Edit Profile (opens in new tab) Hiptmair, Ralf Compute Distance To: Compute Author ID: hiptmair.ralf Published as: Hiptmair, Ralf; Hiptmair, R. Documents Indexed: 140 Publications since 1994, including 1 Book 6 Contributions as Editor · 1 Further Contribution Co-Authors: 89 Co-Authors with 127 Joint Publications 1,996 Co-Co-Authors all top 5 Co-Authors 20 single-authored 14 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 Valli, Alberto 3 Zheng, Weiying 2 Alonso Rodríguez, Ana 2 Ayuso de Dios, Blanca 2 Beck, Rudolf 2 Börm, Steffen 2 Gittelson, Claude Jeffrey 2 Grohs, Philipp 2 Meury, Patrick 2 Panchal, Piyush 2 Pechstein, Clemens 2 Peng, Zhen 2 Pintarelli, Simon 2 Schmidt, Kersten 2 Widmer, Gerhard 2 Xu, Jinchao 1 Beck, Rudi 1 Bermúdez, Alfredo 1 Bespalov, Alexei 1 Boffi, Daniele 1 Casagrande, Raffael 1 Chaillat-Loseille, Stéphanie 1 Codecasa, Lorenzo 1 Costabel, Martin 1 Dauge, Monique 1 Demkowicz, Leszek F. 1 Deuflhard, Peter 1 Eberle-Blick, Sarah 1 Florian, Francesco 1 Fonn, Eivind 1 Fuhrmann, Henning 1 Ganesh, Mahadevan 1 Giacomel, Lorenzo 1 Haddar, Houssem 1 Hawkins, Stuart Collin 1 Heuer, Norbert 1 Hohage, Thorsten 1 Kotiuga, Peter Robert 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 Rodríguez, Rodolfo 1 Sargheini, S. 1 Sauter, Stefan A. 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 Tordeux, Sébastien 1 Toselli, Andrea 1 von Petersdorff, Tobias 1 Wardetzky, Max 1 Winkelmann, Christoph 1 Wu, Haijun 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 Oberwolfach Reports 4 IMA Journal of Numerical Analysis 4 Mathematics of Computation 4 Computing 4 Advances in Computational Mathematics 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Computers & Mathematics with Applications 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 SMAI Journal of Computational Mathematics 2 Inverse Problems 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Journal of Functional Analysis 2 Numerical Algorithms 2 SIAM Journal on Scientific Computing 2 ETNA. Electronic Transactions on Numerical Analysis 2 Foundations of Computational Mathematics 2 Computational Methods in Applied Mathematics 2 Journal of Numerical Mathematics 2 Discrete and Continuous Dynamical Systems. Series S 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 Journal of Scientific Computing 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 Computing and Visualization in Science 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 121 Numerical analysis (65-XX) 84 Partial differential equations (35-XX) 71 Optics, electromagnetic theory (78-XX) 22 Fluid mechanics (76-XX) 12 Integral equations (45-XX) 8 General and overarching topics; collections (00-XX) 7 Potential theory (31-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Mechanics of deformable solids (74-XX) 3 Functional analysis (46-XX) 2 Approximations and expansions (41-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 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-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 118 Publications have been cited 2,245 times in 1,304 Documents Cited by ▼ Year ▼ Finite elements in computational electromagnetism. Zbl 1123.78320Hiptmair, R. 347 2002 Nodal auxiliary space preconditioning in H(curl) and H(div) spaces. Zbl 1153.78006Hiptmair, Ralf; Xu, Jinchao 115 2007 Plane wave discontinuous Galerkin methods: Analysis of the \(h\)-version. Zbl 1165.65076Gittelson, Claude J.; Hiptmair, Ralf; Perugia, Ilaria 104 2009 Multigrid method for Maxwell’s equations. Zbl 0922.65081Hiptmair, R. 101 1998 Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the \(p\)-version. Zbl 1229.65215Hiptmair, R.; Moiola, A.; Perugia, I. 87 2011 Residual based a posteriori error estimators for eddy current computation. Zbl 0949.65113Beck, Rudi; Hiptmair, Ralf; Hoppe, Ronald H. W.; Wohlmuth, Barbara 86 2000 Canonical construction of finite elements. Zbl 0938.65132Hiptmair, R. 68 1999 Galerkin boundary element methods for electromagnetic