Edit Profile Hiptmair, Ralf Compute Distance To: Compute Author ID: hiptmair.ralf Published as: Hiptmair, R.; Hiptmair, Ralf Documents Indexed: 135 Publications since 1994, including 1 Book all top 5 Co-Authors 20 single-authored 12 Claeys, Xavier 12 Perugia, Ilaria 10 Hoppe, Ronald H. W. 10 Moiola, Andrea 8 Jerez-Hanckes, Carlos 6 Heumann, Holger 6 Li, Jingzhi 6 Ostrowski, Jörg 6 Schwab, Christoph 5 Buffa, Annalisa 5 Wohlmuth, Barbara I. 5 Zou, Jun 4 Langer, Ulrich 4 Pagliantini, Cecilia 4 Urzúa-Torres, Carolina 3 Gradinaru, Vasile 3 Joly, Patrick 3 Mao, Shipeng 3 Paganini, Alberto 3 Spindler, Elke 3 Zheng, Weiying 2 Alonso Rodríguez, Ana 2 Ayuso de Dios, Blanca 2 Beck, Rudi 2 Beck, Rudolf 2 Börm, Steffen 2 Casati, Daniele 2 Gittelson, Claude Jeffrey 2 Grohs, Philipp 2 Meury, Patrick 2 Peng, Zhen 2 Pintarelli, Simon 2 Schmidt, Kersten 2 Valli, Alberto 2 Widmer, Gerhard 2 Xu, Jinchao 1 Bespalov, Alexei 1 Boffi, Daniele 1 Casagrande, Raffael 1 Chaillat-Loseille, Stéphanie 1 Costabel, Martin 1 Dauge, Monique 1 Demkowicz, Leszek F. 1 Deuflhard, Peter 1 Eberle, Sarah 1 Eckhardt, Jonas 1 Engelmann, Bruce E. 1 Florian, Francesco 1 Fonn, Eivind 1 Fuhrmann, Henning 1 Ganesh, Mahadevan 1 Hawkins, Stuart Collin 1 Heuer, Norbert 1 Hohage, Thorsten 1 Kotiuga, Peter Robert 1 Kramer, Felix 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 Neymeyr, Klaus 1 Panchal, P. 1 Pechstein, Clemens 1 Phillips, G. T. 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 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 6 BIT 5 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 International Journal for Numerical Methods in Engineering 3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Inverse Problems 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Numerical Algorithms 2 SIAM Journal on Mathematical Analysis 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 Journal of Functional Analysis 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 Review 1 SIAM Journal on Scientific Computing 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 Computational Methods in Applied Mathematics 1 Acta Numerica 1 Numerical Mathematics: Theory, Methods and Applications all top 5 Fields 113 Numerical analysis (65-XX) 78 Partial differential equations (35-XX) 63 Optics, electromagnetic theory (78-XX) 18 Fluid mechanics (76-XX) 7 General and overarching topics; collections (00-XX) 7 Integral equations (45-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Potential theory (31-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 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 108 Publications have been cited 1,755 times in 1,036 Documents Cited by ▼ Year ▼ Finite elements in computational electromagnetism. Zbl 1123.78320Hiptmair, R. 278 2002 Multigrid method for Maxwell’s equations. Zbl 0922.65081Hiptmair, R. 92 1998 Nodal auxiliary space preconditioning in H(curl) and H(div) spaces. Zbl 1153.78006Hiptmair, Ralf; Xu, Jinchao 91 2007 Plane wave discontinuous Galerkin methods: Analysis of the \(h\)-version. Zbl 1165.65076Gittelson, Claude J.; Hiptmair, Ralf; Perugia, Ilaria 85 2009 Residual based a posteriori error estimators for eddy current computation. Zbl 0949.65113Beck, Rudi; Hiptmair, Ralf; Hoppe, Ronald H. W.; Wohlmuth, Barbara 75 2000 Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the \(p\)-version. Zbl 1229.65215Hiptmair, R.; Moiola, A.; Perugia, I. 69 2011 Canonical construction of finite elements. Zbl 0938.65132Hiptmair, R. 60 1999 Boundary element methods for Maxwell transmission problems in Lipschitz domains. Zbl 1071.65160Buffa, Annalisa; Hiptmair, Ralf; von Petersdorff, Tobias; Schwab, Christoph 45 2003 Galerkin boundary element methods for electromagnetic scattering. Zbl 1055.78013Buffa, Annalisa; Hiptmair, Ralf 43 2003 Plane wave approximation of homogeneous Helmholtz solutions. Zbl 1263.35070Moiola, A.; Hiptmair, R.; Perugia, I. 37 2011 Operator preconditioning. Zbl 1125.65037Hiptmair, R. 36 2006 Symmetric coupling for eddy current problems. Zbl 1010.78011Hiptmair, R. 35 2002 Discrete Hodge operators. Zbl 0993.65130Hiptmair, R. 30 2001 Comparison of approximate shape gradients. Zbl 1320.65099Hiptmair, R.; Paganini, A.; Sargheini, S. 