Kühn, "Local spectra of adaptive domain decomposition methods". Domain Decomposition Methods in Science and Engineering XXV. DD 2018. Lecture Notes in Computational Science and Engineering, vol 138. Springer, Cham, 2020. https://doi.org/10.1007/978-3-030-56750-7_18, Preprint.
  98. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber, "Machine Learning in Adaptive FETI-DP - A Comparison of Smart and Random Training Data". Domain Decomposition Methods in Science and Engineering XXV. DD 2018. Lecture Notes in Computational Science and Engineering, vol 138. Springer, Cham, 2020. https://doi.org/10.1007/978-3-030-56750-7_24, Preprint.
  99. Axel Klawonn, Martin Kühn, Oliver Rheinbach, "A closer look at local eigenvalue solvers for adaptive FETI-DP and BDDC". Domain Decomposition Methods in Science and Engineering XXV. DD 2018. Lecture Notes in Computational Science and Engineering, vol 138. Springer, Cham, 2020. https://doi.org/10.1007/978-3-030-56750-7_26,  Preprint.
  100. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "A Frugal FETI-DP and BDDC Coarse Space for Heterogeneous Problems". Electronic Transactions on Numerical Analysis (ETNA), Vol. 53, pp. 562-591, 2020. Preprint and https://doi.org/10.1553/etna_vol53s562.
  101. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Machine Learning in Adaptive FETI-DP - Reducing the Effort in Sampling". Proceedings of the ENUMATH 2019 conference, Springer LNCSE, Vol. 139, pp. 593-603, 2021. Preprint.
  102. Matthias Eichinger, Alexander Heinlein, Axel Klawonn. "Stationary flow predictions using convolutional neural networks". Proceedings of the ENUMATH 2019 conference, Springer LNCSE, Vol. 139, pp. 541-549, 2021. Preprint.
  103. Alexander Heinlein, Christian Hochmuth, Axel Klawonn. "Fully algebraic two-level overlapping Schwarz preconditioners for elasticity problems". Proceedings of the ENUMATH 2019 conference, Springer LNCSE, Vol. 139, pp. 531-539, 2021. Preprint and https://doi.org/10.1007/978-3-030-55874-1_52.
  104. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Combining Machine Learning and Domain Decomposition Methods - A Review". In GAMM Mitteilungen, 2021. Preprint and https://onlinelibrary.wiley.com/doi/full/10.1002/gamm.202100001
  105. Axel Klawonn, Martin Lanser, Oliver Rheinbach, Matthias Uran "Fully-Coupled Micro-Macro Finite Element Simulations of the Nakajima Test Using Parallel Computational Homogenization". Computational Mechanics, Vol. 68, pages 1153–1178, Springer Nature, 2021. https://doi.org/10.1007/s00466-021-02063-9,  Preprint.
  106. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Combining Machine Learning and Adaptive Coarse Spaces - A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions". SIAM J. Sci. Comput., Special Section Copper Mountain 2020, published 2021. Preprint, https://doi.org/10.1137/20M1344913.
  107. Viktor Grimm, Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber. "Estimating the time-dependent contact rate of SIR and SEIR models in mathematical epidemiology using physics-informed neural networks". Electronic Transactions on Numerical Analysis (ETNA), Volume 56, pp. 1–27, 2022. http://doi.org/10.1553/etna_vol56s1, Preprint.
  108. Matthias Eichinger, Alexander Heinlein, Axel Klawonn. "Surrogate Convolutional Neural Network Models for Steady Computational Fluid Dynamics Simulations". Electronic Transactions on Numerical Analysis (ETNA), Vol. 56, pp. 235-255, 2022. http://doi.org/10.1553/etna_vol56s235​​​​​​​, Preprint.
  109. Alexander Heinlein, Axel Klawonn, Jascha Knepper, Oliver Rheinbach, Olof B. Widlund. "Adaptive GDSW coarse spaces of reduced dimension for overlapping Schwarz methods". SIAM J. Sci. Comput., Vol. 44, no. 3, 2022. http://doi.org/10.1137/20M1364540, PDF, Preprint.
  110. Alexander Heinlein, Axel Klawonn, Martin Lanser, "Adaptive Nonlinear Domain Decomposition Methods with an Application to the p-Laplacian". SIAM J. Sci. Comput., SPECIAL SECTION Copper Mountain 2021, published in 2022. https://doi.org/10.1137/21M1433605, Preprint.
  111. Axel Klawonn,Martin Lanser, Adam Wasiak, "Adaptive and Frugal FETI-DP for Virtual Elements". Vietnam Journal of Mathematics, 2022. https://doi.org/10.1007/s10013-022-00580-5, Preprint.
