Edit Profile (opens in new tab) Hiptmair, Ralf Co-Author Distance Author ID: hiptmair.ralf Published as: Hiptmair, Ralf; Hiptmair, R. Documents Indexed: 148 Publications since 1994, including 1 Book and 4 Additional arXiv Preprints 6 Contributions as Editor · 1 Further Contribution Co-Authors: 77 Co-Authors with 120 Joint Publications 2,047 Co-Co-Authors all top 5 Co-Authors 21 single-authored 16 Claeys, Xavier 12 Perugia, Ilaria 11 Moiola, Andrea 10 Hoppe, Ronald H. W. 8 Jerez-Hanckes, Carlos 7 Ostrowski, Jörg 6 Heumann, Holger 6 Li, Jingzhi 6 Schwab, Christoph 5 Buffa, Annalisa 5 Urzúa-Torres, Carolina 5 Wohlmuth, Barbara I. 5 Zou, Jun 4 Langer, Ulrich 4 Pagliantini, Cecilia 4 Schulz, Erick 4 Spindler, Elke 3 Casati, Daniele 3 Gradinaru, Vasile 3 Joly, Patrick 3 Mao, Shipeng 3 Paganini, Alberto 3 Panchal, Piyush 3 Valli, Alberto 3 Zheng, Weiying 2 Alonso Rodríguez, Ana 2 Averseng, Martin 2 Ayuso de Dios, Blanca 2 Beck, Rudolf 2 Börm, Steffen 2 Florian, Francesco 2 Gittelson, Claude Jeffrey 2 Meury, Patrick 2 Pechstein, Clemens 2 Peng, Zhen 2 Sauter, Stefan 2 Schmidt, Kersten 2 Widmer, Gerhard 2 Xu, Jinchao 1 Beck, Rudi 1 Bermúdez, Alfredo 1 Bespalov, Alexei 1 Boffi, Daniele 1 Bubeck, Tilmann 1 Casagrande, Raffael 1 Chaillat-Loseille, Stéphanie 1 Codecasa, Lorenzo 1 Costabel, Martin 1 Cranganu-Cretu, Bogdan 1 Dauge, Monique 1 Demkowicz, Leszek F. 1 Deuflhard, Peter 1 Eberle-Blick, Sarah 1 Fuhrmann, Henning 1 Ganesh, Mahadevan 1 Giacomel, Lorenzo 1 Grubišić, Luka 1 Haddar, Houssem 1 Hawkins, Stuart Collin 1 Heuer, Norbert 1 Hohage, Thorsten 1 Kotiuga, Peter Robert 1 Labarca, Ignacio 1 Ledger, Paul David 1 Lee, Jin-Fa 1 Li, Kun 1 Li, Lingxiao 1 López-Fernández, María 1 MacKie-Mason, Brian 1 Mazurkevitch, George 1 Monk, Peter B. 1 Moro, Federico 1 Neymeyr, Klaus 1 Pauly, Dirk 1 Pintarelli, Simon 1 Ren, Ning 1 Renner, Diego 1 Rodríguez, Rodolfo 1 Sargheini, S. 1 Scarabosio, Laura 1 Schädle, Achim 1 Schiekofer, Thomas 1 Schillings, Claudia 1 Schumacher, Henrik 1 Shao, Yang 1 Sinha, Gaurav 1 Smajic, Jasmin 1 Spence, Euan A. 1 Steinbach, Olaf 1 Steinmetz, Thorsten 1 Sterz, Oliver 1 Tonnon, Wouter 1 Tordeux, Sébastien 1 Toselli, Andrea 1 von Petersdorff, Tobias 1 Wardetzky, Max 1 Winkelmann, Christoph 1 Wu, Haijun 1 Yserentant, Harry 1 Zeller, Benedikt all top 5 Serials 11 SIAM Journal on Numerical Analysis 8 Numerische Mathematik 7 BIT 6 Integral Equations and Operator Theory 5 Advances in Computational Mathematics 5 Oberwolfach Reports 4 Mathematics of Computation 4 Computing 4 Computational Methods in Applied Mathematics 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Computers & Mathematics with Applications 3 IMA Journal of Numerical Analysis 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 International Journal for Numerical Methods in Engineering 3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Journal on Mathematical Analysis 3 Computing and Visualization in Science 2 Inverse Problems 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Journal of Functional Analysis 2 Journal of Scientific Computing 2 Numerical Algorithms 2 SIAM Journal on Scientific Computing 2 ETNA. Electronic Transactions on Numerical Analysis 2 Foundations of Computational Mathematics 2 Journal of Numerical Mathematics 2 Discrete and Continuous Dynamical Systems. Series S 2 SMAI Journal of Computational Mathematics 1 Classical and Quantum Gravity 1 Communications on Pure and Applied Mathematics 1 Journal of Computational Physics 1 Journal of Engineering Mathematics 1 Mathematical Methods in the Applied Sciences 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Computational and Applied Mathematics 1 Mathematische Zeitschrift 1 Numerical Functional Analysis and Optimization 1 SIAM Journal on Computing 1 Journal of Computational Mathematics 1 Applied Numerical Mathematics 1 COMPEL 1 Numerical Methods for Partial Differential Equations 1 Surveys on Mathematics for Industry 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 East-West Journal of Numerical Mathematics 1 Discrete and Continuous Dynamical Systems 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 International Journal of Numerical Modelling 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 IEEE Transactions on Antennas and Propagation 1 Acta Numerica 1 Augsburger Mathematisch-Naturwissenschaftliche Schriften 1 Lecture Notes in Mathematics 1 Communications in Computational Physics 1 Numerical Mathematics: Theory, Methods and Applications all top 5 Fields 125 Numerical analysis (65-XX) 87 Partial differential equations (35-XX) 74 Optics, electromagnetic theory (78-XX) 22 Fluid mechanics (76-XX) 11 Integral equations (45-XX) 9 