papers TUBS

2024

A. Eftekhari, L. Gaedke-Merzhäuser, D. Pasadakis, M. Bollhöfer, S. Scheidegger, O. Schenk. Algorithm1042: Sparse Precision Matrix Estimation With SQUIC.
ACM Transactions on Mathematical Software 50(2):13:1-13:18, 2024 DOI:10.1145/3650108, Collected Algorithms.

2

L. Hermann, M. Bollhöfer, U Römer. Statistical reduced order modelling for the parametric Helmholtz equation.
arXiv:2407.04438, DOI:10.48550/arXiv.2407.04438, submitted.

3

Y. Hüpel, U. Römer, M. Bollhöfer, S. Langer. Efficient low rank model order reduction of vibroacoustic problems under stochastic loads.
arXiv:2408.08402, DOI:10.48550/arXiv.2408.08402, submitted.

2023

1

D. Pasadakis, M. Bollhöfer, and O. Schenk. Sparse Quadratic Approximation for Graph Learning.
IEEE Transactions on Pattern Analysis and Machine Intelligence 45(9):11256-11269, 2023 DOI:10.1109/TPAMI.2023.3263969.

2022

1: D. Pasadakis, M. Bollhöfer, and O. Schenk. Sparse Quadratic Approximation for Graph Learning.
DOI:10.36227/techrxiv.19635990.v1.

2021

1

Matthias Bollhöfer, Olaf Schenk, Fabio Verbosio. A High Performance Level-Block Approximate LU Factorization Preconditioner Algorithm.
Applied Numerical Mathematics 162:265-282, 2021. ISSN: 0168-9274. DOI:10.1016/j.apnum.2020.12.023.

2

A. Eftekhari, D. Pasadakis, M. Bollhöfer, S. Scheidegger, and O. Schenk. Block-Enhanced Precision Matrix Estimation for Large-Scale Datasets.
Journal of Computational Science 53(101389):1-13, 2021. ISSN: 1877-7503. DOI:10.1016/j.jocs.2021.101389.

3

U. Römer, M. Bollhöfer, H. K. Sreekumar, C. Blech, S. C. Langer. An adaptive sparse grid rational Arnoldi method for uncertainty quantification of dynamical systems in the frequency domain.
International Journal for Numerical Methods in Engineering 122(20):5487-5511, 2021. ISSN: 1097-0207. DOI:10.1002/nme.6761.

4

A. Eftekhari, L. Gaedke-Merzhäuser, D. Pasadakis, M. Bollhöfer, S. Scheidegger, and O. Schenk. Large-Scale Precision Matrix Estimation With SQUIC.
submitted, 2021. DOI:10.2139/ssrn.3904001.

5

C. Blech, H.K. Sreekumar, U. Römer, M. Bollhöfer, S.C. Langer. Ein adaptives hybrides Verfahren zur Modellordnungsreduktion von dynamischen Systemen im Frequenzbereich.
Fortschritte der Akustik, DAGA 2021, Jahrestagung der Deutschen Gesellschaft für Akustik, Wien, 2021.

2020

1

Matthias Bollhöfer, Olaf Schenk, Radim Janalik, Steve Hamm, Kiran Gullapalli. State-of-The-Art Sparse Direct Solvers. in Parallel Algorithms in Computational Science and Engineering, Ananth Grama, Ahmed H. Sameh (eds.), ISBN 978-3-030-43735-0, pp.3-33, 2020. DOI:10.1007/978-3-030-43736-7_1.

2

Patrick Sanan, Dave A. May, Matthias Bollhöfer, and Olaf Schenk. Pragmatic Solvers for 3D Stokes and Elasticity Problems with Heterogeneous Coefficients: Evaluating Modern Incomplete LDL^T Preconditioners.
Solid Earth 11:2031-2045, 2020. DOI:10.5194/se-2020-79.

2019

1

M. Bollhöfer, A. Eftekhari, S. Scheidegger, and O. Schenk. Large-Scale Sparse Inverse Covariance Matrix Estimation.
SIAM J. Sci. Comput., 41(1), A380-A401, 2019. DOI:10.1137/17M1147615.

2

Matthias Bollhöfer, Olaf Schenk, Fabio Verbosio. High Performance Block Incomplete LU Factorization. arXiv:1908.10169, submitted.

3

Amin Rafiei, Matthias Bollhöfer, Fayssal Benkhaldoun. A block version of left-looking AINV preconditioner with one by one or two by two block pivots.
Applied Mathematics and Computation 350 (2019) 366-385. DOI:10.1016/j.amc.2019.01.012.

2018

1

J.I. Aliaga, M. Bollhöfer, E. Dufrechou, P. Ezzatti, E.S. Quintana-Orti. Extending ILUPACK with a Task-Parallel Version of BiCG for Dual-GPU Servers.
PMAM'18 Proceedings of the 9th International Workshop on Programming Models and Applications for Multicores and Manycores, 2018:71-78. DOI: 10.1145/3178442.3178450.