scattering. Zbl 1055.78013Buffa, Annalisa; Hiptmair, Ralf 51 2003 Plane wave approximation of homogeneous Helmholtz solutions. Zbl 1263.35070Moiola, A.; Hiptmair, R.; Perugia, I. 51 2011 Boundary element methods for Maxwell transmission problems in Lipschitz domains. Zbl 1071.65160Buffa, Annalisa; Hiptmair, Ralf; von Petersdorff, Tobias; Schwab, Christoph 51 2003 Operator preconditioning. Zbl 1125.65037Hiptmair, R. 51 2006 Comparison of approximate shape gradients. Zbl 1320.65099Hiptmair, R.; Paganini, A.; Sargheini, S. 48 2015 A fully divergence-free finite element method for magnetohydrodynamic equations. Zbl 1393.65031Hiptmair, Ralf; Li, Lingxiao; Mao, Shipeng; Zheng, Weiying 44 2018 A survey of Trefftz methods for the Helmholtz equation. Zbl 1357.65282Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 38 2016 Discrete Hodge operators. Zbl 0993.65130Hiptmair, R. 36 2001 Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations. Zbl 1269.78013Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 35 2013 Symmetric coupling for eddy current problems. Zbl 1010.78011Hiptmair, R. 35 2002 Multiple traces boundary integral formulation for Helmholtz transmission problems. Zbl 1261.65123Hiptmair, R.; Jerez-Hanckes, C. 31 2012 Natural boundary element methods for the electric field integral equation on polyhedra. Zbl 1010.78014Hiptmair, Ralf; Schwab, Christoph 27 2002 Adaptive multilevel methods for edge element discretizations of Maxwell’s equations. Zbl 0939.65136Beck, Rudolf; Deuflhard, Peter; Hiptmair, Ralf; Hoppe, Ronald H. W.; Wohlmuth, Barbara 25 1999 Regularized combined field integral equations. Zbl 1067.65137Buffa, A.; Hiptmair, R. 25 2005 Multi-trace boundary integral formulation for acoustic scattering by composite structures. Zbl 1366.74030Claeys, Xavier; Hiptmair, Ralf 24 2013 Large deformation shape uncertainty quantification in acoustic scattering. Zbl 1402.35321Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch. 23 2018 Stability results for the time-harmonic Maxwell equations with impedance boundary conditions. Zbl 1331.35335Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 22 2011 Coupling of finite elements and boundary elements in electromagnetic scattering. Zbl 1049.78021Hiptmair, R. 22 2003 Multigrid method for \(H\text{(div)}\) in three dimensions. Zbl 0897.65046Hiptmair, R. 22 1997 Sparse adaptive finite elements for radiative transfer. Zbl 1147.65095Widmer, G.; Hiptmair, R.; Schwab, Ch. 21 2008 Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes. Zbl 1288.65166Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 21 2014 Mixed finite element approximation of eddy current problems. Zbl 1114.78012Alonso Rodríguez, Ana; Hiptmair, Ralf; Valli, Alberto 20 2004 Convergence analysis of finite element methods for \(H\) (curl; \(\Omega \))-elliptic interface problems. Zbl 1268.78020Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 19 2012 Plane wave discontinuous Galerkin methods: exponential convergence of the \(hp\)-version. Zbl 1347.65176Hiptmair, R.; Moiola, A.; Perugia, I. 19 2016 A coercive combined field integral equation for electromagnetic scattering. Zbl 1082.78003Buffa, A.; Hiptmair, R. 18 2004 Stabilized FEM-BEM coupling for Helmholtz transmission problems. Zbl 1221.65308Hiptmair, R.; Meury, P. 16 2006 Electromagnetic scattering at composite objects: a novel multi-trace boundary integral formulation. Zbl 1277.78032Claeys, Xavier; Hiptmair, Ralf 16 2012 Overlapping and multilevel Schwarz methods for vector valued elliptic problems in three dimensions. Zbl 0961.65109Hiptmair, Ralf; Toselli, Andrea 15 2000 Analysis of tensor product multigrid. Zbl 0973.65118Börm, S.; Hiptmair, R. 15 2001 Dispersion analysis of plane wave discontinuous Galerkin methods. Zbl 1352.65503Gittelson, Claude J.; Hiptmair, Ralf 15 2014 Multitrace boundary integral equations. Zbl 1291.78040Claeys, Xavier; Hiptmair, Ralf; Jerez-Hanckes, Carlos 15 2013 Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz \(hp\)-dGFEM. Zbl 1295.31004Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria; Schwab, Christoph 15 2014 Whitney elements on pyramids. Zbl 0970.65120Gradinaru, V.; Hiptmair, R. 14 1999 Novel multitrace boundary integral equations for transmission boundary value problems. Zbl 1346.65066Claeys, X.; Hiptmair, R.; Jerez-Hanckes, C.; Pintarelli, S. 14 2015 Convergence analysis of finite element methods for \(H(\mathrm{div};\Omega )\)-elliptic interface problems. Zbl 1203.65227Hiptmair, R.; Li, J.; Zou, J. 14 2010 Hierarchical error estimator for eddy current computation. Zbl 0970.78006Beck, R.; Hiptmair, R.; Wohlmuth, B. 13 2000 Convergence analysis with parameter estimates for a reduced basis acoustic scattering T-matrix method. Zbl 1275.65074Ganesh, M.; Hawkins, S. C.; Hiptmair, R. 13 2012 Convergence of the natural \(hp\)-BEM for the electric field integral equation on polyhedral surfaces. Zbl 1223.65083Bespalov, A.; Heuer, N.; Hiptmair, R. 12 2010 Local multigrid in \(\boldsymbol{H} (\mathbf{curl})\). Zbl 1212.65486Hiptmair, Ralf; Zheng, Weiying 12 2009 A hybrid formulation of eddy current problems. Zbl 1079.78023Alonso Rodrigez, Ana; Hiptmair, Ralf; Valli, Alberto 11 2005 A second-kind Galerkin boundary element method for scattering at composite objects. Zbl 1316.65105Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 11 2015 Shape derivatives in differential forms. I: An intrinsic perspective. Zbl 1278.35056Hiptmair, Ralf; Li, Jingzhi 11 2013 Multilevel method for mixed eigenproblems. Zbl 1013.65120Hiptmair, R.; Neymeyr, K. 10 2002 Auxiliary space preconditioning in \(H_0(\text{curl};\Omega)\). Zbl 1094.65118Hiptmair, R.; Widmer, G.; Zou, J. 10 2006 Self-adjoint curl operators. Zbl 1275.47100Hiptmair, Ralf; Kotiuga, Peter Robert; Tordeux, Sébastien 10 2012 Analysis of multilevel methods for eddy current problems. Zbl 1018.78008Hiptmair, R. 10 2003 Mesh-independent operator preconditioning for boundary elements on open curves. Zbl 1310.65155Hiptmair, Ralf; Jerez-Hanckes, Carlos; Urzúa-Torres, Carolina 10 2014 Shape derivatives for scattering problems. Zbl 1421.35352Hiptmair, Ralf; Li, Jingzhi 9 2018 Computation of resonant modes for axisymmetric Maxwell cavities using \(hp\)-version edge finite elements. Zbl 1121.78013Hiptmair, R.; Ledger, P. D. 9 2005 Vekua theory for the Helmholtz operator. Zbl 1266.35016Moiola, A.; Hiptmair, R.; Perugia, I. 9 2011 Generators of \(H_1(\Gamma_{h},\mathbb{Z})\) for triangulated surfaces: Construction and classification. Zbl 1001.05046Hiptmair, R.; Ostrowski, J. 9 2002 Shape optimization by pursuing diffeomorphisms. Zbl 1321.49076Hiptmair, Ralf; Paganini, Alberto 9 2015 Fast convolution quadrature based impedance boundary conditions. Zbl 1301.65106Hiptmair, Ralf; López-Fernández, María; Paganini, Alberto 9 2014 Current and voltage excitations for the eddy current model. Zbl 1099.78021Hiptmair, R.; Sterz, O. 9 2005 Integral equations on multi-screens. Zbl 1292.45001Claeys, X.; Hiptmair, R. 9 2013 Discrete regular decompositions of tetrahedral discrete 1-forms. Zbl 1445.78011Hiptmair, Ralf; Pechstein, Clemens 8 2019 Uniform convergence of adaptive multigrid methods for elliptic problems and Maxwell’s equations. Zbl 1274.65287Hiptmair, Ralf; Wu, Haijun; Zheng, Weiying 8 2012 Multigrid computation of axisymmetric electromagnetic fields. Zbl 0998.65124Börm, S.; Hiptmair, R. 8 2002 Multilevel solution of the time-harmonic Maxwell’s equations based on edge elements. Zbl 0930.35167Beck, Rudolf; Hiptmair, Ralf 8 1999 Universal extension for Sobolev spaces of differential forms and applications. Zbl 1302.46024Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 8 2012 Discrete compactness for the \(p\)-version of discrete differential forms. Zbl 1230.78025Boffi, Daniele; Costabel, Martin; Dauge, Monique; Demkowicz, Leszek; Hiptmair, Ralf 8 2011 Multilevel methods for mixed finite elements in three dimensions. Zbl 0929.65124Hiptmair, Ralf; Hoppe, Ronald