Global analysis, analysis on manifolds (58-XX) 8 General and overarching topics; collections (00-XX) 7 Potential theory (31-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 5 Mechanics of deformable solids (74-XX) 4 Functional analysis (46-XX) 2 Approximations and expansions (41-XX) 2 Operator theory (47-XX) 2 Probability theory and stochastic processes (60-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Integral transforms, operational calculus (44-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 121 Publications have been cited 1,663 times in 1,032 Documents Cited by ▼ Year ▼ Finite elements in computational electromagnetism. Zbl 1123.78320 Hiptmair, R. 389 2002 Nodal auxiliary space preconditioning in H(curl) and H(div) spaces. Zbl 1153.78006 Hiptmair, Ralf; Xu, Jinchao 137 2007 Multigrid method for Maxwell’s equations. Zbl 0922.65081 Hiptmair, R. 111 1998 Plane wave discontinuous Galerkin methods: Analysis of the \(h\)-version. Zbl 1165.65076 Gittelson, Claude J.; Hiptmair, Ralf; Perugia, Ilaria 108 2009 Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the \(p\)-version. Zbl 1229.65215 Hiptmair, R.; Moiola, A.; Perugia, I. 98 2011 Residual based a posteriori error estimators for eddy current computation. Zbl 0949.65113 Beck, Rudi; Hiptmair, Ralf; Hoppe, Ronald H. W.; Wohlmuth, Barbara 95 2000 Canonical construction of finite elements. Zbl 0938.65132 Hiptmair, R. 74 1999 A fully divergence-free finite element method for magnetohydrodynamic equations. Zbl 1393.65031 Hiptmair, Ralf; Li, Lingxiao; Mao, Shipeng; Zheng, Weiying 64 2018 Comparison of approximate shape gradients. Zbl 1320.65099 Hiptmair, R.; Paganini, A.; Sargheini, S. 62 2015 Operator preconditioning. Zbl 1125.65037 Hiptmair, R. 61 2006 Boundary element methods for Maxwell transmission problems in Lipschitz domains. Zbl 1071.65160 Buffa, Annalisa; Hiptmair, Ralf; von Petersdorff, Tobias; Schwab, Christoph 58 2003 Plane wave approximation of homogeneous Helmholtz solutions. Zbl 1263.35070 Moiola, A.; Hiptmair, R.; Perugia, I. 56 2011 Galerkin boundary element methods for electromagnetic scattering. Zbl 1055.78013 Buffa, Annalisa; Hiptmair, Ralf 55 2003 A survey of Trefftz methods for the Helmholtz equation. Zbl 1357.65282 Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 54 2016 Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations. Zbl 1269.78013 Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 43 2013 Discrete Hodge operators. Zbl 0993.65130 Hiptmair, R. 42 2001 Symmetric coupling for eddy current problems. Zbl 1010.78011 Hiptmair, R. 36 2002 Multiple traces boundary integral formulation for Helmholtz transmission problems. Zbl 1261.65123 Hiptmair, R.; Jerez-Hanckes, C. 34 2012 Large deformation shape uncertainty quantification in acoustic scattering. Zbl 1402.35321 Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch. 29 2018 Multigrid method for \(H\text{(div)}\) in three dimensions. Zbl 0897.65046 Hiptmair, R. 28 1997 Natural boundary element methods for the electric field integral equation on polyhedra. Zbl 1010.78014 Hiptmair, Ralf; Schwab, Christoph 27 2002 Stability results for the time-harmonic Maxwell equations with impedance boundary conditions. Zbl 1331.35335 Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 26 2011 Adaptive multilevel methods for edge element discretizations of Maxwell’s equations. Zbl 0939.65136 Beck, Rudolf; Deuflhard, Peter; Hiptmair, Ralf; Hoppe, Ronald H. W.; Wohlmuth, Barbara 25 1999 Regularized combined field integral equations. Zbl 1067.65137 Buffa, A.; Hiptmair, R. 25 2005 Multi-trace boundary integral formulation for acoustic scattering by composite structures. Zbl 1366.74030 Claeys, Xavier; Hiptmair, Ralf 25 2013 Sparse adaptive finite elements for radiative transfer. Zbl 1147.65095 Widmer, G.; Hiptmair, R.; Schwab, Ch. 25 2008 Coupling of finite elements and boundary elements in electromagnetic scattering. Zbl 1049.78021 Hiptmair, R. 23 2003 Convergence analysis of finite element methods for \(H\) (curl; \(\Omega \))-elliptic interface problems. Zbl 1268.78020 Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 23 2012 Mixed finite element approximation of eddy current problems. Zbl 1114.78012 Alonso Rodríguez, Ana; Hiptmair, Ralf; Valli, Alberto 22 2004 Plane wave discontinuous Galerkin methods: exponential convergence of the \(hp\)-version. Zbl 1347.65176 Hiptmair, R.; Moiola, A.; Perugia, I. 21 2016 Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes. Zbl 1288.65166 Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 20 2014 Convergence analysis of finite element methods for \(H(\mathrm{div};\Omega )\)-elliptic interface