29 2015 Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations. Zbl 1269.78013Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 26 2013 Natural boundary element methods for the electric field integral equation on polyhedra. Zbl 1010.78014Hiptmair, Ralf; Schwab, Christoph 25 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 A survey of Trefftz methods for the Helmholtz equation. Zbl 1357.65282Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 24 2016 Multiple traces boundary integral formulation for Helmholtz transmission problems. Zbl 1261.65123Hiptmair, R.; Jerez-Hanckes, C. 24 2012 Regularized combined field integral equations. Zbl 1067.65137Buffa, A.; Hiptmair, R. 20 2005 Multigrid method for \(H\text{(div)}\) in three dimensions. Zbl 0897.65046Hiptmair, R. 20 1997 A fully divergence-free finite element method for magnetohydrodynamic equations. Zbl 1393.65031Hiptmair, Ralf; Li, Lingxiao; Mao, Shipeng; Zheng, Weiying 18 2018 Stability results for the time-harmonic Maxwell equations with impedance boundary conditions. Zbl 1331.35335Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 18 2011 A coercive combined field integral equation for electromagnetic scattering. Zbl 1082.78003Buffa, A.; Hiptmair, R. 18 2004 Mixed finite element approximation of eddy current problems. Zbl 1114.78012Alonso Rodríguez, Ana; Hiptmair, Ralf; Valli, Alberto 18 2004 Coupling of finite elements and boundary elements in electromagnetic scattering. Zbl 1049.78021Hiptmair, R. 18 2003 Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes. Zbl 1288.65166Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 16 2014 Plane wave discontinuous Galerkin methods: exponential convergence of the \(hp\)-version. Zbl 1347.65176Hiptmair, R.; Moiola, A.; Perugia, I. 15 2016 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 Multi-trace boundary integral formulation for acoustic scattering by composite structures. Zbl 1366.74030Claeys, Xavier; Hiptmair, Ralf 15 2013 Sparse adaptive finite elements for radiative transfer. Zbl 1147.65095Widmer, G.; Hiptmair, R.; Schwab, Ch. 15 2008 Convergence analysis of finite element methods for \(H\) (curl; \(\Omega \))-elliptic interface problems. Zbl 1268.78020Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 14 2012 Overlapping and multilevel Schwarz methods for vector valued elliptic problems in three dimensions. Zbl 0961.65109Hiptmair, Ralf; Toselli, Andrea 14 2000 Multitrace boundary integral equations. Zbl 1291.78040Claeys, Xavier; Hiptmair, Ralf; Jerez-Hanckes, Carlos 13 2013 Whitney elements on pyramids. Zbl 0970.65120Gradinaru, V.; Hiptmair, R. 13 1999 Electromagnetic scattering at composite objects: a novel multi-trace boundary integral formulation. Zbl 1277.78032Claeys, Xavier; Hiptmair, Ralf 12 2012 Convergence analysis of finite element methods for \(H(\mathrm{div};\Omega )\)-elliptic interface problems. Zbl 1203.65227Hiptmair, R.; Li, J.; Zou, J. 12 2010 Stabilized FEM-BEM coupling for Helmholtz transmission problems. Zbl 1221.65308Hiptmair, R.; Meury, P. 12 2006 Large deformation shape uncertainty quantification in acoustic scattering. Zbl 1402.35321Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch. 11 2018 Dispersion analysis of plane wave discontinuous Galerkin methods. Zbl 1352.65503Gittelson, Claude J.; Hiptmair, Ralf 11 2014 Convergence of the natural \(hp\)-BEM for the electric field integral equation on polyhedral surfaces. Zbl 1223.65083Bespalov, A.; Heuer, N.; Hiptmair, R. 11 2010 Analysis of tensor product multigrid. Zbl 0973.65118Börm, S.; Hiptmair, R. 11 2001 Hierarchical error estimator for eddy current computation. Zbl 0970.78006Beck, R.; Hiptmair, R.; Wohlmuth, B. 11 2000 Self-adjoint curl operators. Zbl 1275.47100Hiptmair, Ralf; Kotiuga, Peter Robert; Tordeux, Sébastien 10 2012 Local multigrid in \(\boldsymbol{H} (\mathbf{curl})\). Zbl 1212.65486Hiptmair, Ralf; Zheng, Weiying 10 2009 Novel multitrace boundary integral equations for transmission boundary value problems. Zbl 1346.65066Claeys, X.; Hiptmair, R.; Jerez-Hanckes, C.; Pintarelli, S. 9 2015 Shape derivatives in differential forms. I: An intrinsic perspective. Zbl 1278.35056Hiptmair, Ralf; Li, Jingzhi 