List of publications
Seminar for Applied Mathematics

List of publications

Prof. Dr. Ralf Hiptmair

[Recent publications] [Refereed publications in journals or collections] [Books and Book Chapters] [Other Publications] [Theses]

RECENT PUBLICATIONS / SAM REPORTS

  1. R. Hiptmair and A. Moiola and I. Perugia Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes, Submitted, SAM Report 2012/06, link_samreport, bibtex

  2. R. Hiptmair and G. Phillips and G. Sinha Multiple point evaluation on combined tensor product supports, Submitted, SAM Report 2011/63, link_samreport, bibtex

  3. H. Heumann and R. Hiptmair Refined convergence theory for semi-Lagrangian schemes for pure advection, Submitted, SAM Report 2011/60, link_samreport, bibtex

  4. X. Claeys and R. Hiptmair Electromagnetic scattering at composite objects: A novel multi-trace boundary integral formulation, Submitted, SAM Report 2011/58, link_samreport, bibtex

  5. H. Heumann and R. Hiptmair Convergence of lowest order semi-Lagrangian schemes, Submitted, SAM Report 2011/47, link_samreport, bibtex

  6. X. Claeys and R. Hiptmair Boundary integral formulation of the first kind for acoustic scattering by composite structures, Submitted, SAM Report 2011/45, link_samreport, bibtex

  7. R. Hiptmair and J. Li Shape derivatives in differential forms I: An intrinsic perspective, Accepted, Annali di Matematica Pura et Applicata (2011), SAM Report 2011/42, link_samreport, bibtex

  8. H. Heumann and R. Hiptmair and K. Li and J.-C. Xu Semi-lagrangian methods for advection of differential forms, Submitted, BIT (2011), SAM Report 2011/21, link_samreport, bibtex

  9. R. Hiptmair and A. Moiola and I. Perugia Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations, Accepted, Mathematics of Computation (2011), SAM Report 2011/09, link_samreport, bibtex

  10. M. Ganesh and S. Hawkins and R. Hiptmair Convergence analysis with parameter estimates for a reduced basis acoustic scattering t-matrix method, Accepted, IMA Journal of Numerical Analysis (2011), SAM Report 2011/04, link_samreport, bibtex

  11. R. Hiptmair and J.-Z. Li and J. Zou Universal extension for sobolev spaces of differential forms and applications, Submitted, J. Func. Anal. (2011), SAM Report 2009/22, link_samreport, bibtex

  12. H. Heumann and R. Hiptmair and J. Xu A semi-Lagrangian method for convection of differential forms, Submitted, SAM Report 2009/09, link_samreport, bibtex

  13. R. Hiptmair and J.-Z. Li and J. Zou Convergence analysis of finite element methods for h(curl)-elliptic interface problems, Accepted, Numerische Mathematik (2009), SAM Report 2009/04, link_samreport, bibtex

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REFEREED PUBLICATIONS IN JOURNALS OR COLLECTIONS

  1. R. Hiptmair and J.-Z. Li and J. Zou Real interpolation of spaces of differential forms, Mathematische Zeitschrift, 270/1 (2012), pp. 395-402, SAM Report 2009/23, doi, bibtex

  2. R. Hiptmair and S.-P. Mao Stable multilevel splittings of boundary edge element spaces, BIT (2011), SAM Report 2011/28, doi, bibtex

  3. R. Hiptmair and A. Moiola and I. Perugia Stability results for the time-harmonic maxwell equations with impedance boundary conditions, M3AS, 21/11 (2011), pp. 2263-2287, SAM Report 2010/39, doi, bibtex

  4. R. Hiptmair and C. Jerez-Hanckes Multiple traces boundary integral formulation for helmholtz transmission problems, Adv. Appl. Math. (2011), SAM Report 2010/35, doi, bibtex

  5. R. Hiptmair and A. Moiola and I. Perugia Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: Analysis of the p-version, SIAM J. Numer. Anal., 49/1 (2011), pp. 264-284, SAM Report 2009/20, doi, bibtex

  6. R. Hiptmair and P. Kotiuga and S. Tordeux Self-adjoint curl operators, Annali di Matematica Pura ed Applicata (2011), SAM Report 2008/27, doi, bibtex

  7. D. Boffi and M. Costabel and M. Dauge and L. Demkowicz and R. Hiptmair Discrete compactness for the p-version of discrete differential forms, SIAM J. Numer. Anal., 49/1 (2011), pp. 135-158, doi, bibtex