problems. Zbl 1203.65227 Hiptmair, R.; Li, J.; Zou, J. 20 2010 A coercive combined field integral equation for electromagnetic scattering. Zbl 1082.78003 Buffa, A.; Hiptmair, R. 19 2004 Electromagnetic scattering at composite objects: a novel multi-trace boundary integral formulation. Zbl 1277.78032 Claeys, Xavier; Hiptmair, Ralf 18 2012 Overlapping and multilevel Schwarz methods for vector valued elliptic problems in three dimensions. Zbl 0961.65109 Hiptmair, Ralf; Toselli, Andrea 17 2000 Multitrace boundary integral equations. Zbl 1291.78040 Claeys, Xavier; Hiptmair, Ralf; Jerez-Hanckes, Carlos 17 2013 Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz \(hp\)-dGFEM. Zbl 1295.31004 Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria; Schwab, Christoph 17 2014 Dispersion analysis of plane wave discontinuous Galerkin methods. Zbl 1352.65503 Gittelson, Claude J.; Hiptmair, Ralf 17 2014 Stabilized FEM-BEM coupling for Helmholtz transmission problems. Zbl 1221.65308 Hiptmair, R.; Meury, P. 17 2006 Novel multitrace boundary integral equations for transmission boundary value problems. Zbl 1346.65066 Claeys, X.; Hiptmair, R.; Jerez-Hanckes, C.; Pintarelli, S. 16 2015 Whitney elements on pyramids. Zbl 0970.65120 Gradinaru, V.; Hiptmair, R. 15 1999 Analysis of tensor product multigrid. Zbl 0973.65118 Börm, S.; Hiptmair, R. 15 2001 Mesh-independent operator preconditioning for boundary elements on open curves. Zbl 1310.65155 Hiptmair, Ralf; Jerez-Hanckes, Carlos; Urzúa-Torres, Carolina 14 2014 Hierarchical error estimator for eddy current computation. Zbl 0970.78006 Beck, R.; Hiptmair, R.; Wohlmuth, B. 14 2000 A second-kind Galerkin boundary element method for scattering at composite objects. Zbl 1316.65105 Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 13 2015 Convergence analysis with parameter estimates for a reduced basis acoustic scattering T-matrix method. Zbl 1275.65074 Ganesh, M.; Hawkins, S. C.; Hiptmair, R. 13 2012 Convergence of the natural \(hp\)-BEM for the electric field integral equation on polyhedral surfaces. Zbl 1223.65083 Bespalov, A.; Heuer, N.; Hiptmair, R. 13 2010 Self-adjoint curl operators. Zbl 1275.47100 Hiptmair, Ralf; Kotiuga, Peter Robert; Tordeux, Sébastien 13 2012 Multilevel method for mixed eigenproblems. Zbl 1013.65120 Hiptmair, R.; Neymeyr, K. 12 2002 Auxiliary space preconditioning in \(H_0(\text{curl};\Omega)\). Zbl 1094.65118 Hiptmair, R.; Widmer, G.; Zou, J. 12 2006 Shape derivatives in differential forms. I: An intrinsic perspective. Zbl 1278.35056 Hiptmair, Ralf; Li, Jingzhi 12 2013 Local multigrid in \(\boldsymbol{H} (\mathbf{curl})\). Zbl 1212.65486 Hiptmair, Ralf; Zheng, Weiying 12 2009 Generators of \(H_1(\Gamma_{h},\mathbb{Z})\) for triangulated surfaces: Construction and classification. Zbl 1001.05046 Hiptmair, R.; Ostrowski, J. 11 2002 Shape optimization by pursuing diffeomorphisms. Zbl 1321.49076 Hiptmair, Ralf; Paganini, Alberto 11 2015 A hybrid formulation of eddy current problems. Zbl 1079.78023 Alonso Rodrigez, Ana; Hiptmair, Ralf; Valli, Alberto 11 2005 Universal extension for Sobolev spaces of differential forms and applications. Zbl 1302.46024 Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 11 2012 Discrete regular decompositions of tetrahedral discrete 1-forms. Zbl 1445.78011 Hiptmair, Ralf; Pechstein, Clemens 11 2019 Shape derivatives for scattering problems. Zbl 1421.35352 Hiptmair, Ralf; Li, Jingzhi 10 2018 Discrete compactness for the \(p\)-version of discrete differential forms. Zbl 1230.78025 Boffi, Daniele; Costabel, Martin; Dauge, Monique; Demkowicz, Leszek; Hiptmair, Ralf 10 2011 Analysis of multilevel methods for eddy current problems. Zbl 1018.78008 Hiptmair, R. 10 2003 Integral equations on multi-screens. Zbl 1292.45001 Claeys, X.; Hiptmair, R. 9 2013 Fast convolution quadrature based impedance boundary conditions. Zbl 1301.65106 Hiptmair, Ralf; López-Fernández, María; Paganini, Alberto 9 2014 Computation of resonant modes for axisymmetric Maxwell cavities using \(hp\)-version edge finite elements. Zbl 1121.78013 Hiptmair, R.; Ledger, P. D. 9 2005 Current and voltage excitations for the eddy current model. Zbl 1099.78021 Hiptmair, R.; Sterz, O. 9 2005 Vekua theory for the Helmholtz operator. Zbl 1266.35016 Moiola, A.; Hiptmair, R.; Perugia, I. 9 2011 Multilevel solution of the time-harmonic Maxwell’s equations based on edge elements. Zbl 0930.35167 Beck, Rudolf; Hiptmair, Ralf 8 1999 Multigrid computation of axisymmetric electromagnetic fields. Zbl 0998.65124 Börm, S.; Hiptmair, R. 8 2002 Uniform convergence of adaptive multigrid methods for elliptic problems and Maxwell’s equations. Zbl 1274.65287 