Edit Profile Börm, Steffen Compute Distance To: Compute Author ID: borm.steffen Published as: Börm, S.; Börm, Steffen External Links: ORCID · dblp Documents Indexed: 40 Publications since 2001, including 2 Books all top 5 Co-Authors 13 single-authored 8 Hackbusch, Wolfgang 4 Grasedyck, Lars 3 Melenk, Jens Markus 2 Börst, Christina 2 Hiptmair, Ralf 2 Le Borne, Sabine 2 Reimer, Knut 2 Sauter, Stefan A. 1 Benner, Peter 1 Berghammer, Rudolf 1 Betcke, Timo 1 Christophersen, Sven 1 Gördes, Jessica 1 Krzebek, Nico 1 Löhndorf, Maike 1 Mach, Thomas 1 Martinsson, Per-Gunnar 1 Mehl, Christian 1 Ostrowski, Jörg 1 Winter, Michael all top 5 Serials 6 Computing 5 Numerische Mathematik 3 Computing and Visualization in Science 2 Mathematics of Computation 2 Numerical Algorithms 2 SIAM Journal on Scientific Computing 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal for Numerical Methods in Fluids 1 Journal of Computational Physics 1 Applied Mathematics and Computation 1 Applied Numerical Mathematics 1 SIAM Journal on Matrix Analysis and Applications 1 Mathematica Bohemica 1 Linear Algebra and its Applications 1 Numerical Linear Algebra with Applications 1 Advances in Computational Mathematics 1 Engineering Analysis with Boundary Elements 1 Oberwolfach Reports 1 EMS Tracts in Mathematics 1 PAMM. Proceedings in Applied Mathematics and Mechanics all top 5 Fields 38 Numerical analysis (65-XX) 17 Partial differential equations (35-XX) 7 Integral equations (45-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Optics, electromagnetic theory (78-XX) 2 Approximations and expansions (41-XX) 2 Computer science (68-XX) 1 General and overarching topics; collections (00-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Fluid mechanics (76-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 32 Publications have been cited 408 times in 250 Documents Cited by ▼ Year ▼ Introduction to hierarchical matrices with applications. Zbl 1035.65042Börm, Steffen; Grasedyck, Lars; Hackbusch, Wolfgang 97 2003 Data-sparse approximation by adaptive \({\mathcal H}^2\)-matrices. Zbl 1012.65023Hackbusch, W.; Börm, S. 49 2002 \(\mathcal H^2\)-matrix approximation of integral operators by interpolation. Zbl 1019.65103Hackbusch, Wolfgang; Börm, Steffen 34 2002 Hybrid cross approximation of integral operators. Zbl 1104.65120Börm, Steffen; Grasedyck, Lars 33 2005 Efficient numerical methods for non-local operators. \(\mathcal H^2\)-matrix compression, algorithms and analysis. Zbl 1208.65037Börm, Steffen 27 2010 An introduction to hierarchical matrices. Zbl 1007.65032Hackbusch, Wolfgang; Grasedyck, Lars; Börm, Steffen 18 2002 Approximation of solution operators of elliptic partial differential equations by \({\mathcal H}\)- and \({\mathcal H}^2\)-matrices. Zbl 1191.65148Börm, Steffen 17 2010 Approximation of integral operators by variable-order interpolation. Zbl 1076.65121Börm, Steffen; Löhndorf, Maike; Melenk, Jens M. 15 2005 \(\mathcal H\)-LU factorization in preconditioners for augmented Lagrangian and grad-div stabilized saddle point systems. Zbl 1426.76224Börm, Steffen; Le Borne, Sabine 14 2012 Analysis of tensor product multigrid. Zbl 0973.65118Börm, S.; Hiptmair, R. 11 2001 \(\mathcal H^2\)-matrix arithmetics in linear complexity. Zbl 1086.65036Börm, S. 10 2006 Low-rank approximation of integral operators by interpolation. Zbl 1059.65121Börm, Steffen; Grasedyck, Lars 10 2004 Construction of data-sparse \(\mathcal{H}^2\)-matrices by hierarchical compression. Zbl 1193.65043Börm, Steffen 9 2009 Approximation of integral operators by \(\mathcal H^2\)-matrices with adaptive bases. Zbl 1082.65139Börm, S. 8 2005 Multigrid computation of