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Faculty of Mathematics and Natural SciencesProf. Dr. Axel Klawonn

Publications Martin Lanser

Publications

  1. 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.
  2. 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
  3. Axel Klawonn, Martin Lanser, and Oliver Rheinbach. "EXASTEEL - Computational Scale Bridging using a FE2TI approach with ex_nl/FE^2". In Dirk Brömmel, Wolfgang Frings, and Brian J. N. Wylie, editor, JUQUEEN Extreme Scaling Workshop 2015, Technical Report, 2015. Report
  4. 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
  5. 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.
  6. Axel Klawonn, Martin Lanser, and Oliver Rheinbach, "Toward 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.
  7. Axel Klawonn, Martin Lanser, and Oliver Rheinbach. "iFETI: Scalable Nonlinear FETI-DP/Multigrid Methods". In Dirk Brömmel, Wolfgang Frings, and Brian J. N. Wylie, editor, JUQUEEN Extreme Scaling Workshop 2016, Technical Report, 2016. Report
  8. 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.
  9. 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.
  10. 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.
  11. A. Klawonn, M. Lanser, O.Rheinbach, "EXASTEEL - From Micro to Macro Properties", InSiDE, Autumn 2016, pages 80 - 85.
  12. 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.
  13. 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.
  14. 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
  15. 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
  16. A. Klawonn, M. Lanser, L. Scheunemann, J. Schröder, "Hochleistungsrechnen trifft Hochleistungsstahl: Herausforderungen zweier Welten", UNIKATE, Universität Duisburg-Essen, 2017.
  17. 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
  18. 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.
  19. 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
  20. 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.
  21. 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
  22. 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.
  23. 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.
  24. 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
  25. 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
  26. 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.
  27. 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.
  28. 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.
  29. 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
  30. 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.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. Axel Klawonn, Martin Lanser, Janine Weber, "Learning Adaptive Coarse Basis Functions of FETI-DP". Journal of Computational Physics, Vol 496, 2023. https://doi.org/10.1016/j.jcp.2023.112587, Preprint.
  38. 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.
  39. 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.
  40. 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.
  41. 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.​​​​​​​
  42. 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​​​​​​​.​​​​​​​
  43. 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 

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, 2023. 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.

 

Dissertation 

  • Martin Lanser, Nonlinear FETI-DP and BDDC Methods, Dissertation, Universität zu Köln, 2015, Online Publication

 

Links