Publications "Bebendorf, Mario"

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Book / Monograph

Bebendorf, Mario:
Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems.
Berlin : Springer , 2008 . - 290 p. - (Lecture Notes in Computational Science and Engineering ; 63 )
ISBN 978-3-540-77146-3

DOI: https://doi.org/10.1007/978-3-540-77147-0

Article in a journal

Feist, Bernd ; Bebendorf, Mario:
Fractional Laplacian – Quadrature Rules for Singular Double Integrals in 3D.
In: Computational Methods in Applied Mathematics. Vol. 23 (2023) Issue 3 . - pp. 623-645.
ISSN 1609-4840
DOI: https://doi.org/10.1515/cmam-2022-0159

Gathungu, Duncan ; Bebendorf, Mario ; Borzì, Alfio:
Hierarchical-matrix method for a class of diffusion-dominated partial integro-differential equations.
In: Numerical Linear Algebra with Applications. Vol. 29 (2022) Issue 1 . - Nr. e2410.
ISSN 1099-1506
DOI: https://doi.org/10.1002/nla.2410

Bauer, Maximilian ; Bebendorf, Mario ; Feist, Bernd:
Kernel-independent adaptive construction of H²-matrix approximations.
In: Numerische Mathematik. Vol. 150 (2022) Issue 1 . - pp. 1-32.
ISSN 0029-599X
DOI: https://doi.org/10.1007/s00211-021-01255-y

Bauer, Maximilian ; Bebendorf, Mario:
Block-adaptive Cross Approximation of Discrete Integral Operators.
In: Computational Methods in Applied Mathematics. Vol. 21 (2021) Issue 1 . - pp. 13-29.
ISSN 1609-4840
DOI: https://doi.org/10.1515/cmam-2019-0085

Bebendorf, Mario:
Low-rank approximation of elliptic boundary value problems with high-contrast coefficients.
In: SIAM Journal on Mathematical Analysis. Vol. 48 (2016) Issue 2 . - pp. 932-949.
ISSN 1095-7154
DOI: https://doi.org/10.1137/140991030

Bebendorf, Mario ; Bollhöfer, Matthias ; Bratsch, Michael:
On the Spectral Equivalence of Hierarchical Matrix Preconditioners for Elliptic Problems.
In: Mathematics of Computation. Vol. 85 (2016) Issue 302 . - pp. 2839-2861.
ISSN 0025-5718
DOI: https://doi.org/10.1090/mcom/3086

Bebendorf, Mario ; Kuske, Christian ; Venn, Raoul:
Wideband nested cross approximation for Helmholtz problems.
In: Numerische Mathematik. Vol. 130 (2015) Issue 1 . - pp. 1-34.
ISSN 0029-599X
DOI: https://doi.org/10.1007/s00211-014-0656-7

Bebendorf, Mario ; Kuske, Christian:
Separation of variables for function generated high-order tensors.
In: Journal of Scientific Computing. Vol. 61 (2014) Issue 1 . - pp. 145-165.
ISSN 1573-7691

Bebendorf, Mario ; Hardesty, Sean:
Adaptive cross approximation of tensors arising in the discretization of boundary integral operator shape derivatives.
Universität Bonn, Institut für Numerische Simulation
In: Engineering Analysis with Boundary Elements. Vol. 37 (2013) Issue 1 . - pp. 60-67.
ISSN 0955-7997
DOI: https://doi.org/10.1016/j.enganabound.2012.09.003

Bebendorf, Mario ; Kühnemund, Andreas ; Rjasanow, S.:
An equi-directional generalization of adaptive cross approximation for higher-order tensors.
In: Applied Numerical Mathematics. Vol. 74 (2013) . - pp. 1-16.
ISSN 1873-5460
DOI: https://doi.org/10.1016/j.apnum.2013.08.001

Bebendorf, Mario ; Bollhöfer, Matthias ; Bratsch, Michael:
Hierarchical matrix approximation with blockwise constraints.
In: BIT Numerical Mathematics. Vol. 53 (2013) Issue 2 . - pp. 311-339.
ISSN 0006-3835
DOI: https://doi.org/10.1007/s10543-012-0413-1

Bebendorf, Mario ; Krämer, Florian:
Hierarchical Matrix Preconditioning for Low-Frequency–Full-Maxwell Simulations.
In: Proceedings of the IEEE. Vol. 101 (2013) Issue 2 . - pp. 423-433.
ISSN 0018-9219
DOI: https://doi.org/10.1109/JPROC.2012.2204849

