Publications

Refereed Publications

    1. Taylor-Series Expansion Based Numerical Methods: A Primer, Performance Benchmarking and New Approaches for Problems with Non-smooth Solutions (with T. Jacquemin, K. Agathos, S. Mohseni-Mofidi, and S.P.A. Bordas). Arch. Comput. Methods Eng, Published 30 August 2019, 27, 1465-1513, 2020.

    2. Quantifying discretization errors for soft-tissue simulation in computer assisted surgery: a preliminary study (with M. Duprez, S. Bordas, M. Bucki, H.P. Bui, F. Chouly, V. Lleras, C. Lobos, A. Lozinski, P.Y. Rohan). Appl. Math. Model, Available online 9 August 2019, 77(1), 709-723, 2020. Also available at HAL:01616322 and arXiv:1806.06944.

    3. Weak and strong from meshless methods for linear elastic problem under fretting contact conditions (with G. Kosec, J. Slak, M. Depolli, R. Trobec, K. Pereira, T. Jacquemin, S.P.A. Bordas, and M. Abdel Wahab). Tribology International, Available online 3 June 2019, 138, 392-402, 2019.

    4. Corotational Cut Finite Element Method for real-time surgical simulation: application to needle insertion simulation (with H.P. Bui and S. Bordas). Comput. Methods Appl. Mech. Engrg., 345 (1), 183-211, 2019. Free access till January 13, 2019. Also available at arXiv:1712.03052.

    5. Adaptive Isogeometric analysis for plate vibrations: an efficient approach of local refinement based on hierarchical a posterior error estimation (with P. Yu, C. Anitescu, S. Bordas and P. Kerfriden). Comput. Methods Appl. Mech. Engrg., 342 (1), 251-286, 2018. Free access till October 12, 2018. Also available at arXiv:1804.03191

    6. Weakening the tight coupling between geometry and simulation in isogeometric analysis: from sub- and super- geometric analysis to Geometry Independent Field Approximation (GIFT) (with E. Atroshchenko, G. Xu, and S. Bordas). Int. J. Numer. Meth. Engrg., 114(10), 1131-1159, 2018. Also available at arXiv:1706.06371 and Orbi.lu:10993/31469

    7. Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation (with H.P. Bui, H. Courtecuisse, M. Audette, S. Cotin and S. Bordas). Int. J. Numer. Meth. Biomed. Engng., 34(5), e2958, 2018. Also available at arXiv:1704.07636 and Orbi.lu:10993/30937

    8. Real time error control for surgical simulation (with H.P. Bui, H. Courtecuisse, S. Cotin and S. Bordas). IEEE Transactions on Biomedical Engineering (TBME), 65(3), 596-607, 2018. Also available at arXiv:1610.02570 and Orbi.lu:10993/28624.

    9. On the convergence of stresses in fretting fatigue (with K. Pereira, S. Bordas, R. Trobec, M. Depolli, G. Kosec and M. Abdel Wahab). Materials, 9 (8), 639, 2016.

    10. Two-sided robust and sharp a posteriori error estimates in isogeometric discretization of elliptic problems (with S.K. Kleiss). In Proceedings of Isogeometric Analysis and Applications 2014, Juettler and Simeon Eds, LNCSE 107, 231--246, 2015, Springer.

    11. Guaranteed and sharp a posteriori error estimates in isogeometric analysis (with S.K. Kleiss). Comput. Math. Appl., 70 (3), 167-190, 2015. Also available at arXiv:1304.7712.

    12. Algebraic multilevel preconditioning in isogeometric analysis: Construction and numerical studies (with K.P.S. Gahalaut and J. Kraus). Comput. Methods Appl. Mech. Engrg., 266, 40-56, 2013.

    13. Robust algebraic multilevel preconditioning in H(curl) and H(div). Comput. Math. Appl., 66 (6), 1024-1046, 2013.

    14. Multigrid Methods for Isogeometric Discretization (with K.P.S. Gahalaut and J. Kraus). Comput. Methods Appl. Mech. Engrg., 253, 413-425, 2013.

    15. IETI - Isogeometric Tearing and Interconnecting (with B.J. Juettler, S.K. Kleiss and C. Pechstein). Comput. Methods Appl. Mech. Engrg., 247-248, 201-215, 2012.