  8. H. Heumann and R. Hiptmair Eulerian and semi-lagrangian methods for convection-diffusion for differential forms, Disc. Cont. Dyn. Sys., 29/4 (2011), pp. 1471-1495, doi, bibtex

  9. A. Moiola and R. Hiptmair and I. Perugia Vekua theory for the Helmholtz operator, ZAMP, 62/5 (2011), pp. 779-807, doi, bibtex

  10. A. Moiola and R. Hiptmair and I. Perugia Plane wave approximation of homogeneous Helmholtz solutions, ZAMP, 62/5 (2011), pp. 809-837, doi, bibtex

  11. R. Hiptmair and J.-Z. Li and J. Zou Convergence analysis of finite element methods for H(div)-elliptic interface problems, J. Numer. Math., 18/3 (2010), pp. 187-218, SAM Report 2010/14, doi, bibtex

  12. A. Bespalov and N. Heuer and R. Hiptmair Convergence of natural hp-BEM for the electric field integral equation on polyhedral surfaces, SIAM J. Numer. Anal., 48/4 (2010), pp. 1518-1529, SAM Report 2009/24, doi, bibtex

  13. J. Ostrowski and M. Bebendorf and R. Hiptmair and F. Krämer H-matrix based operator preconditioning for full Maxwell at low frequencies, IEEE Transactions Magnetics, 46/8 (2010), pp. 3193-3196, doi, bibtex

  14. C. J. Gittelson and R. Hiptmair and I. Perugia Plane wave discontinuous Galerkin methods: analysis of the $h$-version, M2AN Math. Model. Numer. Anal., 43/2 (2009), pp. 297-331, SAM Report 2008/04, doi, bibtex

  15. R. Hiptmair and W.-Y. Zheng Local multigrid in $H(curl)$, J. Comput. Math., 27/5 (2009), pp. 573-603, doi, bibtex

  16. G. Widmer and R. Hiptmair and C. Schwab Sparse adaptive finite elements for radiative transfer, J. Comput. Phys., 227/12 (2008), pp. 6071-6105 , doi, bibtex

  17. R. Hiptmair and F. Krämer and J. Ostrowski A robust Maxwell formulation for all frequencies, IEEE Trans. Magnetics, 44/6 (2008), pp. 682-685, doi, bibtex

  18. R. Hiptmair and J. Xu Auxiliary space preconditioning for edge elements, IEEE Trans. Magnetics, 44/6 (2008), pp. 938-941, doi, bibtex

  19. K. Schmidt and O. Sterz and R. Hiptmair Estimating the eddy-current modelling error, IEEE Trans. Magnetics, 44/6 (2008), pp. 686-689, doi, bibtex

  20. R. Hiptmair and J. Xu Nodal auxiliary space preconditioning in $H(curl)$ and $H({\rm div})$ spaces, SIAM J. Numer. Anal., 45/6 (2007), pp. 2483-2509, doi, bibtex

  21. J. Ostrowski and R. Hiptmair and H. Fuhrmann Electric 3D-simulation of metallized film capacitors, COMPEL, 26/2 (2007), pp. 524-543, doi, bibtex

  22. R. Hiptmair Operator preconditioning, Comput. Math. Appl., 52/5 (2006), pp. 699-706, doi, bibtex

  23. R. Hiptmair and P. Meury Stabilized FEM-BEM coupling for Helmholtz transmission problems, SIAM J. Numer. Anal., 44/5 (2006), pp. 2107-2130, doi, bibtex

  24. B. Zeller and R. Hiptmair Conservative discretization of the Einstein-Dirac equations in spherically symmetric spacetime, Classical Quantum Gravity, 23/16 (2006), pp. 615-634, doi, bibtex

  25. R. Hiptmair and G. Widmer and J. Zou Auxiliary space preconditioning in $H_0({\rm curl}; \Omega)$, Numer. Math., 103/3 (2006), pp. 435-459, doi, bibtex

  26. B. Cranganu-Cretu and Hiptmair Direct boundary integral equation method for electromagnetic scattering by partly coated dielectric objects, Comput. Vis. Sci., 8/3-4 (2005), pp. 145-158, doi, bibtex

  27. T. Bubeck and R. Hiptmair and H. Yserentant The finite mass mesh method, Comput. Vis. Sci., 8/2 (2005), pp. 49-68, doi, bibtex

  28. A. Alonso Rodríguez and R. Hiptmair and A. Valli A hybrid formulation of eddy current problems, Numer. Methods Partial Differential Equations, 21/4 (2005), pp. 742-763, doi, bibtex