H. W. 7 1999 Closed-form inverses of the weakly singular and hypersingular operators on disks. Zbl 1390.45026Hiptmair, R.; Jerez-Hanckes, C.; Urzúa-Torres, C. 7 2018 Hyperbolic cross approximation for the spatially homogeneous Boltzmann equation. Zbl 1330.76101Fonn, E.; Grohs, P.; Hiptmair, R. 7 2015 Stable multilevel splittings of boundary edge element spaces. Zbl 1266.78033Hiptmair, Ralf; Mao, Shipeng 7 2012 Extension by zero in discrete trace spaces: inverse estimates. Zbl 1321.65179Hiptmair, Ralf; Jerez-Hanckes, Carlos; Mao, Shipeng 6 2015 Asymptotic boundary element methods for thin conducting sheets. Zbl 1302.78027Schmidt, Kersten; Hiptmair, Ralf 6 2015 Second kind boundary integral equation for multi-subdomain diffusion problems. Zbl 1381.65094Claeys, X.; Hiptmair, R.; Spindler, Elke 5 2017 Non-reflecting boundary conditions for Maxwell’s equations. Zbl 1042.78010Hiptmair, R.; Schädle, A. 5 2003 Stabilized FEM-BEM coupling for Maxwell transmission problems. Zbl 1144.78026Hiptmair, R.; Meury, P. 5 2008 Domain decomposition for boundary integral equations via local multi-trace formulations. Zbl 1382.65429Hiptmair, Ralf; Jerez-Hanckes, Carlos; Lee, Jin-Fa; Peng, Zhen 5 2014 Maxwell’s equations: continuous and discrete. Zbl 1331.78035Hiptmair, Ralf 5 2015 Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Zbl 1211.65126Heumann, Holger; Hiptmair, Ralf 5 2011 Boundary element methods for eddy current computation. Zbl 1298.78032Hiptmair, Ralf 5 2007 Mixed plane wave discontinuous Galerkin methods. Zbl 1180.65148Hiptmair, Ralf; Perugia, Ilaria 5 2009 Tensor-product discretization for the spatially inhomogeneous and transient Boltzmann equation in two dimensions. Zbl 1416.82038Grohs, Philipp; Hiptmair, Ralf; Pintarelli, Simon 5 2017 First-kind boundary integral equations for the Hodge-Helmholtz operator. Zbl 1409.35062Claeys, Xavier; Hiptmair, Ralf 4 2019 Domain decomposition preconditioning for surface integral equations in solving challenging electromagnetic scattering problems. Zbl 1374.78043Peng, Zhen; Hiptmair, Ralf; Shao, Yang; MacKie-Mason, Brian 4 2016 Convergence of lowest-order semi-Lagrangian schemes. Zbl 1273.65121Heumann, Holger; Hiptmair, Ralf 4 2013 Integral equations for electromagnetic scattering at multi-screens. Zbl 1337.78008Claeys, X.; Hiptmair, R. 4 2016 Multilevel preconditioned augmented Lagrangian techniques for \(2\)nd order mixed problems. Zbl 0904.65106Hiptmair, R.; Schiekofer, T.; Wohlmuth, B. 3 1996 Multilevel preconditioning for mixed problems in three dimensions. Zbl 0851.65089Hiptmair, Ralf 3 1996 Real interpolation of spaces of differential forms. Zbl 1242.46026Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 3 2012 Multilevel gauging for edge elements. Zbl 0955.65087Hiptmair, R. 3 2000 Fully discrete semi-Lagrangian methods for advection of differential forms. Zbl 1267.65130Heumann, Holger; Hiptmair, Ralf; Li, Kun; Xu, Jinchao 3 2012 Integral equations for acoustic scattering by partially impenetrable composite objects. Zbl 1315.65101Claeys, X.; Hiptmair, R. 3 2015 Coupled boundary-element scheme for eddy-current computation. Zbl 1066.78017Hiptmair, Ralf; Ostrowski, Jörg 3 2005 Splitting-based structure preserving discretizations for magnetohydrodynamics. Zbl 1416.76343Hiptmair, Ralf; Pagliantini, Cecilia 3 2018 Second-kind boundary integral equations for electromagnetic scattering at composite objects. Zbl 1397.65307Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 3 2017 Compact equivalent inverse of the electric field integral operator on screens. Zbl 1446.45015Hiptmair, R.; Urzúa-Torres, C. 2 2020 First-kind Galerkin boundary element methods for the Hodge-Laplacian in three dimensions. Zbl 1446.31002Claeys, Xavier; Hiptmair, Ralf 2 2020 DG treatment of non-conforming interfaces in 3D curl-curl problems. Zbl 1383.78034Casagrande, Raffael; Winkelmann, Christoph; Hiptmair, Ralf; Ostrowski, Joerg 2 2016 Stabilized Galerkin for transient advection