Hiptmair, Ralf; Wu, Haijun; Zheng, Weiying 8 2012 Multilevel methods for mixed finite elements in three dimensions. Zbl 0929.65124 Hiptmair, Ralf; Hoppe, Ronald H. W. 7 1999 Closed-form inverses of the weakly singular and hypersingular operators on disks. Zbl 1390.45026 Hiptmair, R.; Jerez-Hanckes, C.; Urzúa-Torres, C. 7 2018 Stable multilevel splittings of boundary edge element spaces. Zbl 1266.78033 Hiptmair, Ralf; Mao, Shipeng 7 2012 Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Zbl 1211.65126 Heumann, Holger; Hiptmair, Ralf 7 2011 Non-reflecting boundary conditions for Maxwell’s equations. Zbl 1042.78010 Hiptmair, R.; Schädle, A. 7 2003 Domain decomposition for boundary integral equations via local multi-trace formulations. Zbl 1382.65429 Hiptmair, Ralf; Jerez-Hanckes, Carlos; Lee, Jin-Fa; Peng, Zhen 6 2014 Maxwell’s equations: continuous and discrete. Zbl 1331.78035 Hiptmair, Ralf 6 2015 Splitting-based structure preserving discretizations for magnetohydrodynamics. Zbl 1416.76343 Hiptmair, Ralf; Pagliantini, Cecilia 6 2018 Boundary element methods for eddy current computation. Zbl 1298.78032 Hiptmair, Ralf 6 2007 Extension by zero in discrete trace spaces: inverse estimates. Zbl 1321.65179 Hiptmair, Ralf; Jerez-Hanckes, Carlos; Mao, Shipeng 6 2015 First-kind boundary integral equations for the Hodge-Helmholtz operator. Zbl 1409.35062 Claeys, Xavier; Hiptmair, Ralf 6 2019 Asymptotic boundary element methods for thin conducting sheets. Zbl 1302.78027 Schmidt, Kersten; Hiptmair, Ralf 5 2015 Second kind boundary integral equation for multi-subdomain diffusion problems. Zbl 1381.65094 Claeys, X.; Hiptmair, R.; Spindler, Elke 5 2017 Mixed plane wave discontinuous Galerkin methods. Zbl 1180.65148 Hiptmair, Ralf; Perugia, Ilaria 5 2009 Stabilized FEM-BEM coupling for Maxwell transmission problems. Zbl 1144.78026 Hiptmair, R.; Meury, P. 5 2008 Convergence of lowest-order semi-Lagrangian schemes. Zbl 1273.65121 Heumann, Holger; Hiptmair, Ralf 5 2013 DG treatment of non-conforming interfaces in 3D curl-curl problems. Zbl 1383.78034 Casagrande, Raffael; Winkelmann, Christoph; Hiptmair, Ralf; Ostrowski, Joerg 4 2016 Domain decomposition preconditioning for surface integral equations in solving challenging electromagnetic scattering problems. Zbl 1374.78043 Peng, Zhen; Hiptmair, Ralf; Shao, Yang; MacKie-Mason, Brian 4 2016 Integral equations for electromagnetic scattering at multi-screens. Zbl 1337.78008 Claeys, X.; Hiptmair, R. 4 2016 Multilevel preconditioning for mixed problems in three dimensions. Zbl 0851.65089 Hiptmair, Ralf 4 1996 Real interpolation of spaces of differential forms. Zbl 1242.46026 Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 4 2012 A review of regular decompositions of vector fields: continuous, discrete, and structure-preserving. Zbl 1484.65257 Hiptmair, Ralf; Pechstein, Clemens 4 2020 Fully discrete semi-Lagrangian methods for advection of differential forms. Zbl 1267.65130 Heumann, Holger; Hiptmair, Ralf; Li, Kun; Xu, Jinchao 4 2012 Multilevel gauging for edge elements. Zbl 0955.65087 Hiptmair, R. 3 2000 Second-kind boundary integral equations for electromagnetic scattering at composite objects. Zbl 1397.65307 Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 3 2017 Integral equations for acoustic scattering by partially impenetrable composite objects. Zbl 1315.65101 Claeys, X.; Hiptmair, R. 3 2015 Multilevel preconditioned augmented Lagrangian techniques for \(2\)nd order mixed problems. Zbl 0904.65106 Hiptmair, R.; Schiekofer, T.; Wohlmuth, B. 3 1996 Coupled boundary-element scheme for eddy-current computation. Zbl 1066.78017 Hiptmair, Ralf; Ostrowski, Jörg 3 2005 Auxiliary space preconditioners for SIP-DG discretizations of \(\mathrm{H}(\mathbf{curl})\)-elliptic problems with discontinuous coefficients. Zbl 1433.65264 Ayuso de Dios, Blanca; Hiptmair, Ralf; Pagliantini, Cecilia 3 2017 Stabilized Galerkin for transient advection of differential forms. Zbl 1334.65148 Pagliantini, Cecilia; Hiptmair, Ralf; Heumann, Holger 3 2016 Coupling finite elements and auxiliary sources. Zbl 1442.65349 Casati, Daniele; Hiptmair, R. 3 2019 Numerical simulation of electrorheological fluids based on an extended Bingham model. Zbl 1094.76534 Engelmann, B.; Hiptmair, R.; Hoppe, R. H. W.; Mazurkevitch, G. 2 2000 Traces for Hilbert complexes. Zbl 1519.46021 Hiptmair, Ralf; Pauly, Dirk; Schulz, Erick 1 2023 Force computation for dielectrics using shape calculus. Zbl 1524.78081 Panchal, Piyush; Ren, Ning; Hiptmair, Ralf 1 2023 Electrostatic force computation with boundary element methods. Zbl 1490.65300 Panchal, Piyush; Hiptmair, Ralf 1 2022 Trefftz co-chain calculus. Zbl 1489.65156 