  112. Axel Klawonn, Martin Lanser, Matthias Uran, "Adaptive Nonlinear Elimination in Nonlinear FETI-DP Methods". Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, vol 145. Springer, 2023. https://link.springer.com/chapter/10.1007/978-3-030-95025-5_35, Preprint.
  113. Alexander Heinlein, Axel Klawonn, Martin Lanser, Janine Weber, "Predicting the geometric location of critical edges  in adaptive GDSW overlapping domain decomposition methods using deep learning". Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, vol 145. Springer, 2023. https://link.springer.com/chapter/10.1007/978-3-030-95025-5_32, Preprint.
  114. Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, Friederike Röver, "A Three-Level Extension for Fast and Robust Overlapping Schwarz (FROSch) Preconditioners with Reduced Dimensional Coarse Space". Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, vol 145. Springer, 2023. https://link.springer.com/chapter/10.1007/978-3-030-95025-5_54, Preprint.
  115. Daniel Balzani, Alexander Heinlein, Axel Klawonn, Oliver Rheinbach, Jörg Schröder, "Comparison of Arterial Wall Models in Fluid-Structure Interaction Simulations". Computational Mechanics, Springer Nature, 2023. https://doi.org/10.1007/s00466-023-02321-y, Preprint.
  116. Axel Klawonn, Martin Lanser, Janine Weber, "Learning Adaptive Coarse Basis Functions of FETI-DP". Journal of Computational Physics, Vol 496, Elsevier, 2023. https://doi.org/10.1016/j.jcp.2023.112587, Preprint.
  117. Daniel Balzani, Alexander Heinlein, Axel Klawonn, Jascha Knepper, Sharan Nurani Ramesh, Oliver Rheinbach, Lea Sassmannshausen, Klemens Uhlmann, "A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods", GAMM-Mitteilungen, Wiley, 2024. https://onlinelibrary.wiley.com/doi/10.1002/gamm.202370002, Preprint.
  118. Axel Klawonn, Martin Lanser, Janine Weber, "Learning Adaptive FETI-DP Constraints for Irregular Domain Decompositions". Domain Decomposition Methods in Science and Engineering XXVII. Lecture Notes in Computational Science and Engineering, vol 149. Springer, 2024. https://link.springer.com/chapter/10.1007/978-3-031-50769-4_33, Preprint.
  119. Axel Klawonn, Martin Lanser, Janine Weber, "Adaptive Three-level BDDC Using Frugal Constraints". Domain Decomposition Methods in Science and Engineering XXVII. Lecture Notes in Computational Science and Engineering, vol 149. Springer, 2024. https://link.springer.com/chapter/10.1007/978-3-031-50769-4_34, Preprint.
  120. Axel Klawonn, Martin Lanser, Adam Wasiak, "Three-level BDDC for Virtual Elements". Domain Decomposition Methods in Science and Engineering XXVII. Lecture Notes in Computational Science and Engineering, vol 149. Springer, 2024. https://link.springer.com/chapter/10.1007/978-3-031-50769-4_51​​​​​​​,  Preprint.
  121. Axel Klawonn, Martin Lanser, "Efficient Adaptive Elimination Strategies in Nonlinear FETI-DP Methods in Combination with Adaptive Spectral Coarse Spaces". Domain Decomposition Methods in Science and Engineering XXVII. Lecture Notes in Computational Science and Engineering, vol 149. Springer, 2024.​​​​​​​​​​​​​​​​​​​ https://link.springer.com/chapter/10.1007/978-3-031-50769-4_35​​​​​​​, Preprint.​​​​​​​
  122. Viktor Grimm, Alexander Heinlein, Axel Klawonn, "A short note on solving partial differential equations using convolutional neural networks". Domain Decomposition Methods in Science and Engineering XXVII. Lecture Notes in Computational Science and Engineering, vol 149. Springer, 2024.​​​​​​​​​​​​​​​​​​ https://link.springer.com/chapter/10.1007/978-3-031-50769-4_1,​​​ Preprint.​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
  123. Christoph Alt, Martin Lanser, Jonas Plewinski, Atin Janki, Axel Klawonn, Harald Köstler, Michael Selzer, Ulrich Rüde, "A continuous benchmarking infrastructure for high-performance computing applications". International Journal of Parallel, Emergent and Distributed Systems, pages 1–23, 2024. https://doi.org/10.1080/17445760.2024.2360190, Preprint​​​​​​​.
  124. Axel Klawonn, Martin Lanser, Janine Weber, "A Domain Decomposition-Based CNN-DNN Architecture for Model Parallel Training Applied to Image Recognition Problems". SIAM J. Sci. Comput, Vol 46(5), 2024. https://doi.org/10.1137/23M1562202, https://arxiv.org/abs/2302.06564 