of differential forms. Zbl 1334.65148Pagliantini, Cecilia; Hiptmair, Ralf; Heumann, Holger 2 2016 Coupled domain-boundary variational formulations for Hodge-Helmholtz operators. Zbl 1491.35409Schulz, Erick; Hiptmair, Ralf 1 2022 Spurious resonances in coupled domain-boundary variational formulations of transmission problems in electromagnetism and acoustics. Zbl 1507.78007Schulz, Erick; Hiptmair, Ralf 1 2022 A stable boundary integral formulation of an acoustic wave transmission problem with mixed boundary conditions. Zbl 1467.65115Eberle, S.; Florian, F.; Hiptmair, R.; Sauter, S. A. 1 2021 Frequency-stable full Maxwell in electro-quasistatic gauge. Zbl 1479.35853Ostrowski, Jörg; Hiptmair, Ralf 1 2021 Compact equivalent inverse of the electric field integral operator on screens. Zbl 1446.45015Hiptmair, R.; Urzúa-Torres, C. 2 2020 First-kind Galerkin boundary element methods for the Hodge-Laplacian in three dimensions. Zbl 1446.31002Claeys, Xavier; Hiptmair, Ralf 2 2020 A review of regular decompositions of vector fields: continuous, discrete, and structure-preserving. Zbl 1484.65257Hiptmair, Ralf; Pechstein, Clemens 2 2020 Preconditioning the EFIE on screens. Zbl 1451.78044Hiptmair, Ralf; Urzúa-Torres, Carolina 1 2020 Coupling FEM with a multiple-subdomain Trefftz method. Zbl 1447.35130Casati, Daniele; Hiptmair, Ralf 1 2020 Discrete regular decompositions of tetrahedral discrete 1-forms. Zbl 1445.78011Hiptmair, Ralf; Pechstein, Clemens 8 2019 First-kind boundary integral equations for the Hodge-Helmholtz operator. Zbl 1409.35062Claeys, Xavier; Hiptmair, Ralf 4 2019 Elastic energy regularization for inverse obstacle scattering problems. Zbl 1432.35249Eckhardt, J.; Hiptmair, R.; Hohage, T.; Schumacher, H.; Wardetzky, M. 1 2019 Coupling finite elements and auxiliary sources. Zbl 1442.65349Casati, Daniele; Hiptmair, R. 1 2019 A fully divergence-free finite element method for magnetohydrodynamic equations. Zbl 1393.65031Hiptmair, Ralf; Li, Lingxiao; Mao, Shipeng; Zheng, Weiying 44 2018 Large deformation shape uncertainty quantification in acoustic scattering. Zbl 1402.35321Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch. 23 2018 Shape derivatives for scattering problems. Zbl 1421.35352Hiptmair, Ralf; Li, Jingzhi 9 2018 Closed-form inverses of the weakly singular and hypersingular operators on disks. Zbl 1390.45026Hiptmair, R.; Jerez-Hanckes, C.; Urzúa-Torres, C. 7 2018 Splitting-based structure preserving discretizations for magnetohydrodynamics. Zbl 1416.76343Hiptmair, Ralf; Pagliantini, Cecilia 3 2018 Second-kind boundary integral equations for scattering at composite partly impenetrable objects. Zbl 1488.65699Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 1 2018 Second kind boundary integral equation for multi-subdomain diffusion problems. Zbl 1381.65094Claeys, X.; Hiptmair, R.; Spindler, Elke 5 2017 Tensor-product discretization for the spatially inhomogeneous and transient Boltzmann equation in two dimensions. Zbl 1416.82038Grohs, Philipp; Hiptmair, Ralf; Pintarelli, Simon 5 2017 Second-kind boundary integral equations for electromagnetic scattering at composite objects. Zbl 1397.65307Claeys, 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 1433.65264Ayuso de Dios, Blanca; Hiptmair, Ralf; Pagliantini, Cecilia 2 2017 Asymptotic expansion techniques for singularly perturbed boundary integral equations. Zbl 1378.65181Schmidt, Kersten; Hiptmair, Ralf 1 2017 A survey of Trefftz methods for the Helmholtz equation. Zbl 1357.65282Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 38 2016 Plane wave discontinuous Galerkin methods: exponential convergence of the \(hp\)-version. Zbl 1347.65176Hiptmair, R.; Moiola, A.; Perugia, I. 19 2016 Domain decomposition preconditioning for surface integral equations in solving challenging electromagnetic scattering problems. Zbl 1374.78043Peng, Zhen; Hiptmair, Ralf; Shao, Yang; MacKie-Mason, Brian 4 2016 Integral equations for electromagnetic