Casati, Daniele; Codecasa, Lorenzo; Hiptmair, Ralf; Moro, Federico 1 2022 Spurious resonances in coupled domain-boundary variational formulations of transmission problems in electromagnetism and acoustics. Zbl 1507.78007 Schulz, Erick; Hiptmair, Ralf 1 2022 Spurious quasi-resonances in boundary integral equations for the Helmholtz transmission problem. Zbl 1497.35105 Hiptmair, Ralf; Moiola, Andrea; Spence, Euan A. 1 2022 Coupled domain-boundary variational formulations for Hodge-Helmholtz operators. Zbl 1491.35409 Schulz, Erick; Hiptmair, Ralf 1 2022 Frequency-stable full Maxwell in electro-quasistatic gauge. Zbl 1479.35853 Ostrowski, Jörg; Hiptmair, Ralf 2 2021 A stable boundary integral formulation of an acoustic wave transmission problem with mixed boundary conditions. Zbl 1467.65115 Eberle, S.; Florian, F.; Hiptmair, R.; Sauter, S. A. 1 2021 A review of regular decompositions of vector fields: continuous, discrete, and structure-preserving. Zbl 1484.65257 Hiptmair, Ralf; Pechstein, Clemens 4 2020 Compact equivalent inverse of the electric field integral operator on screens. Zbl 1446.45015 Hiptmair, R.; Urzúa-Torres, C. 2 2020 First-kind Galerkin boundary element methods for the Hodge-Laplacian in three dimensions. Zbl 1446.31002 Claeys, Xavier; Hiptmair, Ralf 2 2020 Preconditioning the EFIE on screens. Zbl 1451.78044 Hiptmair, Ralf; Urzúa-Torres, Carolina 1 2020 Coupling FEM with a multiple-subdomain Trefftz method. Zbl 1447.35130 Casati, Daniele; Hiptmair, Ralf 1 2020 Discrete regular decompositions of tetrahedral discrete 1-forms. Zbl 1445.78011 Hiptmair, Ralf; Pechstein, Clemens 11 2019 First-kind boundary integral equations for the Hodge-Helmholtz operator. Zbl 1409.35062 Claeys, Xavier; Hiptmair, Ralf 6 2019 Coupling finite elements and auxiliary sources. Zbl 1442.65349 Casati, Daniele; Hiptmair, R. 3 2019 Elastic energy regularization for inverse obstacle scattering problems. Zbl 1432.35249 Eckhardt, J.; Hiptmair, R.; Hohage, T.; Schumacher, H.; Wardetzky, M. 1 2019 A fully divergence-free finite element method for magnetohydrodynamic equations. Zbl 1393.65031 Hiptmair, Ralf; Li, Lingxiao; Mao, Shipeng; Zheng, Weiying 64 2018 Large deformation shape uncertainty quantification in acoustic scattering. Zbl 1402.35321 Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch. 29 2018 Shape derivatives for scattering problems. Zbl 1421.35352 Hiptmair, Ralf; Li, Jingzhi 10 2018 Closed-form inverses of the weakly singular and hypersingular operators on disks. Zbl 1390.45026 Hiptmair, R.; Jerez-Hanckes, C.; Urzúa-Torres, C. 7 2018 Splitting-based structure preserving discretizations for magnetohydrodynamics. Zbl 1416.76343 Hiptmair, Ralf; Pagliantini, Cecilia 6 2018 Second-kind boundary integral equations for scattering at composite partly impenetrable objects. Zbl 1488.65699 Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 1 2018 Second kind boundary integral equation for multi-subdomain diffusion problems. Zbl 1381.65094 Claeys, X.; Hiptmair, R.; Spindler, Elke 5 2017 Second-kind boundary integral equations for electromagnetic scattering at composite objects. Zbl 1397.65307 Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 3 2017 Auxiliary space preconditioners for SIP-DG discretizations of \(\mathrm{H}(\mathbf{curl})\)-elliptic problems with discontinuous coefficients. Zbl 1433.65264 Ayuso de Dios, Blanca; Hiptmair, Ralf; Pagliantini, Cecilia 3 2017 Asymptotic expansion techniques for singularly perturbed boundary integral equations. Zbl 1378.65181 Schmidt, Kersten; Hiptmair, Ralf 2 2017 A survey of Trefftz methods for the Helmholtz equation. Zbl 1357.65282 Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 54 2016 Plane wave discontinuous Galerkin methods: exponential convergence of the \(hp\)-version. Zbl 1347.65176 Hiptmair, R.; Moiola, A.; Perugia, I. 21 2016 DG treatment of non-conforming interfaces in 3D curl-curl problems. Zbl 1383.78034 Casagrande, Raffael; Winkelmann, Christoph; Hiptmair, Ralf; Ostrowski, Joerg 4 2016 Domain decomposition preconditioning for surface integral equations in solving challenging electromagnetic scattering problems. Zbl 1374.78043 Peng, Zhen; Hiptmair, Ralf; Shao, Yang; MacKie-Mason, Brian 4 2016 Integral equations for electromagnetic scattering at multi-screens. Zbl 1337.78008 Claeys, X.; Hiptmair, R. 4 2016 Stabilized Galerkin for transient advection of differential forms. Zbl 1334.65148 Pagliantini, Cecilia; Hiptmair, Ralf; Heumann, Holger 3 2016 Comparison of approximate shape gradients. Zbl 1320.65099 Hiptmair, R.; Paganini, A.; Sargheini, S. 62 2015 Novel multitrace boundary integral equations for transmission boundary