axisymmetric electromagnetic fields. Zbl 0998.65124Börm, S.; Hiptmair, R. 7 2002 Data-sparse approximation of non-local operators by \(\mathcal H^2\)-matrices. Zbl 1115.65041Börm, Steffen 6 2007 Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis. Zbl 1375.35098Börm, Steffen; Melenk, Jens M. 5 2017 Hierarchical quadrature for singular integrals. Zbl 1068.65038Börm, S.; Hackbusch, W. 5 2005 BEM with linear complexity for the classical boundary integral operators. Zbl 1069.65131Börm, Steffen; Sauter, Stefan A. 5 2005 Directional \(\mathcal{H}^2\)-matrix compression for high-frequency problems. Zbl 06819613Börm, Steffen 4 2017 Efficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updates. Zbl 1380.65461Börm, Steffen; Reimer, Knut 4 2013 Adaptive variable-rank approximation of general dense matrices. Zbl 1159.65324Börm, Steffen 3 2007 Approximation of boundary element operators by adaptive \({\mathcal H}^2\)-matrices. Zbl 1097.65119Börm, Steffen; Hackbusch, Wolfgang 3 2004 Approximation of integral operators by Green quadrature and nested cross approximation. Zbl 1347.65181Börm, Steffen; Christophersen, Sven 2 2016 Computing the eigenvalues of symmetric \(\mathcal{H}^2\)-matrices by slicing the spectrum. Zbl 1376.65044Benner, Peter; Börm, Steffen; Mach, Thomas; Reimer, Knut 2 2013 Numerical methods for eigenvalue problems. Zbl 1254.65046Börm, Steffen; Mehl, Christian 2 2012 May the singular integrals in BEM be replaced by zero? Zbl 1071.65159Börm, S.; Krzebek, N.; Sauter, S. A. 2 2005 \(\mathcal H^2\)-matrices – multilevel methods for the approximation of integral operators. Zbl 1070.65124Börm, Steffen 2 2004 An analysis of a butterfly algorithm. Zbl 1396.65171Börm, S.; Börst, C.; Melenk, J. M. 1 2017 Low-rank approximation of integral operators by using the Green formula and quadrature. Zbl 1329.65314Börm, Steffen; Gördes, Jessica 1 2013 \(\mathcal{H}^2\)-matrix compression. Zbl 1315.68111Börm, Steffen 1 2012 Fast evaluation of boundary integral operators arising from an eddy current problem. Zbl 1117.78312Börm, S.; Ostrowski, J. 1 2004 Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis. Zbl 1375.35098Börm, Steffen; Melenk, Jens M. 5 2017 Directional \(\mathcal{H}^2\)-matrix compression for high-frequency problems. Zbl 06819613Börm, Steffen 4 2017 An analysis of a butterfly algorithm. Zbl 1396.65171Börm, S.; Börst, C.; Melenk, J. M. 1 2017 Approximation of integral operators by Green quadrature and nested cross approximation. Zbl 1347.65181Börm, Steffen; Christophersen, Sven 2 2016 Efficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updates. Zbl 1380.65461Börm, Steffen; Reimer, Knut 4 2013 Computing the eigenvalues of symmetric \(\mathcal{H}^2\)-matrices by slicing the spectrum. Zbl 1376.65044Benner, Peter; Börm, Steffen; Mach, Thomas; Reimer, Knut 2 2013 Low-rank approximation of integral operators by using the Green formula and quadrature. Zbl 1329.65314Börm, Steffen; Gördes, Jessica 1 2013 \(\mathcal H\)-LU factorization in preconditioners for augmented Lagrangian and grad-div stabilized saddle point systems. Zbl 1426.76224Börm, Steffen; Le Borne, Sabine 14 2012 Numerical methods for eigenvalue problems. Zbl 1254.65046Börm, Steffen; Mehl, Christian 2 2012 \(\mathcal{H}^2\)-matrix compression. Zbl 1315.68111Börm, Steffen 1 2012 Efficient numerical methods for non-local operators. \(\mathcal H^2\)-matrix compression, algorithms and analysis. Zbl 1208.65037Börm, Steffen 27 2010 Approximation of solution operators of elliptic partial differential equations by \({\mathcal H}\)- and \({\mathcal H}^2\)-matrices. Zbl 1191.65148Börm, Steffen 17 2010 Construction of data-sparse \(\mathcal{H}^2\)-matrices by hierarchical compression. Zbl 1193.65043Börm, Steffen 9 2009 Data-sparse approximation of non-local operators by \(\mathcal H^2\)-matrices. Zbl 1115.65041Börm, Steffen 6 2007 Adaptive variable-rank approximation of general dense matrices. Zbl 1159.65324Börm, Steffen 3 2007 \(\mathcal H^2\)-matrix arithmetics in linear complexity. Zbl 1086.65036Börm, S. 10 2006 Hybrid cross approximation of integral operators. Zbl 1104.65120Börm, Steffen; Grasedyck, Lars 33 2005 Approximation of integral operators by variable-order interpolation. Zbl 1076.65121Börm, Steffen; Löhndorf, Maike; Melenk, Jens M. 15 2005 Approximation of integral operators by \(\mathcal H^2\)-matrices with adaptive bases. Zbl 1082.65139Börm, S. 8 2005 Hierarchical quadrature for singular integrals. Zbl 1068.65038Börm, S.; Hackbusch, W. 5 2005 BEM with linear complexity for the classical boundary integral operators. Zbl 1069.65131Börm, Steffen; Sauter, Stefan A. 5 2005 May the singular integrals in BEM be replaced by zero? Zbl 1071.65159Börm, S.; Krzebek, N.; Sauter, S. A. 2 2005 Low-rank approximation of integral operators by interpolation. Zbl 1059.65121Börm, Steffen; Grasedyck, Lars 10 2004 Approximation of boundary element operators by adaptive \({\mathcal H}^2\)-matrices. Zbl 1097.65119Börm, Steffen; Hackbusch, Wolfgang 3 2004 \(\mathcal H^2\)-matrices – multilevel methods for the approximation of integral operators. Zbl 1070.65124Börm, Steffen 2 2004 Fast evaluation of boundary integral operators arising from an eddy current problem. Zbl 1117.78312Börm, S.; Ostrowski, J. 1 2004 Introduction to hierarchical matrices with applications. Zbl 1035.65042Börm, Steffen; Grasedyck, Lars; Hackbusch, Wolfgang 97 2003 Data-sparse approximation by adaptive \({\mathcal H}^2\)-matrices. Zbl 1012.65023Hackbusch, W.; Börm, S. 49 2002 \(\mathcal H^2\)-matrix approximation of integral operators by interpolation. Zbl 1019.65103Hackbusch, Wolfgang; Börm, Steffen 34 2002 An introduction to hierarchical matrices. Zbl 1007.65032Hackbusch, Wolfgang; Grasedyck, Lars; Börm, Steffen 18 2002 Multigrid computation of axisymmetric electromagnetic fields. Zbl 0998.65124Börm, S.; Hiptmair, R. 7 2002 Analysis of tensor product multigrid. Zbl 0973.65118Börm, S.; Hiptmair, R. 11 2001 all cited Publications top 5 cited Publications all top 5 Cited by 420 Authors 19 Börm, Steffen 10 Darve, Eric 9 Le Borne, Sabine 9 Ying, Lexing 8 Hackbusch, Wolfgang 8 Praetorius, Dirk 8 Rebholz, Leo G. 8 Xia, Jianlin 7 Martinsson, Per-Gunnar 6 Gillman, Adrianna 6 Grasedyck, Lars 6 Kressner, Daniel 6 Melenk, Jens Markus 5 Greengard, Leslie F. 5 Xiao, Jinyou 4 Ambikasaran, Sivaram 4 Chaillat, Stéphanie 4 Ho, Kenneth L. 4 Li, Xiaoye Sherry 4 Massei, Stefano 4 Ostrowski, Jörg 4 Robol, Leonardo 4 Sauter, Stefan A. 4 Tausch, Johannes 4 Xiao, Mengying 3 Ferri Aliabadi, Mohammad Hossien 3 Ballani, Jonas 3 Barnett, Alex H. 3 Bebendorf, Mario 3 Benner, Peter 3 Bini, Dario Andrea 3 Carstensen, Carsten 3 Coulier, Pieter 3 de Hoop, Maarten V. 3 Dölz, Jürgen 3 Harbrecht, Helmut 3 Khoromskij, Boris N. 3 Kriemann, Ronald 3 Li, Shengguo 3 Mach, Thomas 3 Oseledets, Ivan V. 3 Pan, Victor Yakovlevich 3 Ravnik, Jure 3 Rouet, François-Henry 3 Tuminaro, Raymond S. 2 Aminfar, AmirHossein 2 Balakrishnan, Venkataramanan 2 Beer, Gernot 2 Benedetti, Ivano 2 Betcke, Timo 2 Boman, Erik G. 2 Börst, Christina 2 Cai, Wei 2 Cambier, Léopold 2 Cauley, Stephen 2 Chen, Chao 2 Chow, Edmond G. W. 2 Ciarlet, Patrick jun. 2 Copeland, Dylan M. 2 Corona, Eduardo 2 Dopico, Froilán M. 2 Espig, Mike 2 Fan, Yuwei 2 Faustmann, Markus 2 Gander, Martin Jakob 2 Gatto, Paolo 2 Gopalakrishnan, Jayadeep 2 Gu, Ming 2 