Bebendorf, Mario ; Venn, Raoul:
Constructing nested bases approximations from the entries of non-local operators.
In: Numerische Mathematik. Vol. 121 (2012) Issue 4 . - pp. 609-635.
ISSN 0029-599X
DOI: https://doi.org/10.1007/s00211-012-0449-9

Bebendorf, Mario:
Adaptive Cross Approximation of Multivariate Functions.
In: Constructive Approximation. Vol. 34 (2011) Issue 2 . - pp. 149-179.
ISSN 0176-4276
DOI: https://doi.org/10.1007/s00365-010-9103-x

Bebendorf, Mario ; Fischer, T.:
On the purely algebraic data-sparse approximation of the inverse and the triangular factors of sparse matrices.
In: Numerical Linear Algebra with Applications. Vol. 18 (2011) Issue 1 . - pp. 105-122.
ISSN 1099-1506
DOI: https://doi.org/10.1002/nla.714

Brunner, D. ; Junge, M. ; Rapp, P. ; Bebendorf, Mario ; Gaul, L.:
Comparison of the fast multipole method with hierarchical matrices for the Helmholtz-BEM.
In: Computer Modeling in Engineering and Sciences. Vol. 58 (2010) Issue 2 . - pp. 131-160.
ISSN 1526-1492
DOI: https://doi.org/10.3970/cmes.2010.058.131

Ostrowski, Joerg Marc ; Bebendorf, Mario ; Hiptmair, Ralf ; Krämer, Florian:
H-matrix-based operator preconditioning for full Maxwell at low frequencies.
In: IEEE Transactions on Magnetics. Vol. 46 (2010) Issue 8 . - pp. 3193-3196.
ISSN 0018-9464
DOI: https://doi.org/10.1109/TMAG.2010.2042934

Bebendorf, Mario ; Ostrowski, Joerg Marc:
Parallel hierarchical matrix preconditioners for the curl-curl operator.
In: Journal of Computational Mathematics. Vol. 27 (2009) Issue 5 . - pp. 624-641.
ISSN 0771-050X
DOI: https://doi.org/10.4208/jcm.2009.27.5.014

Bebendorf, Mario ; Kunis, Stefan:
Recompression Techniques for Adaptive Cross Approximation.
In: Journal of Integral Equations and Applications. Vol. 21 (2009) Issue 3 . - pp. 331-357.
DOI: https://doi.org/10.1216/JIE-2009-21-3-331

Steinmetz, T. ; Gödel, N. ; Wimmer, G. ; Clemens, Markus ; Kurz, S. ; Bebendorf, Mario:
Efficient symmetric FEM-BEM coupled simulations of electro-quasistatic fields.
In: IEEE Transactions on Magnetics. Vol. 44 (2008) Issue 6 . - pp. 1346-1349.
ISSN 0018-9464
DOI: https://doi.org/10.1109/TMAG.2008.915785

Bebendorf, Mario ; Chen, Y.:
Efficient solution of nonlinear elliptic problems using hierarchical matrices with Broyden updates.
In: Computing. Vol. 81 (2007) Issue 4 . - pp. 239-257.
ISSN 1436-5057
DOI: https://doi.org/10.1007/s00607-007-0252-0

Smajić, Jasmin ; Andjelić, Zoran ; Bebendorf, Mario:
Fast BEM for Eddy-Current Problems Using H-Matrices and Adaptive Cross Approximation.
In: IEEE Transactions on Magnetics. Vol. 43 (2007) Issue 4 . - pp. 1269-1272.
ISSN 0018-9464
DOI: https://doi.org/10.1109/TMAG.2006.890971

Bebendorf, Mario ; Hackbusch, Wolfgang:
Stabilized rounded addition of hierarchical matrices.
In: Numerical Linear Algebra with Applications. Vol. 14 (2007) Issue 5 . - pp. 407-423.
ISSN 1099-1506
DOI: https://doi.org/10.1002/nla.525

Bebendorf, Mario:
Why finite element discretizations can be factored by triangular hierarchical matrices.
Universität Bonn, Institut für Numerische Simulation
In: SIAM Journal on Numerical Analysis. Vol. 45 (2007) Issue 4 . - pp. 1472-1494.
ISSN 1095-7170
DOI: https://doi.org/10.1137/060669747