  29. R. Hiptmair and J. Ostrowski Coupled boundary element scheme for eddy current computation, J. Engrg. Math., 51/3 (2005), pp. 231-250, doi, bibtex

  30. A. Buffa and R. Hiptmair Regularized combined field integral equations, Numer. Math., 100/1 (2005), pp. 1-19, doi, bibtex

  31. R. Hiptmair and P. Ledger Computation of resonant modes for axisymmetric Maxwell cavities using $hp$-version edge finite elements, Internat. J. Numer. Methods Engrg., 62/12 (2005), pp. 1652-1676, doi, bibtex

  32. B. Cranganu-Cretu and R. Hiptmair and Andjelic Transmission through arbitrary apertures in metal-coated dielectric bodies, IEEE Trans. Magnetics, 41/5 (2005), pp. 1492-1495, doi, bibtex

  33. R. Hiptmair and O. Sterz Current and voltage excitations for the eddy current model, Int. J. Numer. Model, 18/1 (2005), pp. 1-21, doi, bibtex

  34. A. Buffa and R. Hiptmair A coercive combined field integral equation for electromagnetic scattering, SIAM J. Numer. Anal., 42/2 (2004), pp. 621-640, doi, bibtex

  35. A. Alonso Rodríguez and R. Hiptmair and A. Valli Mixed finite element approximation of eddy current problems, IMA J. Numer. Anal., 24/2 (2004), pp. 255-271, doi, bibtex

  36. R. Hiptmair Coercive combined field integral equations, J. Numer. Math., 11/2 (2003), pp. 115-133, SAM Report 2003/08, doi, bibtex

  37. R. Buffa and R. Hiptmair and T. von Petersdorff and Ch. Schwab Boundary element methods for Maxwell transmission problems in Lipschitz domains, Numer. Math., 95/3 (2003), pp. 459-485, SAM Report 2001/05, doi, bibtex

  38. R. Hiptmair and A. Schädle Non-reflecting boundary conditions for Maxwell, Computing, 71/3 (2003), pp. 265-292, doi, bibtex

  39. V. Gradinaru and R. Hiptmair Multigrid for discrete differential forms on sparse grids, Computing, 71/1 (2003), pp. 17-42, doi, bibtex

  40. R. Hiptmair Coupling of finite elements and boundary elements in electromagnetic scattering, SIAM J. Numer. Anal., 41/3 (2003), pp. 919-944, doi, bibtex

  41. R. Hiptmair Boundary element methods for eddy current computation, Lect. Notes Comput. Sci. Eng., 28 (2003), no_doi, bibtex

  42. R. Hiptmair Analysis of multilevel methods for eddy current problems, Math. Comp., 72/243 (2003), pp. 1281-1303, doi, bibtex

  43. V. Gradinaru and R. Hiptmair Mixed finite elements on sparse grids, Numer. Math., 93/3 (2003), pp. 471-495, doi, bibtex

  44. R. Hiptmair and Ch. Schwab Natural boundary element methods for the electric field integral equation on polyhedra, SIAM J. Numer. Anal., 40/1 (2002), pp. 66-86, SAM Report 2001/04, doi, bibtex

  45. R. Hiptmair and J. Ostrowski Generators of $H_1(\Gamma_h,\Bbb Z)$ for triangulated surfaces: construction and classification, SIAM J. Comput., 31/5 (2002), pp. 1405-1423, doi, bibtex

  46. R. Hiptmair and K. Neymeyr Multilevel method for mixed eigenproblems, SIAM J. Sci. Comput., 23/6 (2002), pp. 2141-2164, doi, bibtex

  47. R. Hiptmair Symmetric coupling for eddy current problems, SIAM J. Numer. Anal., 40/1 (2002), pp. 41-65, doi, bibtex

  48. S. Börm and R. Hiptmair Multigrid computation of axisymmetric electromagnetic fields, Adv. Comput. Math., 16/4 (2002), pp. 331-356, doi, bibtex

  49. R. Hiptmair Discrete Hodge operators, Numer. Math., 90/2 (2001), pp. 265-289, doi, bibtex

  50. S. Börm and R. Hiptmair Analysis of tensor product multigrid, Numer. Algorithms, 26/3 (2001), pp. 219-234, doi, bibtex

  51. R. Hiptmair Discrete Hodge operators: An algebraic perspective, Journal of Electromagnetic Waves and Applications, 15/3 (2001), pp. 343-344, doi, bibtex