    16. Algebraic multilevel iteration method for lowest-order Raviart-Thomas space and applications (with J. Kraus). Int. J. Numer. Meth. Engrg., 86, 1175--1196, 2011.

    17. Guaranteed and robust error bounds for nonconforming approximations of elliptic problems (with S. Repin). IMA J. Numer. Anal., 31, 597--615, 2011.

    18. A posteriori error estimates for approximations of evolutionary convection-diffusion problems (with S. Repin). J. Math. Sci. (N.Y.), 170(4), 554--566, 2010.

    19. Boundary element simulation of linear water waves in a model basin (with C. Hofreither, and U. Langer). In Proceedings of 7th International Conference on Large Scale Scientific Computations (LSSC09), Lirkov et al. Eds, LNCS 5910, 132--139, 2010, Springer.

    20. Efficient computable error bounds for discontinuous Galerkin approximations of elliptic problems (with S. Repin). J. Comput. Appl. Math., 226, 358--369, 2009.

    21. Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems (with R. Lazarov and S. Repin). Numer. Methods Partial Differential Equations, 25, 952--971, 2009.

    22. A multilevel method for discontinuous Galerkin approximation of three-dimensional anisotropic elliptic problems (with J. Kraus). Numer. Linear Algebra Appl., 15, 417--438, 2008.

    23. A multilevel method for discontinuous Galerkin approximation of three-dimensional elliptic problems (with J. Kraus). In Domain Decomposition Methods in Science and Engineering XVII, Langer et al. Eds, LNCSE 60, 155--164, 2008, Springer.

    24. Multilevel preconditioning of two-dimensional elliptic problems discretized by a class of discontinuous Galerkin methods (with J. Kraus). SIAM J. Sci. Comput., 30, 684--706, 2008.

    25. A Runge-Kutta discontinuous Galerkin method for linear free-surface gravity waves using high order velocity recovery (with J.J.W. van der Vegt). Comput. Methods Appl. Mech. Engrg., 196, 1984--1996, 2007.

    26. h-p spectral element method for elliptic problems on non-smooth domains using parallel computers Computing, 78, 117--143, 2006.

    27. A parallel h-p spectral element method for elliptic problems on polygonal domains - mixed boundary conditions (with P. Dutt). In Industrial Mathematics, Joshi et al. Eds, 121-136, 2006, Narosa Publishing House, New Delhi.

    28. Discontinuous Galerkin Method for linear free-surface gravity waves (with J.J.W. van der Vegt). J. Sci. Comput., 22/23, 531--567, 2005.

    29. An implicit discontinuous Galerkin finite element method for water waves (with J.J.W. van der Vegt). In Computational Mechanics, Yao et al. Eds, ISBN 7-302-09343-1, 690-695, 2004, Tsinghua University Press & Springer.

    30. Stability estimates for h-p spectral element methods for general elliptic problems on curvilinear domains (with P. Dutt). Proc. Math. Sci., 113, 395--429, 2003, Springer.

    31. An efficient and exponentially accurate parallel h-p spectral element method for elliptic problems on polygonal domains - The Dirichlet case (with P. Dutt and B.V. Rathish Kumar). In High Performance Computing, Sahni et al. Eds, LNCS 2552, 534--544, 2002, Springer.

    32. Stability estimates for h-p spectral element methods for elliptic problems (with P. Dutt and B.V. Rathish Kumar). Proc. Math. Sci., 112, 601--639, 2002, Springer.

Other Publications

    1. Condition number estimates for matrices arising in the isogeometric discretizations (with K.P.S. Gahalaut). In revision (Submitted for publication in October 2012). Available as RICAM Report, 2012-23.

    2. Condition number study of graph theory based preconditioners for isogeometric discretization of Poisson equation (with K.P.S. Gahalaut). RICAM Report, 2012-14.

    3. Parallel h-p Spectral Element Method for Elliptic Problems on Polygonal Domains (with P. Dutt and B.V. Rathish Kumar). In CD-ROM Proceedings of 9th Euro Conference on Numerical Methods and Computational Mechanics, 2002.

    4. h-p Spectral Element Methods for Elliptic Problems on Non-smooth Domains using Parallel Computers (Ph.D. Thesis). Technical Memorandum of Department of Applied Mathematics, University of Twente, Enschede, 3451, ISSN 0169-2690, 2002. http://eprints.eemcs.utwente.nl/3451/