Bebendorf, Mario ; Grzhibovskis, R.:
Accelerating Galerkin BEM for Linear Elasticity using Adaptive Cross Approximation.
In: Mathematical Methods in the Applied Sciences. Vol. 29 (2006) Issue 14 . - pp. 1721-1747.
ISSN 1099-1476
DOI: https://doi.org/10.1002/mma.759

Bebendorf, Mario:
Approximate Inverse Preconditioning of Finite Element Discretizations of Elliptic Operators with Nonsmooth Coefficients.
Universität Bonn, Institut für Numerische Simulation
In: SIAM Journal on Matrix Analysis and Applications. Vol. 27 (2006) Issue 4 . - pp. 909-929.
ISSN 0196-5212
DOI: https://doi.org/10.1137/S0895479803437621

Ostrowski, Joerg Marc ; Andjelić, Zoran ; Bebendorf, Mario ; Cranganu-Cretu, Bogdan ; Smajić, Jasmin:
Fast BEM-solution of Laplace problems with H-matrices and ACA.
In: IEEE Transactions on Magnetics. Vol. 42 (2006) Issue 4 . - pp. 627-630.
ISSN 0018-9464
DOI: https://doi.org/10.1109/TMAG.2006.871642

Bebendorf, Mario:
Efficient inversion of Galerkin matrix of general second-order elliptic operators with nonsmooth coefficients.
In: Mathematics of Computation. Vol. 74 (2005) . - pp. 1179-1199.
ISSN 0025-5718
DOI: https://doi.org/10.1090/S0025-5718-04-01716-8

Bebendorf, Mario ; Kriemann, R.:
Fast parallel solution of boundary integral equations and related problems.
In: Computing and Visualization in Science. Vol. 8 (2005) Issue 3-4 . - pp. 121-135.
ISSN 1433-0369
DOI: https://doi.org/10.1007/s00791-005-0001-x

Bebendorf, Mario:
Hierarchical LU decomposition-based preconditioners for BEM.
In: Computing. Vol. 74 (2005) . - pp. 225-247.
ISSN 1436-5057
DOI: https://doi.org/10.1007/s00607-004-0099-6

Bebendorf, Mario ; Rjasanow, S.:
Adaptive low-rank approximation of collocation matrices.
In: Computing. Vol. 70 (2003) Issue 1 . - pp. 1-24.
ISSN 1436-5057
DOI: https://doi.org/10.1007/s00607-002-1469-6

Bebendorf, Mario ; Hackbusch, Wolfgang:
Existence of H-matrix approximants to the inverse FE-matrix of elliptic operators with L-coefficients.
Universität Bonn, Institut für Numerische Simulation
In: Numerische Mathematik. Vol. 95 (2003) Issue 1 . - pp. 1-28.
ISSN 0029-599X
DOI: https://doi.org/10.1007/s00211-002-0445-6

Bebendorf, Mario ; Hackbusch, Wolfgang:
Low-rank approximation of FE matrix inverses for operators with jumping coefficients.
In: Proceedings in Applied Mathematics and Mechanics. Vol. 2 (2003) Issue 1 . - pp. 25-28.
ISSN 1617-7061
DOI: https://doi.org/10.1002/pamm.200310007

Bebendorf, Mario:
A note on the Poincaré inequality for convex domains.
In: Zeitschrift für Analysis und ihre Anwendungen. Vol. 22 (2003) Issue 4 . - pp. 751-756.
ISSN 1661-4534
DOI: https://doi.org/10.4171/ZAA/1170

Bebendorf, Mario:
Approximation of boundary element matrices.
Universität Bonn, Institut für Numerische Simulation
In: Numerische Mathematik. Vol. 86 (2000) Issue 4 . - pp. 565-589.
ISSN 0029-599X
DOI: https://doi.org/10.1007/PL00005410

Article in a book

Bebendorf, Mario ; Maday, Yvon ; Stamm, Benjamin:
Comparison of Some Reduced Representation Approximations.
In: Quarteroni, Alfio ; Rozza, Gianluigi (Hrsg.): Reduced Order Methods for Modeling and Computational Reduction. - Basel : Springer , 2014 . - pp. 67-100 . - (Modeling, Simulation and Applications ; 9 )
ISBN 978-3-319-02089-1
DOI: https://doi.org/10.1007/978-3-319-02090-7_3