scattering at multi-screens. Zbl 1337.78008Claeys, X.; Hiptmair, R. 4 2016 DG treatment of non-conforming interfaces in 3D curl-curl problems. Zbl 1383.78034Casagrande, Raffael; Winkelmann, Christoph; Hiptmair, Ralf; Ostrowski, Joerg 2 2016 Stabilized Galerkin for transient advection of differential forms. Zbl 1334.65148Pagliantini, Cecilia; Hiptmair, Ralf; Heumann, Holger 2 2016 Comparison of approximate shape gradients. Zbl 1320.65099Hiptmair, R.; Paganini, A.; Sargheini, S. 48 2015 Novel multitrace boundary integral equations for transmission boundary value problems. Zbl 1346.65066Claeys, X.; Hiptmair, R.; Jerez-Hanckes, C.; Pintarelli, S. 14 2015 A second-kind Galerkin boundary element method for scattering at composite objects. Zbl 1316.65105Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 11 2015 Shape optimization by pursuing diffeomorphisms. Zbl 1321.49076Hiptmair, Ralf; Paganini, Alberto 9 2015 Hyperbolic cross approximation for the spatially homogeneous Boltzmann equation. Zbl 1330.76101Fonn, E.; Grohs, P.; Hiptmair, R. 7 2015 Extension by zero in discrete trace spaces: inverse estimates. Zbl 1321.65179Hiptmair, Ralf; Jerez-Hanckes, Carlos; Mao, Shipeng 6 2015 Asymptotic boundary element methods for thin conducting sheets. Zbl 1302.78027Schmidt, Kersten; Hiptmair, Ralf 6 2015 Maxwell’s equations: continuous and discrete. Zbl 1331.78035Hiptmair, Ralf 5 2015 Integral equations for acoustic scattering by partially impenetrable composite objects. Zbl 1315.65101Claeys, X.; Hiptmair, R. 3 2015 Stabilized Galerkin for linear advection of vector fields. Zbl 1328.65240Heumann, Holger; Hiptmair, Ralf 1 2015 Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes. Zbl 1288.65166Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 21 2014 Dispersion analysis of plane wave discontinuous Galerkin methods. Zbl 1352.65503Gittelson, Claude J.; Hiptmair, Ralf 15 2014 Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz \(hp\)-dGFEM. Zbl 1295.31004Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria; Schwab, Christoph 15 2014 Mesh-independent operator preconditioning for boundary elements on open curves. Zbl 1310.65155Hiptmair, Ralf; Jerez-Hanckes, Carlos; Urzúa-Torres, Carolina 10 2014 Fast convolution quadrature based impedance boundary conditions. Zbl 1301.65106Hiptmair, Ralf; López-Fernández, María; Paganini, Alberto 9 2014 Domain decomposition for boundary integral equations via local multi-trace formulations. Zbl 1382.65429Hiptmair, Ralf; Jerez-Hanckes, Carlos; Lee, Jin-Fa; Peng, Zhen 5 2014 Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations. Zbl 1269.78013Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 35 2013 Multi-trace boundary integral formulation for acoustic scattering by composite structures. Zbl 1366.74030Claeys, Xavier; Hiptmair, Ralf 24 2013 Multitrace boundary integral equations. Zbl 1291.78040Claeys, Xavier; Hiptmair, Ralf; Jerez-Hanckes, Carlos 15 2013 Shape derivatives in differential forms. I: An intrinsic perspective. Zbl 1278.35056Hiptmair, Ralf; Li, Jingzhi 11 2013 Integral equations on multi-screens. Zbl 1292.45001Claeys, X.; Hiptmair, R. 9 2013 Convergence of lowest-order semi-Lagrangian schemes. Zbl 1273.65121Heumann, Holger; Hiptmair, Ralf 4 2013 Stabilized Galerkin methods for magnetic advection. Zbl 1293.76088Heumann, Holger; Hiptmair, Ralf 1 2013 Multiple traces boundary integral formulation for Helmholtz transmission problems. Zbl 1261.65123Hiptmair, R.; Jerez-Hanckes, C. 31 2012 Convergence analysis of finite element methods for \(H\) (curl; \(\Omega \))-elliptic interface problems. Zbl 1268.78020Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 19 2012 Electromagnetic scattering at composite objects: a novel multi-trace boundary integral formulation. Zbl 1277.78032Claeys, Xavier; Hiptmair, Ralf 16 2012 Convergence analysis with parameter estimates for a reduced basis acoustic scattering T-matrix method. Zbl 1275.65074Ganesh, M.; Hawkins, S. C.; Hiptmair, R. 