9 2013 Convergence analysis with parameter estimates for a reduced basis acoustic scattering T-matrix method. Zbl 1275.65074Ganesh, M.; Hawkins, S. C.; Hiptmair, R. 9 2012 Computation of resonant modes for axisymmetric Maxwell cavities using \(hp\)-version edge finite elements. Zbl 1121.78013Hiptmair, R.; Ledger, P. D. 9 2005 Multilevel method for mixed eigenproblems. Zbl 1013.65120Hiptmair, R.; Neymeyr, K. 9 2002 Mesh-independent operator preconditioning for boundary elements on open curves. Zbl 1310.65155Hiptmair, Ralf; Jerez-Hanckes, Carlos; Urzúa-Torres, Carolina 8 2014 Vekua theory for the Helmholtz operator. Zbl 1266.35016Moiola, A.; Hiptmair, R.; Perugia, I. 8 2011 Current and voltage excitations for the eddy current model. Zbl 1099.78021Hiptmair, R.; Sterz, O. 8 2005 Generators of \(H_1(\Gamma_{h},\mathbb{Z})\) for triangulated surfaces: Construction and classification. Zbl 1001.05046Hiptmair, R.; Ostrowski, J. 8 2002 Multilevel solution of the time-harmonic Maxwell’s equations based on edge elements. Zbl 0930.35167Beck, Rudolf; Hiptmair, Ralf 8 1999 Fast convolution quadrature based impedance boundary conditions. Zbl 1301.65106Hiptmair, Ralf; López-Fernández, María; Paganini, Alberto 7 2014 Stable multilevel splittings of boundary edge element spaces. Zbl 1266.78033Hiptmair, Ralf; Mao, Shipeng 7 2012 Universal extension for Sobolev spaces of differential forms and applications. Zbl 1302.46024Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 7 2012 A hybrid formulation of eddy current problems. Zbl 1079.78023Alonso Rodrigez, Ana; Hiptmair, Ralf; Valli, Alberto 7 2005 Analysis of multilevel methods for eddy current problems. Zbl 1018.78008Hiptmair, R. 7 2003 Multigrid computation of axisymmetric electromagnetic fields. Zbl 0998.65124Börm, S.; Hiptmair, R. 7 2002 Multilevel methods for mixed finite elements in three dimensions. Zbl 0929.65124Hiptmair, Ralf; Hoppe, Ronald H. W. 7 1999 Shape optimization by pursuing diffeomorphisms. Zbl 1321.49076Hiptmair, Ralf; Paganini, Alberto 6 2015 Domain decomposition for boundary integral equations via local multi-trace formulations. Zbl 1382.65429Hiptmair, Ralf; Jerez-Hanckes, Carlos; Lee, Jin-Fa; Peng, Zhen 6 2014 Integral equations on multi-screens. Zbl 1292.45001Claeys, X.; Hiptmair, R. 6 2013 Auxiliary space preconditioning in \(H_0(\text{curl};\Omega)\). Zbl 1094.65118Hiptmair, R.; Widmer, G.; Zou, J. 6 2006 Closed-form inverses of the weakly singular and hypersingular operators on disks. Zbl 1390.45026Hiptmair, R.; Jerez-Hanckes, C.; Urzúa-Torres, C. 5 2018 Hyperbolic cross approximation for the spatially homogeneous Boltzmann equation. Zbl 1330.76101Fonn, E.; Grohs, P.; Hiptmair, R. 5 2015 Uniform convergence of adaptive multigrid methods for elliptic problems and Maxwell’s equations. Zbl 1274.65287Hiptmair, Ralf; Wu, Haijun; Zheng, Weiying 5 2012 Extension by zero in discrete trace spaces: inverse estimates. Zbl 1321.65179Hiptmair, Ralf; Jerez-Hanckes, Carlos; Mao, Shipeng 4 2015 A second-kind Galerkin boundary element method for scattering at composite objects. Zbl 1316.65105Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 4 2015 Convergence of lowest-order semi-Lagrangian schemes. Zbl 1273.65121Heumann, Holger; Hiptmair, Ralf 4 2013 Discrete compactness for the \(p\)-version of discrete differential forms. Zbl 1230.78025Boffi, Daniele; Costabel, Martin; Dauge, Monique; Demkowicz, Leszek; Hiptmair, Ralf 4 2011 Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Zbl 1211.65126Heumann, Holger; Hiptmair, Ralf 4 2011 Mixed plane wave discontinuous Galerkin methods. Zbl 1180.65148Hiptmair, Ralf; Perugia, Ilaria 4 2009 Non-reflecting boundary conditions for Maxwell’s equations. Zbl 1042.78010Hiptmair, R.; Schädle, A. 4 2003 Shape derivatives for scattering problems. Zbl 1421.35352Hiptmair, Ralf; Li, Jingzhi 3 2018 Asymptotic boundary element methods for thin conducting sheets. Zbl 1302.78027Schmidt, Kersten; Hiptmair, Ralf 3 2015 Real interpolation of spaces of differential forms. Zbl 1242.46026Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 3 2012 Coupled boundary-element scheme for eddy-current computation. Zbl 1066.78017Hiptmair, Ralf; Ostrowski, Jörg 