Bartels, Sören ; Bebendorf, Mario ; Bratsch, Michael:
A Fast and Accurate Numerical Method for the Computation of Unstable Micromagnetic Configurations.
In: Griebel, Michael (Hrsg.): Singular Phenomena and Scaling in Mathematical Models. - Springer : Basel , 2014 . - pp. 413-434
ISBN 978-3-319-00785-4
DOI: https://doi.org/10.1007/978-3-319-00786-1_18

Bebendorf, Mario:
Wideband nested cross approximation for Helmholtz problems.
In: Oberwolfach reports, Vol. 10,1. - Oberwolfach , 2013 . - pp. 142-146
DOI: https://doi.org/10.4171/OWR/2013/03

Bebendorf, Mario ; Fischer, Thomas:
Efficient solution of non-linear systems at metal forming processes using hierarchical matrices.
In: Hirt, Gerhard (ed.): Modelling of incremental forming processes : Final report of the DFG priority programme SPP 1146. - Aachen : Shaker Verlag , 2010 . - pp. 195-213
ISBN 9783832295325

Bebendorf, Mario ; Ostrowski, Joerg Marc:
Hierarchical matrix preconditioners for the curl-curl operator.
In: Oberwolfach reports, Vol. 7,1. - Oberwolfach , 2010 . - pp. 424-428
DOI: https://doi.org/10.4171/OWR/2010/10

Krämer, Florian ; Bebendorf, Mario ; Ostrowski, Joerg Marc ; Hiptmair, Ralf:
Hierarchical matrix preconditioners for eddy current problems.
In: Institute of Electrical and Electronics Engineers: International Conference on Electromagnetics in Advanced Applications, 2009. - Piscataway, NJ : IEEE , 2009 . - pp. 724-727
ISBN 978-1-4244-3385-8
DOI: https://doi.org/10.1109/ICEAA.2009.5297293

Bebendorf, Mario ; Fischer, T.:
A Purely Algebraic Approach to Preconditioning Based on Hierarchical LU Factorizations.
In: Kunisch, Karl ; Of, Günther ; Steinbach, Olaf (Hrsg.): Numerical Mathematics and Advanced Applications : Proceedings of ENUMATH 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications, Graz, Austria, September 2007. - Berlin : Springer , 2008 . - pp. 135-142
ISBN 978-3-540-69777-0
DOI: https://doi.org/10.1007/978-3-540-69777-0_15

Bebendorf, Mario ; Kunis, Stefan:
Recompression Techniques for Adaptive Cross Approximation.
In: Trevelyan, J. (ed.): Advances in Boundary Integral Methods : Proceedings of the 6th UK Conference on Boundary Integral Methods. - Durham : Durham University , 2007 . - pp. 1-11

Steinmetz, T. ; Gödel, N. ; Wimmer, G. ; Clemens, Markus ; Kurz, S. ; Bebendorf, Mario ; Rjasanow, S.:
Symmetric Coupling of the Finite-Element and the Boundary-Element Method for Electro-Quasistatic Field Simulations.
In: Ciuprina, Gabriela ; Ioan, Daniel (Hrsg.): Scientific Computing in Electrical Engineering. - Berlin : Springer , 2007 . - pp. 309-315 . - (Mathematics in Industry ; 11 )
ISBN 978-3-540-71980-9
DOI: https://doi.org/10.1007/978-3-540-71980-9_33

Smajić, Jasmin ; Andjelić, Zoran ; Bebendorf, Mario:
Fast BEM for Eddy-Current Problems using H-Matrices and Adaptive Cross Approximation.
In: Electromagnetic Field Computation, 12th Biennial IEEE Conference. - Miami, Florida : Institute of Electrical and Electronics Engineers (IEEE) , 2006 . - p. 258

Smajić, Jasmin ; Cranganu-Cretu, Bogdan ; Andjelić, Zoran ; Bebendorf, Mario:
Fast multipole algorithm versus ACA in computational electromagnetics.
In: IABEM 2006 conference : Book of abstracts. - Graz, Österreich : Universität Graz , 2006 . - pp. 251-254
ISBN 3-902465-23-9