value problems. Zbl 1346.65066 Claeys, X.; Hiptmair, R.; Jerez-Hanckes, C.; Pintarelli, S. 16 2015 A second-kind Galerkin boundary element method for scattering at composite objects. Zbl 1316.65105 Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 13 2015 Shape optimization by pursuing diffeomorphisms. Zbl 1321.49076 Hiptmair, Ralf; Paganini, Alberto 11 2015 Maxwell’s equations: continuous and discrete. Zbl 1331.78035 Hiptmair, Ralf 6 2015 Extension by zero in discrete trace spaces: inverse estimates. Zbl 1321.65179 Hiptmair, Ralf; Jerez-Hanckes, Carlos; Mao, Shipeng 6 2015 Asymptotic boundary element methods for thin conducting sheets. Zbl 1302.78027 Schmidt, Kersten; Hiptmair, Ralf 5 2015 Integral equations for acoustic scattering by partially impenetrable composite objects. Zbl 1315.65101 Claeys, X.; Hiptmair, R. 3 2015 Stabilized Galerkin for linear advection of vector fields. Zbl 1328.65240 Heumann, Holger; Hiptmair, Ralf 1 2015 Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes. Zbl 1288.65166 Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 20 2014 Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz \(hp\)-dGFEM. Zbl 1295.31004 Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria; Schwab, Christoph 17 2014 Dispersion analysis of plane wave discontinuous Galerkin methods. Zbl 1352.65503 Gittelson, Claude J.; Hiptmair, Ralf 17 2014 Mesh-independent operator preconditioning for boundary elements on open curves. Zbl 1310.65155 Hiptmair, Ralf; Jerez-Hanckes, Carlos; Urzúa-Torres, Carolina 14 2014 Fast convolution quadrature based impedance boundary conditions. Zbl 1301.65106 Hiptmair, Ralf; López-Fernández, María; Paganini, Alberto 9 2014 Domain decomposition for boundary integral equations via local multi-trace formulations. Zbl 1382.65429 Hiptmair, Ralf; Jerez-Hanckes, Carlos; Lee, Jin-Fa; Peng, Zhen 6 2014 Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations. Zbl 1269.78013 Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 43 2013 Multi-trace boundary integral formulation for acoustic scattering by composite structures. Zbl 1366.74030 Claeys, Xavier; Hiptmair, Ralf 25 2013 Multitrace boundary integral equations. Zbl 1291.78040 Claeys, Xavier; Hiptmair, Ralf; Jerez-Hanckes, Carlos 17 2013 Shape derivatives in differential forms. I: An intrinsic perspective. Zbl 1278.35056 Hiptmair, Ralf; Li, Jingzhi 12 2013 Integral equations on multi-screens. Zbl 1292.45001 Claeys, X.; Hiptmair, R. 9 2013 Convergence of lowest-order semi-Lagrangian schemes. Zbl 1273.65121 Heumann, Holger; Hiptmair, Ralf 5 2013 Stabilized Galerkin methods for magnetic advection. Zbl 1293.76088 Heumann, Holger; Hiptmair, Ralf 1 2013 Multiple traces boundary integral formulation for Helmholtz transmission problems. Zbl 1261.65123 Hiptmair, R.; Jerez-Hanckes, C. 34 2012 Convergence analysis of finite element methods for \(H\) (curl; \(\Omega \))-elliptic interface problems. Zbl 1268.78020 Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 23 2012 Electromagnetic scattering at composite objects: a novel multi-trace boundary integral formulation. Zbl 1277.78032 Claeys, Xavier; Hiptmair, Ralf 18 2012 Convergence analysis with parameter estimates for a reduced basis acoustic scattering T-matrix method. Zbl 1275.65074 Ganesh, M.; Hawkins, S. C.; Hiptmair, R. 13 2012 Self-adjoint curl operators. Zbl 1275.47100 Hiptmair, Ralf; Kotiuga, Peter Robert; Tordeux, Sébastien 13 2012 Universal extension for Sobolev spaces of differential forms and applications. Zbl 1302.46024 Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 11 2012 Uniform convergence of adaptive multigrid methods for elliptic problems and Maxwell’s equations. Zbl 1274.65287 Hiptmair, Ralf; Wu, Haijun; Zheng, Weiying 8 2012 Stable multilevel splittings of boundary edge element spaces. Zbl 1266.78033 Hiptmair, Ralf; Mao, Shipeng 7 2012 Real interpolation of spaces of differential forms. Zbl 1242.46026 Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 4 2012 Fully discrete semi-Lagrangian methods for advection of differential forms. Zbl 1267.65130 Heumann, Holger; Hiptmair, Ralf; Li, Kun; Xu, Jinchao 4 2012 Transient full Maxwell computation of slow processes. Zbl 1247.78041 Ostrowski, J.; Hiptmair, R.; Krämer, F.; Smajic, J.; Steinmetz, T. 1 2012 Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the \(p\)-version. Zbl 1229.65215 Hiptmair, R.; Moiola, A.; Perugia, I. 98 2011 Plane wave approximation of homogeneous Helmholtz solutions. Zbl 1263.35070 Moiola, A.; Hiptmair, R.; Perugia, I. 56 2011 Stability results for the time-harmonic Maxwell equations with impedance boundary conditions. Zbl 1331.35335 Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 26 2011 Discrete compactness for the \(p\)-version of discrete differential forms. Zbl 1230.78025 Boffi, Daniele; Costabel, Martin; Dauge, Monique; Demkowicz, Leszek; Hiptmair, Ralf 10 2011 Vekua theory for the Helmholtz operator. Zbl 1266.35016 Moiola, A.; Hiptmair, R.; Perugia, I. 9 2011 Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Zbl 1211.65126 Heumann, Holger; Hiptmair, Ralf 7 2011 Convergence analysis of finite element methods for \(H(\mathrm{div};\Omega )\)-elliptic interface problems. Zbl 1203.65227 Hiptmair, R.; Li, J.; Zou, J. 20 2010 Convergence of the natural \(hp\)-BEM for the electric field integral equation on polyhedral surfaces. Zbl 1223.65083 Bespalov, A.; Heuer, N.; Hiptmair, R. 13 2010 Plane wave discontinuous Galerkin methods: Analysis of the \(h\)-version. Zbl 1165.65076 Gittelson, Claude J.; Hiptmair, Ralf; Perugia, Ilaria 108 2009 Local multigrid in \(\boldsymbol{H} (\mathbf{curl})\). Zbl 1212.65486 Hiptmair, Ralf; Zheng, Weiying 12 2009 Mixed plane wave discontinuous Galerkin methods. Zbl 1180.65148 Hiptmair, Ralf; Perugia, Ilaria 5 2009 Sparse adaptive finite elements for radiative transfer. Zbl 1147.65095 Widmer, G.; Hiptmair, R.; Schwab, Ch. 25 2008 Stabilized FEM-BEM coupling for Maxwell transmission problems. Zbl 1144.78026 Hiptmair, R.; Meury, P. 5 2008 Nodal auxiliary space preconditioning in H(curl) and H(div) spaces. Zbl 1153.78006 Hiptmair, Ralf; Xu, Jinchao 137 2007 Boundary element methods for eddy current computation. Zbl 1298.78032 Hiptmair, Ralf 6 2007 Operator preconditioning. Zbl 1125.65037 Hiptmair, R. 61 2006 Stabilized FEM-BEM coupling for Helmholtz transmission problems. Zbl 1221.65308 Hiptmair, R.; Meury, P. 17 2006 Auxiliary space preconditioning in \(H_0(\text{curl};\Omega)\). Zbl 1094.65118 Hiptmair, R.; Widmer, G.; Zou, J. 12 2006 Conservative discretization of the Einstein-Dirac equations in spherically symmetric spacetime. Zbl 1191.83007 Zeller, Benedikt; Hiptmair, Ralf 1 2006 Regularized combined field integral equations. Zbl 1067.65137 Buffa, A.; Hiptmair, R. 25 2005 A hybrid formulation of eddy current problems. Zbl 1079.78023 Alonso Rodrigez, Ana; Hiptmair, Ralf; Valli, Alberto 11 2005 Computation of resonant modes for axisymmetric Maxwell cavities using \(hp\)-version edge finite elements. Zbl 1121.78013 Hiptmair, R.; Ledger, P. D. 9 2005 Current and voltage excitations for the eddy current model. Zbl 1099.78021 Hiptmair, R.; Sterz, O. 9 2005 Coupled boundary-element scheme for eddy-current computation. Zbl 1066.78017 Hiptmair, Ralf; Ostrowski, Jörg 3 2005 Mixed finite element approximation of eddy current problems. Zbl 1114.78012 Alonso Rodríguez, Ana; Hiptmair, Ralf; Valli, Alberto 22 2004 A coercive combined field integral equation for electromagnetic scattering. Zbl 1082.78003 Buffa, A.; Hiptmair, R. 19 2004 Boundary element methods for Maxwell transmission problems in Lipschitz domains. Zbl 1071.65160 Buffa, Annalisa; Hiptmair, Ralf; von Petersdorff, Tobias; Schwab, Christoph 58 2003 Galerkin boundary element methods for electromagnetic scattering. Zbl 1055.78013 Buffa, Annalisa; Hiptmair, Ralf 55 2003 Coupling of finite elements and boundary elements in electromagnetic scattering. Zbl 1049.78021 Hiptmair, R. 23 2003 Analysis of multilevel methods for eddy current problems. Zbl 1018.78008 Hiptmair, R. 10 2003 Non-reflecting boundary conditions for Maxwell’s equations. Zbl 1042.78010 Hiptmair, R.; Schädle, A. 7 2003 Coercive combined field integral equations. Zbl 1115.76356 Hiptmair, R. 1 2003 Finite elements in computational electromagnetism. Zbl 1123.78320 Hiptmair, R. 389 2002 ...and 21 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,325 Authors 53 Hiptmair, Ralf 23 Perugia, Ilaria 22 Li, Jichun 20 Moiola, Andrea 19 Claeys, Xavier 19 Jerez-Hanckes, Carlos 17 Hu, Qiya 17 Zhu, Shengfeng 16 Schwab, Christoph 16 Zou, Jun 15 Yuan, Long 15 Zheng, Weiying 14 Huang, Yunqing 14 Nicaise, Serge 13 Chen, Long 13 Xu, Jinchao 12 Mao, Shipeng 12 Monk, Peter B. 12 Spence, Euan A. 12 Yang, Wei 11 Melenk, Jens Markus 11 Shu, Shi 10 Alonso Rodríguez, Ana 10 Hu, Kaibo 10 Hu, Xiaozhe 10 Mascotto, Lorenzo 9 Betcke, Timo 9 Chaumont-Frelet, Théophile 9 Chung, Tsz Shun Eric 9 Demkowicz, Leszek F. 9 Gander, Martin Jakob 9 Harbrecht, Helmut 9 He, Yinnian 9 Hoppe, Ronald H. W. 9 Qiu, Weifeng 9 Zhang, Shuo 9 Zhong, Liuqiang 8 Ding, Qianqian 8 Gopalakrishnan, Jay 8 Rodríguez, Rodolfo 8 Wu, Haijun 8 Yousept, Irwin 7 Chen, Jinru 7 Führer, Thomas 7 Guo, Ruchi 7 Li, Lingxiao 7 Schöberl, Joachim 7 Xu, Liwei 7 Zech, Jakob 6 Cao, Shuhao 6 Creusé, Emmanuel 6 Dapogny, Charles 6 Egger, Herbert 6 Heuer, Norbert 