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Börm, Steffen

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 Author ID: borm.steffen Published as: Börm, S.; Börm, Steffen External Links: ORCID · dblp
 Documents Indexed: 40 Publications since 2001, including 2 Books
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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
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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
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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)

Citations contained in zbMATH

32 Publications have been cited 408 times in 250 Documents Cited by Year
Introduction to hierarchical matrices with applications. Zbl 1035.65042
Börm, Steffen; Grasedyck, Lars; Hackbusch, Wolfgang
2003
Data-sparse approximation by adaptive $${\mathcal H}^2$$-matrices. Zbl 1012.65023
Hackbusch, W.; Börm, S.
2002
$$\mathcal H^2$$-matrix approximation of integral operators by interpolation. Zbl 1019.65103
Hackbusch, Wolfgang; Börm, Steffen
2002
Hybrid cross approximation of integral operators. Zbl 1104.65120
Börm, Steffen; Grasedyck, Lars
2005
Efficient numerical methods for non-local operators. $$\mathcal H^2$$-matrix compression, algorithms and analysis. Zbl 1208.65037
Börm, Steffen
2010
An introduction to hierarchical matrices. Zbl 1007.65032
Hackbusch, Wolfgang; Grasedyck, Lars; Börm, Steffen
2002
Approximation of solution operators of elliptic partial differential equations by $${\mathcal H}$$- and $${\mathcal H}^2$$-matrices. Zbl 1191.65148
Börm, Steffen
2010
Approximation of integral operators by variable-order interpolation. Zbl 1076.65121
Börm, Steffen; Löhndorf, Maike; Melenk, Jens M.
2005
$$\mathcal H$$-LU factorization in preconditioners for augmented Lagrangian and grad-div stabilized saddle point systems. Zbl 1426.76224
Börm, Steffen; Le Borne, Sabine
2012
Analysis of tensor product multigrid. Zbl 0973.65118
Börm, S.; Hiptmair, R.
2001
$$\mathcal H^2$$-matrix arithmetics in linear complexity. Zbl 1086.65036
Börm, S.
2006
Low-rank approximation of integral operators by interpolation. Zbl 1059.65121
Börm, Steffen; Grasedyck, Lars
2004
Construction of data-sparse $$\mathcal{H}^2$$-matrices by hierarchical compression. Zbl 1193.65043
Börm, Steffen
2009
Approximation of integral operators by $$\mathcal H^2$$-matrices with adaptive bases. Zbl 1082.65139
Börm, S.
2005
Multigrid computation of axisymmetric electromagnetic fields. Zbl 0998.65124
Börm, S.; Hiptmair, R.
2002
Data-sparse approximation of non-local operators by $$\mathcal H^2$$-matrices. Zbl 1115.65041
Börm, Steffen
2007
Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis. Zbl 1375.35098
Börm, Steffen; Melenk, Jens M.
2017
Hierarchical quadrature for singular integrals. Zbl 1068.65038
Börm, S.; Hackbusch, W.
2005
BEM with linear complexity for the classical boundary integral operators. Zbl 1069.65131
Börm, Steffen; Sauter, Stefan A.
2005
Directional $$\mathcal{H}^2$$-matrix compression for high-frequency problems. Zbl 06819613
Börm, Steffen
2017
Efficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updates. Zbl 1380.65461
Börm, Steffen; Reimer, Knut
2013
Adaptive variable-rank approximation of general dense matrices. Zbl 1159.65324
Börm, Steffen
2007
Approximation of boundary element operators by adaptive $${\mathcal H}^2$$-matrices. Zbl 1097.65119
Börm, Steffen; Hackbusch, Wolfgang
2004
Approximation of integral operators by Green quadrature and nested cross approximation. Zbl 1347.65181
Börm, Steffen; Christophersen, Sven
2016
Computing the eigenvalues of symmetric $$\mathcal{H}^2$$-matrices by slicing the spectrum. Zbl 1376.65044
Benner, Peter; Börm, Steffen; Mach, Thomas; Reimer, Knut
2013
Numerical methods for eigenvalue problems. Zbl 1254.65046
Börm, Steffen; Mehl, Christian
2012
May the singular integrals in BEM be replaced by zero? Zbl 1071.65159
Börm, S.; Krzebek, N.; Sauter, S. A.
2005
$$\mathcal H^2$$-matrices – multilevel methods for the approximation of integral operators. Zbl 1070.65124
Börm, Steffen
2004
An analysis of a butterfly algorithm. Zbl 1396.65171
Börm, S.; Börst, C.; Melenk, J. M.
2017
Low-rank approximation of integral operators by using the Green formula and quadrature. Zbl 1329.65314
Börm, Steffen; Gördes, Jessica
2013