Hesthaven, Jan S. 2 Hiptmair, Ralf 2 Hu, Xiaozhe 2 Jiang, Shidong 2 Jiang, Ying 2 John, Volker 2 Karniadakis, George Em 2 Kitanidis, Peter K. 2 Kurz, Stefan 2 Layton, William J. 2 Li, Yingzhou 2 Lin, Lin 2 Liu, Xiao 2 Meszmer, Peter 2 Müller, Eike Hermann 2 Napov, Artem 2 Oh, Minah 2 Owhadi, Houman 2 Peters, Michael D. 2 Pomés, Kenet 2 Pouransari, Hadi 2 Rajamanickam, Sivasankaran 2 Reimer, Knut 2 Rokhlin, Vladimir 2 Rong, Yao 2 Scheichl, Robert 2 Schmitz, Phillip G. 2 Schöps, Sebastian 2 Škerget, Leopold 2 Tibaut, Jan 2 Venn, Raoul 2 Wang, Shaobo ...and 320 more Authors all top 5 Cited in 54 Serials 26 Journal of Computational Physics 26 SIAM Journal on Scientific Computing 15 Numerische Mathematik 15 Engineering Analysis with Boundary Elements 14 Computer Methods in Applied Mechanics and Engineering 13 Computing 12 SIAM Journal on Matrix Analysis and Applications 10 Computing and Visualization in Science 9 Mathematics of Computation 9 Journal of Computational and Applied Mathematics 9 Journal of Scientific Computing 7 Numerical Linear Algebra with Applications 5 Applied Numerical Mathematics 5 Linear Algebra and its Applications 4 Journal of Mathematical Analysis and Applications 4 Computational Mechanics 4 Advances in Computational Mathematics 3 Computers & Mathematics with Applications 3 Communications on Pure and Applied Mathematics 3 BIT 3 International Journal for Numerical Methods in Engineering 3 Numerical Algorithms 3 Applied and Computational Harmonic Analysis 3 Journal of Numerical Mathematics 2 Applied Mathematics and Computation 2 COMPEL 2 SIAM Review 2 Multiscale Modeling & Simulation 2 Mathematical Geosciences 2 Research in the Mathematical Sciences 1 International Journal of Solids and Structures 1 Inverse Problems 1 Journal of Engineering Mathematics 1 ACM Transactions on Mathematical Software 1 Calcolo 1 Mathematics and Computers in Simulation 1 Numerical Functional Analysis and Optimization 1 SIAM Journal on Numerical Analysis 1 Optimal Control Applications & Methods 1 Zeitschrift für Analysis und ihre Anwendungen 1 Bulletin of the Iranian Mathematical Society 1 Constructive Approximation 1 Journal of Integral Equations and Applications 1 Journal of Mathematical Imaging and Vision 1 Journal of Mathematical Sciences (New York) 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Vietnam Journal of Mathematics 1 Computational Geosciences 1 International Journal of Computational Methods 1 GAMM-Mitteilungen 1 SIAM Journal on Imaging Sciences 1 S\(\vec{\text{e}}\)MA Journal 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 SIAM/ASA Journal on Uncertainty Quantification all top 5 Cited in 33 Fields 225 Numerical analysis (65-XX) 74 Partial differential equations (35-XX) 24 Linear and multilinear algebra; matrix theory (15-XX) 23 Fluid mechanics (76-XX) 22 Optics, electromagnetic theory (78-XX) 17 Integral equations (45-XX) 17 Mechanics of deformable solids (74-XX) 11 Probability theory and stochastic processes (60-XX) 10 Computer science (68-XX) 8 Approximations and expansions (41-XX) 6 Operator theory (47-XX) 6 Geophysics (86-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Potential theory (31-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Statistics (62-XX) 4 Operations research, mathematical programming (90-XX) 4 Biology and other natural sciences (92-XX) 3 Functions of a complex variable (30-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Information and communication theory, circuits (94-XX) 2 Combinatorics (05-XX) 2 Field theory and polynomials (12-XX) 2 Ordinary differential equations (34-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) Citations by Year