  52. R. Hiptmair Higher order Whitney forms, Geometric Methods for Computational Electromagnetics, F. Teixeira, ed., vol. 32 of PIER, EMW Publishing, Cambridge, MA, 2001 (2001), pp. 271-299, no_doi, bibtex

  53. R. Hiptmair and A. Toselli Overlapping and multilevel Schwarz methods for vector valued elliptic problems in three dimensions, IMA Vol. Math. Appl., 120 (2000), pp. 181-208, no_doi, bibtex

  54. R. Hiptmair Multilevel gauging for edge elements, Computing, 64/2 (2000), pp. 97-122, doi, bibtex

  55. R. Beck and R. Hiptmair and R. Hoppe and B. Wohlmuth Residual based a posteriori error estimators for eddy current computation, M2AN Math. Model. Numer. Anal., 34/1 (2000), pp. 159-182, doi, bibtex

  56. B. Engelmann and R. Hiptmair and R. Hoppe and G. Mazurkevich Numerical simulation of electrorheological fluids based on an extended Bingham model, Computing and Visualization in Science, 2/4 (2000), pp. 211-219, doi, bibtex

  57. R. Beck and R. Hiptmair and B. Wohlmuth A hierarchical error estimator for eddy current computation, World Sci. Publ. (2000), pp. 110-120, no_doi, bibtex

  58. V. Gradinaru and R. Hiptmair Whitney elements on pyramids, Electron. Trans. Numer. Anal., 8 (1999), pp. 154-168, no_doi, bibtex

  59. R. Beck and P. Deuflhard and R. Hiptmair and R. Hoppe and B. Wohlmuth Adaptive multilevel methods for edge element discretizations of Maxwell\'s equations, Surveys Math. Indust., 8/3-4 (1999), pp. 271-312, no_doi, bibtex

  60. R. Beck and R. Hiptmair Multilevel solution of the time-harmonic Maxwell\'s equations based on edge elements, Internat. J. Numer. Methods Engrg., 45/7 (1999), pp. 901-920, doi, bibtex

  61. R. Hiptmair and R. Hoppe Multilevel methods for mixed finite elements in three dimensions, Numer. Math., 82/2 (1999), pp. 253-279, doi, bibtex

  62. R. Hiptmair Canonical construction of finite elements, Mathematics of Computation, 68/228 (1999), pp. 1325-1346, doi, bibtex

  63. R. Hiptmair Multigrid method for Maxwell\'s equations, SIAM J. Numer. Anal., 36/1 (1999), pp. 204-225, doi, bibtex

  64. R. Hiptmair Multigrid method for $H({\rm div})$ in three dimensions, Electron. Trans. Numer. Anal., 6 (1997), pp. 133-152, no_doi, bibtex

  65. R. Hiptmair Nonconforming vector valued finite elements, East-West J. Numer. Math., 5/3 (1997), pp. 163-182, no_doi, bibtex

  66. R. Hiptmair and R. Schiekofer and B. Wohlmuth Multilevel preconditioned augmented Lagrangian techniques for 2nd order mixed problems, Computing, 57/1 (1996), pp. 25-48, doi, bibtex

  67. R. Hiptmair and R. Hoppe Mixed finite element discretization of continuity equations arising in semiconductor device simulation, Internat. Ser. Numer. Math., 117 (1994), pp. 197-217, no_doi, bibtex

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BOOKS AND BOOK CHAPTERS

  1. J. Ostrowski and R. Hiptmair and F. Kraemer and J. Smajic and T. Steinmetz Transient Full Maxwell Computation of Slow Processes, Scientific Computing in Electrical Engineering SCEE 2010, 16, pp. 87-95, Springer Berlin (2012), doi, bibtex

  2. R. Hiptmair and I. Perugia Mixed plane wave discontinuous {G}alerkin methods, Domain decomposition methods in science and engineering XVIII, Lect. Notes Comput. Sci. Eng., 70, pp. 51-62, Springer (2009), doi, bibtex

  3. R. Hiptmair Boundary element methods for eddy current computation, Lect. Notes Appl. Comput. Mech., 29, pp. 213-248, Springer (2007), doi, bibtex

  4. R. Hiptmair and P. Meury Stabilized FEM-BEM coupling for Maxwell transmission problems, Lecture Notes in Computational Science and Engineering, 59, pp. 1-39, Springer (2007), no_doi, bibtex

  5. A. Buffa and R. Hiptmair Galerkin boundary element methods for electromagnetic scattering, Lect. Notes Comput. Sci. Eng., 31, pp. 83-124 (2003), no_doi, bibtex

