List of Publications

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, Abstract and Article .
  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,Schriftenreihe der Fakultät für Mathematik, Universität Duisburg-Essen, SM-E-707, December 2009, 15p. GAMM-Mitt. 33, No. 1, 57-72 (2010) DOI 
    http://dx.doi.org/10.1002/gamm.201010005
  42. Marta Jarosova, Axel Klawonn and Oliver Rheinbach,  Projector preconditioning and transformation of basis in FETI-DP algorithms for contact problems, Math. Comp. Simulation, in press, available online Dec. 7th.,2010, http://dx.doi.org/10.1016/j.matcom.2010.10.031
  43. 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 .
  44. 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.
  45. Daniel Balzani, Dirk Böse, Dominik Brankds, Raimund Erbel, Axel Klawonn, Oliver Rheinbach, Jörg Schröder, "Parallel Simulation of Patient-specific Atherosclerotic Arteries for the Enhancement of Intravascular Ultrasound Diagnistics". 19p. Accepted for publication in Engineering Computations.
  46. Dirk Böse, Sarah Brinkhues, Raimund Erbel, Axel Klawonn, Oliver Rheinbach, Jörg Schröder, "A Simultaneous Augmented Lagrange Approach for the Simulation of Soft Biological Tissue", Mai 2011, 8p. Revised version accepted für publcation in the Proceedings of the 20th International Conference on Domain Decomposition Methods in Science and Engineering, February 2011, San Diego, USA, Lecture Notes in Computational Science and Engineering, Springer-Verlag.
  47. Sabrina Gippert, Axel Klawonn, Oliver Rheinbach, "FETI-DP for elasticity with almost incompressible material components". May 2011, 8p. Revised version accepted for publication in the Proceedings of the 20th International Conference on Domain Decomposition Methods in Science and Engineering, February 2011, San Diego, USA, Lecture Notes in Computational Science and Engineering, Springer-Verlag.
  48. Sabrina Gippert, Axel Klawonn, Oliver Rheinbach, "Analysis of FETI-DP and BDDC Algorithms for a linear elasticity problems in 3D with compressible and almost encompressible material components", June 2011, revised January 2012, 27p. Accepted for publication in SIAM J. Numer. Anal. (SINUM).
  49. Sarah Brinkhues, Axel Klawonn, Oliver Rheinbach, Jörg Schröder, "Augmented Lagrange Methods in the Simulation of Soft Biological Tissue", 19p. October 2011, revised June 2012. Accepted for publication in Int. J. Numer. Methods Biomed. Eng (IJNMBE).

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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.

Prof. Dr. Axel Klawonn

Universität Duisburg-Essen

Institutsgebäude der Fakultät für Mathematik

Lehrstuhl für Numerische Mathematik

WSC-S-04.01

Thea-Leymann-Str. 9

45127 Essen

Tel. +49 201 183 2339 (Sekr. 2600)

Fax  +49 201 183 2601

 

Leiter des Lehrstuhls für Numerische Mathematik und Numerische Simulation