3 2005 Coercive combined field integral equations. Zbl 1115.76356Hiptmair, R. 3 2003 Multilevel preconditioning for mixed problems in three dimensions. Zbl 0851.65089Hiptmair, Ralf 3 1996 Multilevel preconditioned augmented Lagrangian techniques for \(2\)nd order mixed problems. Zbl 0904.65106Hiptmair, R.; Schiekofer, T.; Wohlmuth, B. 3 1996 Tensor-product discretization for the spatially inhomogeneous and transient Boltzmann equation in two dimensions. Zbl 1416.82038Grohs, Philipp; Hiptmair, Ralf; Pintarelli, Simon 2 2017 Integral equations for electromagnetic scattering at multi-screens. Zbl 1337.78008Claeys, X.; Hiptmair, R. 2 2016 Maxwell’s equations: continuous and discrete. Zbl 1331.78035Hiptmair, Ralf 2 2015 Fully discrete semi-Lagrangian methods for advection of differential forms. Zbl 1267.65130Heumann, Holger; Hiptmair, Ralf; Li, Kun; Xu, Jinchao 2 2012 Stabilized FEM-BEM coupling for Maxwell transmission problems. Zbl 1144.78026Hiptmair, R.; Meury, P. 2 2008 Boundary element methods for eddy current computation. Zbl 1298.78032Hiptmair, Ralf 2 2007 From E to edge elements. Zbl 1115.78002Hiptmair, Ralf 2 2003 Multilevel gauging for edge elements. Zbl 0955.65087Hiptmair, R. 2 2000 Compact equivalent inverse of the electric field integral operator on screens. Zbl 1446.45015Hiptmair, R.; Urzúa-Torres, C. 1 2020 Discrete regular decompositions of tetrahedral discrete 1-forms. Zbl 1445.78011Hiptmair, Ralf; Pechstein, Clemens 1 2019 First-kind boundary integral equations for the Hodge-Helmholtz operator. Zbl 1409.35062Claeys, Xavier; Hiptmair, Ralf 1 2019 Splitting-based structure preserving discretizations for magnetohydrodynamics. Zbl 1416.76343Hiptmair, Ralf; Pagliantini, Cecilia 1 2018 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 1 2017 Second-kind boundary integral equations for electromagnetic scattering at composite objects. Zbl 1397.65307Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 1 2017 Second kind boundary integral equation for multi-subdomain diffusion problems. Zbl 1381.65094Claeys, X.; Hiptmair, R.; Spindler, Elke 1 2017 Asymptotic expansion techniques for singularly perturbed boundary integral equations. Zbl 1378.65181Schmidt, Kersten; Hiptmair, Ralf 1 2017 Domain decomposition preconditioning for surface integral equations in solving challenging electromagnetic scattering problems. Zbl 1374.78043Peng, Zhen; Hiptmair, Ralf; Shao, Yang; MacKie-Mason, Brian 1 2016 Compact equivalent inverse of the electric field integral operator on screens. Zbl 1446.45015Hiptmair, R.; Urzúa-Torres, C. 1 2020 Discrete regular decompositions of tetrahedral discrete 1-forms. Zbl 1445.78011Hiptmair, Ralf; Pechstein, Clemens 1 2019 First-kind boundary integral equations for the Hodge-Helmholtz operator. Zbl 1409.35062Claeys, Xavier; Hiptmair, Ralf 1 2019 A fully divergence-free finite element method for magnetohydrodynamic equations. Zbl 1393.65031Hiptmair, Ralf; Li, Lingxiao; Mao, Shipeng; Zheng, Weiying 18 2018 Large deformation shape uncertainty quantification in acoustic scattering. Zbl 1402.35321Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch. 11 2018 Closed-form inverses of the weakly singular and hypersingular operators on disks. Zbl 1390.45026Hiptmair, R.; Jerez-Hanckes, C.; Urzúa-Torres, C. 5 2018 Shape derivatives for scattering problems. Zbl 1421.35352Hiptmair, Ralf; Li, Jingzhi 3 2018 Splitting-based structure preserving discretizations for magnetohydrodynamics. Zbl 1416.76343Hiptmair, Ralf; Pagliantini, Cecilia 1 2018 Tensor-product discretization for the spatially inhomogeneous and transient Boltzmann equation in two dimensions. Zbl 1416.82038Grohs, Philipp; Hiptmair, Ralf; Pintarelli, Simon 2 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 1 2017 Second-kind boundary integral equations for electromagnetic scattering at composite objects. Zbl 1397.65307Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 1 2017 Second kind boundary integral equation for multi-subdomain diffusion problems. Zbl 1381.65094Claeys, X.; Hiptmair, R.; Spindler, Elke 1 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 24 2016 Plane wave discontinuous Galerkin methods: exponential convergence of the \(hp\)-version. Zbl 1347.65176Hiptmair, R.; Moiola, A.; Perugia, I. 15 2016 Integral equations for electromagnetic scattering at multi-screens. Zbl 1337.78008Claeys, X.; Hiptmair, R. 2 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 1 2016 Stabilized Galerkin for transient advection of differential forms. Zbl 1334.65148Pagliantini, Cecilia; Hiptmair, Ralf; Heumann, Holger 1 2016 Comparison of approximate shape gradients. Zbl 1320.65099Hiptmair, R.; Paganini, A.; Sargheini, S. 29 2015 Novel multitrace boundary integral equations for transmission boundary value problems. Zbl 1346.65066Claeys, X.; Hiptmair, R.; Jerez-Hanckes, C.; Pintarelli, S. 9 2015 Shape optimization by pursuing diffeomorphisms. Zbl 1321.49076Hiptmair, Ralf; Paganini, Alberto 6 2015 Hyperbolic cross approximation for the spatially homogeneous Boltzmann equation. Zbl 1330.76101Fonn, E.; Grohs, P.; Hiptmair, R. 5 2015 Extension by zero in discrete trace spaces: inverse estimates. Zbl 1321.65179Hiptmair, Ralf; Jerez-Hanckes, Carlos; Mao, Shipeng 4 2015 A second-kind Galerkin boundary element method for scattering at composite objects. Zbl 1316.65105Claeys, Xavier; Hiptmair, Ralf; Spindler, Elke 4 2015 Asymptotic boundary element methods for thin conducting sheets. Zbl 1302.78027Schmidt, Kersten; Hiptmair, Ralf 3 2015 Maxwell’s equations: continuous and discrete. Zbl 1331.78035Hiptmair, Ralf 2 2015 Stabilized Galerkin for linear advection of vector fields. Zbl 1328.65240Heumann, Holger; Hiptmair, Ralf 1 2015 Integral equations for acoustic scattering by partially impenetrable composite objects. Zbl 1315.65101Claeys, X.; Hiptmair, R. 1 2015 Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes. Zbl 1288.65166Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 16 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 Dispersion analysis of plane wave discontinuous Galerkin methods. Zbl 1352.65503Gittelson, Claude J.; Hiptmair, Ralf 11 2014 Mesh-independent operator preconditioning for boundary elements on open curves. Zbl 1310.65155Hiptmair, Ralf; Jerez-Hanckes, Carlos; Urzúa-Torres, Carolina 8 2014 Fast convolution quadrature based impedance boundary conditions. Zbl 1301.65106Hiptmair, Ralf; López-Fernández, María; Paganini, Alberto 7 2014 Domain decomposition for boundary integral equations via local multi-trace formulations. Zbl 1382.65429Hiptmair, 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 1269.78013Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 26 2013 Multi-trace boundary integral formulation for acoustic scattering by composite structures. Zbl 1366.74030Claeys, Xavier; Hiptmair, Ralf 15 2013 Multitrace boundary integral equations. Zbl 1291.78040Claeys, Xavier; Hiptmair, Ralf; Jerez-Hanckes, Carlos 13 2013 Shape derivatives in differential forms. I: An intrinsic perspective. Zbl 1278.35056Hiptmair, Ralf; Li, Jingzhi 9 2013 Integral equations on multi-screens. Zbl 1292.45001Claeys, X.; Hiptmair, R. 6 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 Sparse tensor edge elements. Zbl 1298.78033Hiptmair, Ralf; Jerez-Hanckes, Carlos; Schwab, Christoph 1 2013 Multiple traces boundary integral formulation for Helmholtz transmission problems. Zbl 1261.65123Hiptmair, R.; Jerez-Hanckes, C. 24 2012 Convergence analysis of finite element methods for \(H\) (curl; \(\Omega \))-elliptic interface problems. Zbl 1268.78020Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 14 2012 Electromagnetic scattering at composite objects: a novel multi-trace boundary integral formulation. Zbl 1277.78032Claeys, Xavier; Hiptmair, Ralf 12 2012 Self-adjoint curl operators. Zbl 1275.47100Hiptmair, Ralf; Kotiuga, Peter Robert; Tordeux, Sébastien 10 2012 Convergence analysis with parameter estimates for a reduced basis acoustic scattering T-matrix method. Zbl 1275.65074Ganesh, M.; Hawkins, S. C.; Hiptmair, R. 9 2012 Stable multilevel splittings of boundary edge element spaces. Zbl 1266.78033Hiptmair, Ralf; Mao, Shipeng 7 2012 Universal extension for Sobolev spaces of differential forms and applications. Zbl 1302.46024Hiptmair, Ralf; Li, Jingzhi; Zou, Jun 7 2012 Uniform convergence of adaptive multigrid methods for elliptic problems and Maxwell’s equations. Zbl 1274.65287Hiptmair, Ralf; Wu, Haijun; Zheng, Weiying 5 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 2 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. 