  6. R. Hiptmair Finite elements in computational electromagnetism, Acta Numer., 11, pp. 237-339 (2002), doi, bibtex

OTHER PUBLICATIONS

  1. A. Moiola and R. Hiptmair and I. Perugia Approximation by plane waves, SAM Report 2009/27, link_samreport, bibtex

  2. F. Kraemer and M. Bebendorf and J. Ostrowski and R. Hiptmair Hierarchical matrix preconditioners for eddy current problems, Proc. ICEAA'09 (2009), pp. 724-727, doi, bibtex

  3. R. Hiptmair Discrete compactness for p-version of tetrahedral edge elements, SAM Report 2008/31, link_samreport, link_arxiv, bibtex

  4. H. Heumann and R. Hiptmair Extrusion contraction upwind schemes for convection-diffusion problems, SAM Report 2008/30, link_samreport, bibtex

  5. R. Hiptmair Boundary integral equations for multi-deliectric electromagnetic scattering, Oberwolfach Reports (2008), no_doi, bibtex

  6. R. Hiptmair Low frequency stable maxwell formulations, Oberwolfach Reports (2008), no_doi, bibtex

  7. J. Ostrowski and B. Cranganu-Cretu and F. Kraemer and R. Hiptmair and J. Smajic Hybrid FEM-BEM, CAD Integrated Magnetostatics, Proc. of the IEEE COMPUMAG Conf. (2007), pp. 139-140, no_doi, bibtex

  8. R. Hiptmair Operator preconditioning, Oberwolfach Reports, 2 (2005), pp. 1256-1259, no_doi, bibtex

  9. Z. Chen and R. Hiptmair Convergence of p-FEM for Maxwell eigenvalue problems, SAM Report 2004/02, link_samreport, bibtex

  10. R. Hiptmair Stable coupling in scattering, Oberwolfach Reports, 1 (2004), no_doi, bibtex

  11. R. Hiptmair and P. Ledger A quadrilateral edge element scheme with minimum dispersion, SAM Report 2003/17, link_samreport, bibtex

  12. R. Hiptmair From $E$ to edge elements, Ber. IZWR Interdiszip. Zent. Wiss. Rechn., 1 (2003), pp. 39-48, no_doi, bibtex

  13. R. Hiptmair and J. Ostrowski Symmetric coupling of FEM and BEM for eddy current computations, S. Amini (2003), pp. 117-126, no_doi, bibtex

  14. R. Hiptmair Coupled boundary element scheme for eddy current computation, Lehrstuhl für Umformtechnik (2003), pp. 41-59, no_doi, bibtex

  15. R. Hiptmair and J. Metzger Automated local mode analysis, SFB, 382 (2002), no_doi, bibtex

  16. R. Hiptmair Construction and classification of surface cycles, ONERA, B. Michelsen and F. Decvéle (eds.) (2002), pp. 239-244, no_doi, bibtex

  17. R. Hiptmair Transmission problems in eddy current computation, ONERA (2002), pp. 13-18, no_doi, bibtex

  18. R. Hiptmair Abenteuer Anwendung, Mitt. Dtsch. Math.-Ver., 4 (2001), pp. 19-23, no_doi, bibtex

  19. R. Hiptmair and J. Ostrowski and R. Quast Modelling and simulation of induction heating, Tech. Rep., 149 (2000), no_doi, bibtex

  20. R. Hiptmair Concepts for an object oriented finite element code, Tech. Rep., 335 (1995), no_doi, bibtex

  21. R. Hiptmair Multilevel computation of magnetic fields, Tech. Rep., 342 (1995), no_doi, bibtex

  22. R. Hiptmair and R. Hoppe and B. Wohlmuth Coupling problems in microelectronic device simulation, Notes on Numerical Fluid Mechanics, 51 (1995), pp. 86-95, no_doi, bibtex

  23. R. Hiptmair and I. Schmitt Compatibility conditions for semiconductor equations, Tech. Rep. (1994), no_doi, bibtex

  24. R. Hiptmair and R. Hoppe Mixed finite element discretization of continuity equations arising in semiconductor device simulation, Oberwolfach Proceedings of Conference July 5-11 (1993), pp. 197-217, no_doi, bibtex

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THESES

  1. R. Hiptmair Numerical Methods for Computational Electromagnetism (2002), no_doi, bibtex

  2. R. Hiptmair Multilevel preconditioning for mixed problems in three dimensions, Augsburger Mathematisch-Naturwissenschaftliche Schriften, 8 (1996), no_doi, bibtex