13 2012 Self-adjoint curl operators. Zbl 1275.47100Hiptmair, Ralf; Kotiuga, Peter Robert; Tordeux, Sébastien 10 2012 Uniform convergence of adaptive multigrid methods for elliptic problems and Maxwell’s equations. Zbl 1274.65287Hiptmair, Ralf; Wu, Haijun; Zheng, Weiying 8 2012 Universal extension for Sobolev spaces of differential forms and applications. Zbl 1302.46024Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 8 2012 Stable multilevel splittings of boundary edge element spaces. Zbl 1266.78033Hiptmair, Ralf; Mao, Shipeng 7 2012 Real interpolation of spaces of differential forms. Zbl 1242.46026Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 3 2012 Fully discrete semi-Lagrangian methods for advection of differential forms. Zbl 1267.65130Heumann, Holger; Hiptmair, Ralf; Li, Kun; Xu, Jinchao 3 2012 Transient full Maxwell computation of slow processes. Zbl 1247.78041Ostrowski, 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 1229.65215Hiptmair, R.; Moiola, A.; Perugia, I. 87 2011 Plane wave approximation of homogeneous Helmholtz solutions. Zbl 1263.35070Moiola, A.; Hiptmair, R.; Perugia, I. 51 2011 Stability results for the time-harmonic Maxwell equations with impedance boundary conditions. Zbl 1331.35335Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 22 2011 Vekua theory for the Helmholtz operator. Zbl 1266.35016Moiola, A.; Hiptmair, R.; Perugia, I. 9 2011 Discrete compactness for the \(p\)-version of discrete differential forms. Zbl 1230.78025Boffi, Daniele; Costabel, Martin; Dauge, Monique; Demkowicz, Leszek; Hiptmair, Ralf 8 2011 Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Zbl 1211.65126Heumann, Holger; Hiptmair, Ralf 5 2011 Convergence analysis of finite element methods for \(H(\mathrm{div};\Omega )\)-elliptic interface problems. Zbl 1203.65227Hiptmair, R.; Li, J.; Zou, J. 14 2010 Convergence of the natural \(hp\)-BEM for the electric field integral equation on polyhedral surfaces. Zbl 1223.65083Bespalov, A.; Heuer, N.; Hiptmair, R. 12 2010 Plane wave discontinuous Galerkin methods: Analysis of the \(h\)-version. Zbl 1165.65076Gittelson, Claude J.; Hiptmair, Ralf; Perugia, Ilaria 104 2009 Local multigrid in \(\boldsymbol{H} (\mathbf{curl})\). Zbl 1212.65486Hiptmair, Ralf; Zheng, Weiying 12 2009 Mixed plane wave discontinuous Galerkin methods. Zbl 1180.65148Hiptmair, Ralf; Perugia, Ilaria 5 2009 Sparse adaptive finite elements for radiative transfer. Zbl 1147.65095Widmer, G.; Hiptmair, R.; Schwab, Ch. 21 2008 Stabilized FEM-BEM coupling for Maxwell transmission problems. Zbl 1144.78026Hiptmair, R.; Meury, P. 5 2008 Nodal auxiliary space preconditioning in H(curl) and H(div) spaces. Zbl 1153.78006Hiptmair, Ralf; Xu, Jinchao 115 2007 Boundary element methods for eddy current computation. Zbl 1298.78032Hiptmair, Ralf 5 2007 Operator preconditioning. Zbl 1125.65037Hiptmair, R. 51 2006 Stabilized FEM-BEM coupling for Helmholtz transmission problems. Zbl 1221.65308Hiptmair, R.; Meury, P. 16 2006 Auxiliary space preconditioning in \(H_0(\text{curl};\Omega)\). Zbl 1094.65118Hiptmair, R.; Widmer, G.; Zou, J. 10 2006 Conservative discretization of the Einstein-Dirac equations in spherically symmetric spacetime. Zbl 1191.83007Zeller, Benedikt; Hiptmair, Ralf 1 2006 Regularized combined field integral equations. Zbl 1067.65137Buffa, A.; Hiptmair, R. 25 2005 A hybrid formulation of eddy current problems. Zbl 1079.78023Alonso Rodrigez, Ana; Hiptmair, Ralf; Valli, Alberto 11 2005 Computation of resonant modes for axisymmetric Maxwell cavities using \(hp\)-version edge finite elements. Zbl 1121.78013Hiptmair, R.; Ledger, P. D. 9 2005 Current and voltage excitations for the eddy current model. Zbl 1099.78021Hiptmair, R.; Sterz, O. 9 2005 Coupled boundary-element scheme for eddy-current computation. Zbl 1066.78017Hiptmair, Ralf; Ostrowski, Jörg 3 2005 Mixed finite element approximation of eddy current problems. Zbl 1114.78012Alonso Rodríguez, Ana; Hiptmair, Ralf; Valli, Alberto 