69 2011 Plane wave approximation of homogeneous Helmholtz solutions. Zbl 1263.35070Moiola, A.; Hiptmair, R.; Perugia, I. 37 2011 Stability results for the time-harmonic Maxwell equations with impedance boundary conditions. Zbl 1331.35335Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria 18 2011 Vekua theory for the Helmholtz operator. Zbl 1266.35016Moiola, A.; Hiptmair, R.; Perugia, I. 8 2011 Discrete compactness for the \(p\)-version of discrete differential forms. Zbl 1230.78025Boffi, Daniele; Costabel, Martin; Dauge, Monique; Demkowicz, Leszek; Hiptmair, Ralf 4 2011 Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Zbl 1211.65126Heumann, Holger; Hiptmair, Ralf 4 2011 Convergence analysis of finite element methods for \(H(\mathrm{div};\Omega )\)-elliptic interface problems. Zbl 1203.65227Hiptmair, R.; Li, J.; Zou, J. 12 2010 Convergence of the natural \(hp\)-BEM for the electric field integral equation on polyhedral surfaces. Zbl 1223.65083Bespalov, A.; Heuer, N.; Hiptmair, R. 11 2010 Plane wave discontinuous Galerkin methods: Analysis of the \(h\)-version. Zbl 1165.65076Gittelson, Claude J.; Hiptmair, Ralf; Perugia, Ilaria 85 2009 Local multigrid in \(\boldsymbol{H} (\mathbf{curl})\). Zbl 1212.65486Hiptmair, Ralf; Zheng, Weiying 10 2009 Mixed plane wave discontinuous Galerkin methods. Zbl 1180.65148Hiptmair, Ralf; Perugia, Ilaria 4 2009 Sparse adaptive finite elements for radiative transfer. Zbl 1147.65095Widmer, G.; Hiptmair, R.; Schwab, Ch. 15 2008 Stabilized FEM-BEM coupling for Maxwell transmission problems. Zbl 1144.78026Hiptmair, R.; Meury, P. 2 2008 Nodal auxiliary space preconditioning in H(curl) and H(div) spaces. Zbl 1153.78006Hiptmair, Ralf; Xu, Jinchao 91 2007 Boundary element methods for eddy current computation. Zbl 1298.78032Hiptmair, Ralf 2 2007 Operator preconditioning. Zbl 1125.65037Hiptmair, R. 36 2006 Stabilized FEM-BEM coupling for Helmholtz transmission problems. Zbl 1221.65308Hiptmair, R.; Meury, P. 12 2006 Auxiliary space preconditioning in \(H_0(\text{curl};\Omega)\). Zbl 1094.65118Hiptmair, R.; Widmer, G.; Zou, J. 6 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. 20 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. 8 2005 A hybrid formulation of eddy current problems. Zbl 1079.78023Alonso Rodrigez, Ana; Hiptmair, Ralf; Valli, Alberto 7 2005 Coupled boundary-element scheme for eddy-current computation. Zbl 1066.78017Hiptmair, Ralf; Ostrowski, Jörg 3 2005 A coercive combined field integral equation for electromagnetic scattering. Zbl 1082.78003Buffa, A.; Hiptmair, R. 18 2004 Mixed finite element approximation of eddy current problems. Zbl 1114.78012Alonso Rodríguez, Ana; Hiptmair, Ralf; Valli, Alberto 18 2004 Boundary element methods for Maxwell transmission problems in Lipschitz domains. Zbl 1071.65160Buffa, Annalisa; Hiptmair, Ralf; von Petersdorff, Tobias; Schwab, Christoph 45 2003 Galerkin boundary element methods for electromagnetic scattering. Zbl 1055.78013Buffa, Annalisa; Hiptmair, Ralf 43 2003 Coupling of finite elements and boundary elements in electromagnetic scattering. Zbl 1049.78021Hiptmair, R. 18 2003 Analysis of multilevel methods for eddy current problems. Zbl 1018.78008Hiptmair, R. 7 2003 Non-reflecting boundary conditions for Maxwell’s equations. Zbl 1042.78010Hiptmair, R.; Schädle, A. 4 2003 Coercive combined field integral equations. Zbl 1115.76356Hiptmair, R. 3 2003 From E to edge elements. Zbl 1115.78002Hiptmair, Ralf 2 2003 Finite elements in computational electromagnetism. Zbl 1123.78320Hiptmair, R. 278 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 25 2002 Multilevel method for mixed eigenproblems. Zbl 1013.65120Hiptmair, R.; Neymeyr, K. 9 2002 Generators of \(H_1(\Gamma_{h},\mathbb{Z})\) for triangulated surfaces: Construction and classification. Zbl 1001.05046Hiptmair, R.; Ostrowski, J. 8 2002 Multigrid computation of axisymmetric electromagnetic fields. Zbl 0998.65124Börm, S.; Hiptmair, R. 7 2002 Discrete Hodge operators. Zbl 0993.65130Hiptmair, R. 30 2001 Analysis of tensor product