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Accepted for publication

  1. Axel Klawonn, Martin Lanser, Janine Weber, "Learning Adaptive Constraints in Nonlinear FETI-DP Methods". Accepted for Publication in the Proceedings of the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) 2023, 2024. Preprint.​​​​​​​​​​​​​​
  2. Axel Klawonn, Martin Lanser, Janine Weber, "Machine learning and domain decomposition methods - a survey". Accepted for Publication, 2024. Preprint.​​​​​​​

Submitted for publication

  1. Axel Klawonn, Martin Lanser, Janine Weber, "Model Parallel Training and Transfer Learning for Convolutional Neural Networks by Domain Decomposition". Submitted for Publication, 2024. Preprint.
  2. Tommaso Bevilacqua, Axel Klawonn, Martin Lanser,  "Adaptive and frugal BDDC coarse spaces for virtual element discretizations of a Stokes problem with heterogeneous viscosity". Submitted for Publication, 2024.
  3. Axel Klawonn, Martin Lanser,  "Nonlinear Monolithic Two-Level Schwarz Methods for the Navier-Stokes Equations". Submitted for Publication, 2024.
  4. Alexander Heinlein, Kyrill Ho, Axel Klawonn, Martin Lanser,  "Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch". Submitted for Publication, 2024.

Technical Reports

(Not submitted elsewhere)

  • A. Klawonn, An optimal Preconditioner for a Class of Saddle Point Problems with a Penalty Term, Part II: General Theory, April 1995, Schriftenreihe Angewandte Mathematik und Informatik, Bericht Nr. 14/95, TR14-95.ps

  • D. Stefanica and A. Klawonn, A Numerical Study of a Class of FETI Preconditioners for Mortar Finite Elements in Two Dimensions, November 1998, Technical Report TR 773, Courant Instiute of Mathematical Sciences, New York University, New York, USA. TR773.ps

  • A. Klawonn, P. Neff, O. Rheinbach, S. Vanis, Notes on FETI-DP Domain Decomposition Methods for P-Elasticity, Fakultät für Mathematik, Universität Duisburg-Essen, 2010. Report.

 

Dissertation

  • A. Klawonn, Preconditioners for Indefinite Problems , Doctoral Dissertation, Westfälische Wilhelms-Universität Münster, November 1995, appeared as Bericht 8/96-N in Schriftenreihe Angewandte Mathematik und Informatik , Februar 1996.

 

Habilitation 

  • A. Klawonn, Domain Decomposition Methods: Theoretical and Algorithmic Contributions with Applications in Continuum Mechanics , Habilitationsschrift, Universität zu Köln, June 2000.