Ostrowski, Joerg Marc ; Andjelić, Zoran ; Cranganu-Cretu, Bogdan ; Bebendorf, Mario ; Smajić, Jasmin:
Fast BEM-Solution of Laplace problems with H-matrices and ACA.
In: Proceedings of the IEEE Compumag Conference 2005. - Shenyang, China : Institute of Electrical and Electronics Engineers (IEEE) , 2005

Bebendorf, Mario ; Rjasanow, S.:
Numerical Simulation of Exhaust Systems in Car Industry : Efficient Calculation of Radiation Heat Transfer.
In: Jäger, Willi ; Krebs, Hans-Joachim (Hrsg.): Mathematics - Key Technology for the Future. - Berlin : Springer , 2003 . - pp. 55-62
ISBN 978-3-642-62914-3
DOI: https://doi.org/10.1007/978-3-642-55753-8_5

Bebendorf, Mario ; Rjasanow, S. ; Tyrtyshnikov, E. E.:
Approximation using diagonal-plus-skeleton matrices.
In: Bonnet, Marc ; Sändig, Anna-Margarete ; Wendland, Wolfgang L. (Hrsg.): Mathematical aspects of boundary element methods. - Boca Raton, FL : Chapman & Hall/CRC , 2000 . - pp. 45-52 . - (Chapman & Hall/CRC Research Notes in Mathematics Series ; 414 )
ISBN 1-58488-006-6

Bebendorf, Mario ; Rjasanow, S.:
Matrix Compression for the Radiation Heat Transfer in Exhaust Pipes.
In: Sändig, Anna-Margarete ; Schiehlen, Werner ; Wendland, Wolfgang L. (Hrsg.): Multifield Problems : State of the Art. - Berlin : Springer , 2000 . - pp. 183-192
ISBN 978-3-662-04015-7
DOI: https://doi.org/10.1007/978-3-662-04015-7_20

Bakema, Jos ; Bebendorf, Mario ; Laitinen, Mika ; Pessl, Günther ; Stefanidis, Vassilios:
Solder spreading.
In: Proceedings of the 1995 ECMI Modelling Week in Glasgow. - Glasgow : University of Strathclyde , 1996 . - pp. 4-14

Conference item

Bauer, Maximilian ; Bebendorf, Mario:
The Coupling of low-rank Approximations with the Solution Process for discretised Boundary Integral Equations.
2019
Event: International Conference on Scientific Computation and Differential Equations (SciCADE 2019) , 22.-26.7.2019 , Innsbruck, Österreich.
(Conference item: Conference , Speech )

Feist, Bernd ; Bebendorf, Mario:
Fractional Laplacian : Approximation of the Dense FEM Stiffness matrix by H-Matrices.
2019
Event: International Conference on Scientific Computation and Differential Equations (SciCADE 2019) , 22.-26.7.2019 , Innsbruck, Österreich.
(Conference item: Conference , Speech )

Bauer, Maximilian ; Bebendorf, Mario:
Additional adaptive methods for the cross approximation of BEM-matrices.
2017
Event: 15. Workshop on Fast Boundary Element Methods in Industrial Applications , 12.-15.10.2017 , Hirschegg, Österreich.
(Conference item: Workshop , Speech )

Bebendorf, Mario:
Mathematik an der Universität Bayreuth.
2016
Event: Hochschultag an der Hochschule Hof , 5.3.2016 , Hof.
(Conference item: Other Event type, Speech )

Bebendorf, Mario:
Mathematik an der Universität Bayreuth.
2016
Event: Hochschultag an der Universität Bayreuth , 18.2.2016 , Bayreuth.
(Conference item: Other Event type, Speech )

Preprint, postprint

Bauer, Maximilian ; Bebendorf, Mario ; Feist, Bernd:
Kernel-independent adaptive construction of H²-matrix approximations.
Bayreuth , 2020 . - 24 p.

Doctoral thesis

Bebendorf, Mario:
Effiziente numerische Lösung von Randintegralgleichungen unter Verwendung von Niedrigrang-Matrizen.
Berlin : dissertation.de , 2001 . - II, 119 p.
ISBN 3-89825-183-7
( Doctoral thesis, 2000 , Universität Saarbrücken)

Habilitation thesis

Bebendorf, Mario:
Hierarchical Matrices : a Means to Efficiently Solve Elliptic Boundary Value Problems.
Leipzig , 2007
( Habilitation thesis, 2007 , Universität Leipzig)

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