multigrid. Zbl 0973.65118Börm, S.; Hiptmair, R. 11 2001 Residual based a posteriori error estimators for eddy current computation. Zbl 0949.65113Beck, Rudi; Hiptmair, Ralf; Hoppe, Ronald H. W.; Wohlmuth, Barbara 75 2000 Overlapping and multilevel Schwarz methods for vector valued elliptic problems in three dimensions. Zbl 0961.65109Hiptmair, Ralf; Toselli, Andrea 14 2000 Hierarchical error estimator for eddy current computation. Zbl 0970.78006Beck, R.; Hiptmair, R.; Wohlmuth, B. 11 2000 Multilevel gauging for edge elements. Zbl 0955.65087Hiptmair, R. 2 2000 Numerical simulation of electrorheological fluids based on an extended Bingham model. Zbl 1094.76534Engelmann, B.; Hiptmair, R.; Hoppe, R. H. W.; Mazurkevitch, G. 1 2000 Canonical construction of finite elements. Zbl 0938.65132Hiptmair, R. 60 1999 ...and 8 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,372 Authors 53 Hiptmair, Ralf 27 Li, Jichun 23 Perugia, Ilaria 21 Gatica, Gabriel N. 17 Christiansen, Snorre Harald 17 Zou, Jun 16 Huang, Yunqing 15 Nicaise, Serge 14 Claeys, Xavier 14 Moiola, Andrea 13 Jerez-Hanckes, Carlos 13 Meddahi, Salim 13 Monk, Peter B. 13 Xu, Jinchao 12 Buffa, Annalisa 12 Demkowicz, Leszek F. 12 Hu, Qiya 12 Rodríguez, Rodolfo 11 Schöps, Sebastian 10 Alonso Rodríguez, Ana 10 Hu, Kaibo 10 Shu, Shi 10 Yousept, Irwin 10 Zheng, Weiying 9 Chen, Long 9 Gander, Martin Jakob 9 Gopalakrishnan, Jayadeep 9 Hu, Xiaozhe 9 Marquez-Duran, Antonio M. 9 Oyarzúa, Ricardo 9 Sayas, Francisco-Javier 9 Schöberl, Joachim 9 Schwab, Christoph 9 Valli, Alberto 9 Yang, Wei 8 Hoppe, Ronald H. W. 8 Schötzau, Dominik 8 Stephan, Ernst Peter 8 Vassilevski, Panayot Spirov 8 Zhong, Liuqiang 8 Zikatanov, Ludmil T. 7 Chung, Tsz Shun Eric 7 Creusé, Emmanuel 7 Duan, Huoyuan 7 Ganesh, Mahadevan 7 Greif, Chen 7 Hawkins, Stuart Collin 7 Kang, Tong 7 Ledger, Paul David 7 Li, Jingzhi 7 Mascotto, Lorenzo 7 Qiu, Weifeng 7 Weiland, Thomas 7 Winther, Ragnar 6 Beirão da Veiga, Lourenço 6 Bermúdez, Alfredo 6 Chen, Junqing 6 Dolean, Victorita 6 Egger, Herbert 6 Führer, Thomas 6 Kim, Kwang Ik 6 Kolev, Tzanio V. 6 Kurz, Stefan 6 Pardo, David 6 Rapetti, Francesca 6 Sauter, Stefan A. 6 Spence, Euan A. 6 Steinbach, Olaf 6 Tan, Roger C. E. 6 Vazquez, Rafael 6 Wu, Haijun 6 Zhang, Shuo 5 Ainsworth, Mark 5 Axelsson, Axel Owe Holger 5 Betcke, Timo 5 Boffi, Daniele 5 Brenner, Susanne Cecelia 5 Cai, Zhiqiang 5 Campos Pinto, Martin 5 Chen, Zhiming 5 Costabel, Martin 5 Cui, Jintao 5 De Gersem, Herbert 5 Desbrun, Mathieu 5 Gastaldi, Lucia 5 Graham, Ivan G. 5 Harbrecht, Helmut 5 Heuer, Norbert 5 Laurain, Antoine 5 Lee, Jin-Fa 5 Leydecker, Florian 5 Lin, Yanping 5 Ma, Changfeng 5 Mao, Shipeng 5 Mohamed, M. Shadi 5 Pasciak, Joseph E. 5 Praetorius, Dirk 5 Solano, Manuel E. 5 Sonnendrücker, Eric 5 van der Vegt, Jaap J. W. ...and 1,272 more Authors all top 5 Cited in 133 Serials 93 Journal of Computational Physics 68 Mathematics of Computation 66 Computer Methods in Applied Mechanics and Engineering 57 Journal of Computational and Applied Mathematics 55 Numerische Mathematik 52 Computers & Mathematics with Applications 51 Journal of Scientific Computing 50 SIAM Journal on Scientific Computing 33 Applied Numerical Mathematics 28 SIAM Journal on Numerical Analysis 20 BIT 20 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 19 International Journal for Numerical Methods in Engineering 18 Numerical Linear Algebra with Applications 16 Applied Mathematics and Computation 16 Advances in Computational Mathematics 14 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 13 COMPEL 13 Numerical Algorithms 12 Applicable Analysis 12 Engineering Analysis with Boundary Elements 10 Journal of Mathematical Analysis and Applications 10 Numerical Methods for Partial Differential Equations 9 Mathematical Methods in the Applied Sciences 9 Foundations of Computational Mathematics 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Integral Equations and Operator Theory 8 SIAM/ASA Journal on Uncertainty Quantification 7 Computational Geosciences 7 Journal of Numerical Mathematics 6 Mathematics and Computers in Simulation 6 Discrete and Continuous Dynamical Systems. Series S 5 Communications on Pure and Applied Mathematics 5 