6 Li, Jiajie 6 Long, Xiaonian 6 Mohamed, M. Shadi 6 Pauly, Dirk 6 Schöps, Sebastian 6 Stephan, Ernst Peter 6 Xu, Xuejun 5 Aylwin, Rubén 5 Bermúdez, Alfredo 5 Buffa, Annalisa 5 Burman, Erik 5 Chandler-Wilde, Simon N. 5 Chen, Junqing 5 Dolean, Victorita 5 Dong, Xiaojing 5 El Kacimi, Abdellah 5 He, Xiaoming 5 Imbert-Gérard, Lise-Marie 5 Kolev, Tzanio V. 5 Kraus, Johannes K. 5 Laghrouche, Omar 5 Laurain, Antoine 5 Lee, Jin-Fa 5 Li, Jingzhi 5 Li, Peijun 5 Lin, Yanping 5 Ma, Changfeng 5 Meddahi, Salim 5 Multerer, Michael D. 5 Peterseim, Daniel 5 Pichler, Alexander 5 Pinnau, René 5 Praetorius, Dirk 5 Qian, Jianliang 5 Sauter, Stefan 5 Sayas, Francisco-Javier 5 Schnepp, Sascha M. 5 Schulz, Erick 5 Specogna, Ruben 5 Steinbach, Olaf 5 Trevelyan, Jon 5 Urzúa-Torres, Carolina 5 Valli, Alberto 5 Vassilevski, Panayot Spirov 5 Vohralík, Martin 5 Xu, Yifeng ...and 1,225 more Authors all top 5 Cited in 130 Serials 84 Journal of Computational Physics 59 SIAM Journal on Scientific Computing 57 Computer Methods in Applied Mechanics and Engineering 55 Computers & Mathematics with Applications 53 Journal of Scientific Computing 50 Mathematics of Computation 45 Journal of Computational and Applied Mathematics 45 Numerische Mathematik 38 SIAM Journal on Numerical Analysis 27 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 21 Applied Numerical Mathematics 20 International Journal for Numerical Methods in Engineering 18 Advances in Computational Mathematics 15 M\(^3\)AS. 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Electronic Transactions on Numerical Analysis 3 Oberwolfach Reports 3 Inverse Problems and Imaging 3 SMAI Journal of Computational Mathematics 3 Communications on Applied Mathematics and Computation 2 Journal of Engineering Mathematics 2 Journal of Geometry and Physics 2 Journal of Functional Analysis 2 SIAM Journal on Control and Optimization 2 Journal of Integral Equations and Applications 2 Communications in Numerical Methods in Engineering 2 Journal of Mathematical Sciences (New York) 2 Journal of Inverse and Ill-Posed Problems 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Archives of Computational Methods in Engineering 2 Acta Numerica 2 Journal of Computational Acoustics 2 Mathematical Control and Related Fields 2 East Asian Journal on Applied Mathematics 2 Results in Applied Mathematics 1 International Journal of Engineering Science 1 Journal of Mathematical Physics 1 Journal of the Mechanics and Physics of Solids 1 Lithuanian Mathematical Journal 1 Nonlinearity 1 Transport Theory and Statistical Physics 1 ACM Transactions on Mathematical Software 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Applied Mathematics and Mechanics. (English Edition) 1 Constructive Approximation 1 Mathematical and Computer Modelling 1 Science in China. Series A 1 Neural Networks 1 SIAM Review 1 Archive of Applied Mechanics 1 Applied and Computational Harmonic Analysis 1 Electronic Journal of Differential Equations (EJDE) ...and 30 more Serials all top 5 Cited in 45 Fields 842 Numerical analysis (65-XX) 506 Partial differential equations (35-XX) 346 Optics, electromagnetic theory (78-XX) 184 Fluid mechanics (76-XX) 95 Mechanics of deformable solids (74-XX) 72 Calculus of variations and optimal control; optimization (49-XX) 31 Integral equations (45-XX) 29 Global analysis, analysis on manifolds (58-XX) 22 Approximations and expansions (41-XX) 20 Potential theory (31-XX) 19 Operator theory (47-XX) 19 Statistical mechanics, structure of matter (82-XX) 18 Probability theory and stochastic processes (60-XX) 13 Functional analysis (46-XX) 13 Classical thermodynamics, heat transfer (80-XX) 13 Geophysics (86-XX) 12 Computer science (68-XX) 11 Biology and other natural sciences (92-XX) 10 Operations research, mathematical programming (90-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 General and overarching topics; collections (00-XX) 6 Differential geometry (53-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Ordinary differential equations (34-XX) 5 Statistics (62-XX) 4 History and biography (01-XX) 4 Functions of a complex variable (30-XX) 4 Convex and discrete geometry (52-XX) 4 Quantum theory (81-XX) 4 Systems theory; control (93-XX) 4 Information and communication theory, circuits (94-XX) 3 Measure and integration (28-XX) 3 Algebraic topology (55-XX) 3 Astronomy and astrophysics (85-XX) 2 Special functions (33-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral transforms, operational calculus (44-XX) 2 Manifolds and cell complexes (57-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Abstract harmonic analysis (43-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year