$$\mathcal{H}^2$$-matrix compression. Zbl 1315.68111
Börm, Steffen
2012
Fast evaluation of boundary integral operators arising from an eddy current problem. Zbl 1117.78312
Börm, S.; Ostrowski, J.
2004
Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis. Zbl 1375.35098
Börm, Steffen; Melenk, Jens M.
2017
Directional $$\mathcal{H}^2$$-matrix compression for high-frequency problems. Zbl 06819613
Börm, Steffen
2017
An analysis of a butterfly algorithm. Zbl 1396.65171
Börm, S.; Börst, C.; Melenk, J. M.
2017
Approximation of integral operators by Green quadrature and nested cross approximation. Zbl 1347.65181
Börm, Steffen; Christophersen, Sven
2016
Efficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updates. Zbl 1380.65461
Börm, Steffen; Reimer, Knut
2013
Computing the eigenvalues of symmetric $$\mathcal{H}^2$$-matrices by slicing the spectrum. Zbl 1376.65044
Benner, Peter; Börm, Steffen; Mach, Thomas; Reimer, Knut
2013
Low-rank approximation of integral operators by using the Green formula and quadrature. Zbl 1329.65314
Börm, Steffen; Gördes, Jessica
2013
$$\mathcal H$$-LU factorization in preconditioners for augmented Lagrangian and grad-div stabilized saddle point systems. Zbl 1426.76224
Börm, Steffen; Le Borne, Sabine
2012
Numerical methods for eigenvalue problems. Zbl 1254.65046
Börm, Steffen; Mehl, Christian
2012
$$\mathcal{H}^2$$-matrix compression. Zbl 1315.68111
Börm, Steffen
2012
Efficient numerical methods for non-local operators. $$\mathcal H^2$$-matrix compression, algorithms and analysis. Zbl 1208.65037
Börm, Steffen
2010
Approximation of solution operators of elliptic partial differential equations by $${\mathcal H}$$- and $${\mathcal H}^2$$-matrices. Zbl 1191.65148
Börm, Steffen
2010
Construction of data-sparse $$\mathcal{H}^2$$-matrices by hierarchical compression. Zbl 1193.65043
Börm, Steffen
2009
Data-sparse approximation of non-local operators by $$\mathcal H^2$$-matrices. Zbl 1115.65041
Börm, Steffen
2007
Adaptive variable-rank approximation of general dense matrices. Zbl 1159.65324
Börm, Steffen
2007
$$\mathcal H^2$$-matrix arithmetics in linear complexity. Zbl 1086.65036
Börm, S.
2006
Hybrid cross approximation of integral operators. Zbl 1104.65120
Börm, Steffen; Grasedyck, Lars
2005
Approximation of integral operators by variable-order interpolation. Zbl 1076.65121
Börm, Steffen; Löhndorf, Maike; Melenk, Jens M.
2005
Approximation of integral operators by $$\mathcal H^2$$-matrices with adaptive bases. Zbl 1082.65139
Börm, S.
2005
Hierarchical quadrature for singular integrals. Zbl 1068.65038
Börm, S.; Hackbusch, W.
2005
BEM with linear complexity for the classical boundary integral operators. Zbl 1069.65131
Börm, Steffen; Sauter, Stefan A.
2005
May the singular integrals in BEM be replaced by zero? Zbl 1071.65159
Börm, S.; Krzebek, N.; Sauter, S. A.
2005
Low-rank approximation of integral operators by interpolation. Zbl 1059.65121
Börm, Steffen; Grasedyck, Lars
2004
Approximation of boundary element operators by adaptive $${\mathcal H}^2$$-matrices. Zbl 1097.65119
Börm, Steffen; Hackbusch, Wolfgang
2004
$$\mathcal H^2$$-matrices – multilevel methods for the approximation of integral operators. Zbl 1070.65124
Börm, Steffen
2004
Fast evaluation of boundary integral operators arising from an eddy current problem. Zbl 1117.78312
Börm, S.; Ostrowski, J.
2004
Introduction to hierarchical matrices with applications. Zbl 1035.65042
Börm, Steffen; Grasedyck, Lars; Hackbusch, Wolfgang
2003
Data-sparse approximation by adaptive $${\mathcal H}^2$$-matrices. Zbl 1012.65023
Hackbusch, W.; Börm, S.
2002
$$\mathcal H^2$$-matrix approximation of integral operators by interpolation. Zbl 1019.65103
Hackbusch, Wolfgang; Börm, Steffen
2002
An introduction to hierarchical matrices. Zbl 1007.65032
Hackbusch, Wolfgang; Grasedyck, Lars; Börm, Steffen
2002
Multigrid computation of axisymmetric electromagnetic fields. Zbl 0998.65124
Börm, S.; Hiptmair, R.
2002
Analysis of tensor product multigrid. Zbl 0973.65118
Börm, S.; Hiptmair, R.
2001
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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
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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
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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)