Computational Mechanics 5 SIAM Journal on Applied Mathematics 5 SIAM Journal on Mathematical Analysis 5 Computational Methods in Applied Mathematics 4 Inverse Problems 4 Wave Motion 4 Applied Mathematics Letters 4 Applied Mathematical Modelling 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 ETNA. Electronic Transactions on Numerical Analysis 4 Science China. Mathematics 3 Journal of Engineering Mathematics 3 Journal of Mathematical Physics 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Journal of Geometry and Physics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Calcolo 3 Computing 3 Journal of Differential Equations 3 Journal of Optimization Theory and Applications 3 Constructive Approximation 3 Computational and Applied Mathematics 3 Journal of Inverse and Ill-Posed Problems 3 International Journal of Numerical Modelling 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 Multiscale Modeling & Simulation 3 SIAM Journal on Imaging Sciences 3 SMAI Journal of Computational Mathematics 2 Journal of Functional Analysis 2 Mathematische Zeitschrift 2 Mathematical and Computer Modelling 2 SIAM Journal on Matrix Analysis and Applications 2 Journal of Integral Equations and Applications 2 International Journal of Computer Mathematics 2 Computational Optimization and Applications 2 Communications in Numerical Methods in Engineering 2 Journal of Mathematical Sciences (New York) 2 Communications in Nonlinear Science and Numerical Simulation 2 Archives of Computational Methods in Engineering 2 Acta Numerica 2 Journal of Computational Acoustics 2 Frontiers of Mathematics in China 2 Kinetic and Related Models 2 S\(\vec{\text{e}}\)MA Journal 2 Communications on Applied Mathematics and Computation 2 SN Partial Differential Equations and Applications 1 Discrete Applied Mathematics 1 International Journal of Engineering Science 1 International Journal for Numerical Methods in Fluids 1 Journal of the Mechanics and Physics of Solids 1 Nonlinearity 1 Nuclear Physics. B 1 Physics Letters. A 1 Transport Theory and Statistical Physics 1 ACM Transactions on Mathematical Software 1 Applied Mathematics and Optimization 1 Automatica 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 SIAM Journal on Control and Optimization 1 Theoretical Computer Science 1 Advances in Applied Mathematics 1 Systems & Control Letters 1 Applied Mathematics and Mechanics. (English Edition) 1 Computer Aided Geometric Design 1 Physica D 1 Discrete & Computational Geometry 1 Science in China. Series A ...and 33 more Serials all top 5 Cited in 48 Fields 847 Numerical analysis (65-XX) 447 Partial differential equations (35-XX) 397 Optics, electromagnetic theory (78-XX) 162 Fluid mechanics (76-XX) 101 Mechanics of deformable solids (74-XX) 50 Calculus of variations and optimal control; optimization (49-XX) 34 Global analysis, analysis on manifolds (58-XX) 31 Integral equations (45-XX) 20 Approximations and expansions (41-XX) 18 Statistical mechanics, structure of matter (82-XX) 17 Operator theory (47-XX) 16 Probability theory and stochastic processes (60-XX) 13 Functional analysis (46-XX) 12 Potential theory (31-XX) 12 Classical thermodynamics, heat transfer (80-XX) 12 Geophysics (86-XX) 11 Biology and other natural sciences (92-XX) 10 Computer science (68-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 9 Differential geometry (53-XX) 9 Quantum theory (81-XX) 8 Dynamical systems and ergodic theory (37-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Statistics (62-XX) 6 Relativity and gravitational theory (83-XX) 5 Ordinary differential equations (34-XX) 5 Systems theory; control (93-XX) 5 Information and communication theory, circuits (94-XX) 4 History and biography (01-XX) 4 Algebraic geometry (14-XX) 4 Algebraic topology (55-XX) 4 Operations research, mathematical programming (90-XX) 3 General and overarching topics; collections (00-XX) 3 Difference and functional equations (39-XX) 3 Integral transforms, operational calculus (44-XX) 3 Convex and discrete geometry (52-XX) 3 Astronomy and astrophysics (85-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 2 Manifolds and cell complexes (57-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year