20 2004 A coercive combined field integral equation for electromagnetic scattering. Zbl 1082.78003Buffa, A.; Hiptmair, R. 18 2004 Galerkin boundary element methods for electromagnetic scattering. Zbl 1055.78013Buffa, Annalisa; Hiptmair, Ralf 51 2003 Boundary element methods for Maxwell transmission problems in Lipschitz domains. Zbl 1071.65160Buffa, Annalisa; Hiptmair, Ralf; von Petersdorff, Tobias; Schwab, Christoph 51 2003 Coupling of finite elements and boundary elements in electromagnetic scattering. Zbl 1049.78021Hiptmair, R. 22 2003 Analysis of multilevel methods for eddy current problems. Zbl 1018.78008Hiptmair, R. 10 2003 Non-reflecting boundary conditions for Maxwell’s equations. Zbl 1042.78010Hiptmair, R.; Schädle, A. 5 2003 Coercive combined field integral equations. Zbl 1115.76356Hiptmair, R. 1 2003 Finite elements in computational electromagnetism. Zbl 1123.78320Hiptmair, R. 347 2002 Symmetric coupling for eddy current problems. Zbl 1010.78011Hiptmair, R. 35 2002 Natural boundary element methods for the electric field integral equation on polyhedra. Zbl 1010.78014Hiptmair, Ralf; Schwab, Christoph 27 2002 Multilevel method for mixed eigenproblems. Zbl 1013.65120Hiptmair, R.; Neymeyr, K. 10 2002 ...and 18 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,579 Authors 63 Hiptmair, Ralf 29 Li, Jichun 26 Perugia, Ilaria 23 Gatica, Gabriel N. 20 Claeys, Xavier 20 Zou, Jun 19 Jerez-Hanckes, Carlos 18 Hu, Qiya 18 Huang, Yunqing 17 Christiansen, Snorre Harald 17 Moiola, Andrea 16 Nicaise, Serge 16 Xu, Jinchao 15 Meddahi, Salim 15 Monk, Peter B. 14 Yang, Wei 13 Alonso Rodríguez, Ana 13 Hu, Kaibo 13 Yuan, Long 13 Zheng, Weiying 12 Chen, Long 12 Demkowicz, Leszek F. 12 Rodríguez, Rodolfo 12 Zhu, Shengfeng 11 Buffa, Annalisa 11 Chung, Tsz Shun Eric 11 Ganesh, Mahadevan 11 Hu, Xiaozhe 11 Mao, Shipeng 11 Schöberl, Joachim 11 Schöps, Sebastian 11 Schwab, Christoph 11 Shu, Shi 11 Yousept, Irwin 10 Marquez-Duran, Antonio M. 10 Oyarzúa, Ricardo 10 Sayas, Francisco-Javier 10 Spence, Euan A. 10 Zhang, Shuo 10 Zhong, Liuqiang 9 Betcke, Timo 9 Gander, Martin Jakob 9 Mascotto, Lorenzo 9 Rapetti, Francesca 9 Valli, Alberto 9 Zikatanov, Ludmil T. 8 Creusé, Emmanuel 8 Ding, Qianqian 8 Duan, Huoyuan 8 Harbrecht, Helmut 8 Hawkins, Stuart Collin 8 Hoppe, Ronald H. W. 8 Li, Jingzhi 8 Qiu, Weifeng 8 Schötzau, Dominik 8 Stephan, Ernst Peter 8 Vassilevski, Panayot Spirov 7 Campos Pinto, Martin 7 Führer, Thomas 7 Greif, Chen 7 He, Yinnian 7 Kang, Tong 7 Kolev, Tzanio V. 7 Ledger, Paul David 7 Melenk, Jens Markus 7 Tan, Roger C. E. 7 Weiland, Thomas 7 Winther, Ragnar 7 Wu, Haijun 6 Axelsson, Axel Owe Holger 6 Bermúdez, Alfredo 6 Chen, Jinru 6 Chen, Junqing 6 Dolean, Victorita 6 Heuer, Norbert 6 Kim, Kwang Ik 6 Kurz, Stefan 6 Lepe, Felipe 6 Li, Lingxiao 6 Li, Zhilin 6 Ma, Changfeng 6 Pardo, David 6 Sauter, Stefan A. 6 Sonnendrücker, Eric 6 Steinbach, Olaf 6 Xu, Liwei 6 Xu, Xuejun 5 Ainsworth, Mark 5 Barrios, Tomás P. 5 Beirão da Veiga, Lourenço 5 Boffi, Daniele 5 Brenner, Susanne Cecelia 5 Cai, Zhiqiang 5 Cao, Shuhao 5 Chaumont-Frelet, Théophile 5 Chen, Zhiming 5 Costabel, Martin 5 Cui, Jintao 5 Dapogny, Charles 5 De Gersem, Herbert ...and 1,479 more Authors all top 5 Cited in 149 Serials 117 Journal of Computational Physics 78 Mathematics of Computation 75 Computer Methods in Applied Mechanics and Engineering 70 Computers & Mathematics with Applications 68 Journal of Computational and Applied Mathematics 65 SIAM Journal on Scientific Computing 64 Numerische Mathematik 63 Journal of Scientific Computing 41 SIAM Journal on Numerical Analysis 36 Applied Numerical Mathematics 32 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 24 Advances in Computational Mathematics 23 BIT 19 International Journal for Numerical Methods in Engineering 18 Numerical Linear Algebra with Applications 16 Applied Mathematics and Computation 16 Numerical Algorithms 15 M\(^3\)AS. 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