2

A. Eftekhari, M. Bollhöfer, and O. Schenk. Distributed Memory Sparse Inverse Covariance Matrix Estimation on High-Performance Computing Architectures.
In Proceedings of the ACM/IEEE International Conference on High Performance Computing, Networking, Storage and Analysis (SC18), 2018 (acceptance rate: 19% (54/288)). DOI:10.1109/SC.2018.00023

2017

1

J.I. Aliaga, M. Barreda, G. Flegar, M. Bollhöfer, E.S. Quintana-Orti. Communication in task-parallel ILU-preconditioned CG solvers using MPI + OmpSs.
Concurrency and Computation 29(21):e4280,1-18, 2017. ISSN: 1532-0634. DOI:10.1002/cpe.4280.

2

Matthias Bollhöfer and Andre K. Eppler. Low-Rank Cholesky Factor Krylov Subspace Methods for Generalized Projected Lyapunov Equations. System Reduction for Nanoscale IC Design, P. Benner, ed., Series Mathematics in Industry, 20:157-193, (Springer), 2017. ISBN 978-3-319-07235-7.

2016

1

J.I. Aliaga, R.M. Badia, M. Barreda, M. Bollhöfer, E. Dufrechou, P. Ezzatti, E.S. Quintana-Orti. Exploiting task and data parallelism in ILUPACK's preconditioned CG solver on NUMA architectures and many-core accelerators.
Parallel Computing 54:97-107, 2016. ISSN: 0167-8191. DOI:10.1016/j.parco.2015.12.004.

2

J.I. Aliaga, M. Barreda, M. Bollhöfer, E.S. Quintana-Orti. Exploiting task-parallelism in message-passing sparse linear system solvers using OmpSs.
In: Dutot PF., Trystram D. (eds) Euro-Par 2016: Parallel Processing. Euro-Par 2016. Lecture Notes in Computer Science, vol 9833, 631-643. Springer, Cham. ISBN 978-3-319-43658-6. DOI:10.1007/978-3-319-43659-3_46.

3

J.I. Aliaga, M. Bollhöfer, E. Dufrechou, P. Ezzatti, E.S. Quintana-Orti. A Data-Parallel ILUPACK for Sparse General and Symmetric Indefinite Linear Systems.
in: Desprez F. et al. (eds) Euro-Par 2016: Parallel Processing Workshops. Euro-Par 2016. Lecture Notes in Computer Science, vol 10104. Springer, Cham, 2017. 978-3-319-58942-8. DOI: 10.1007/978-3-319-58943-5_10.

4

M. Bebendorf, M. Bollhöfer, and M. Bratsch. On the spectral equivalence of hierarchical matrix preconditioners for elliptic problems. Mathematics of Computation, 85:2839-2861, 2016. ISSN: 0025-5718. DOI:10.1090/mcom/3086.

2015

1: Matthias Bollhöfer. Algebraic Preconditioning Approaches and Their Applications
Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, pp. 257-295, 2015, P. Benner et al eds. ISBN 978-3-319-15259-2. DOI:10.1007/978-3-319-15260-8_10

2014

1
J. I. Aliaga, R.M.Badia, M. Barreda, M. Bollhöfer, E. S. Quintana-Orti. Leveraging Task-Parallelism with OmpSs in ILUPACK's Preconditioned CG Method.
Computer Architecture and High Performance Computing (SBAC-PAD), 2014 IEEE 26th International Symposium on, pp.262-269, 2014. ISSN: 1550-6533. DOI:10.1109/SBAC-PAD.2014.24

2
J.I. Aliaga, M. Bollhöfer, E. Dufrechou, P. Ezzatti, E.S. Quintana-Orti. Leveraging data-parallelism in ILUPACK using graphics processors
2014 IEEE 13th International Symposium on Parallel and Distributed Computing, 2014:119-126. DOI: 10.1109/ISPDC.2014.19

3
Andre Bodendiek and Matthias Bollhöfer. Adaptive expansion point selection for rational Arnoldi-type methods in model order reduction of Maxwell's equations.
BIT Numerical Mathematics 54(2):357-380, 2014. ISSN: 0006-3835. DOI:10.1007/s10543-013-0458-9

4
Amin Rafiei, Behnaz Tolue, Matthias Bollhöfer. Complete pivoting strategy for the left-looking Robust Incomplete Factorization preconditioner.
Computers & Mathematics with Applications 67(11):2055-2070, 2014. ISSN: 08981221. DOI:10.1016/j.camwa.2014.04.013

2013

1
M. Bebendorf, M. Bollhöfer, and M. Bratsch. Hierarchical matrix approximation with blockwise constraints. BIT Numerical Mathematics 53(2):311-339, 2013. ISSN: 0006-3835. DOI:10.1007/s10543-012-0413-1

2
Andre Bodendiek and Matthias Bollhöfer. Efficient Krylov subspace methods in moment matching based model order reduction. Technical report.

3
Andre Bodendiek and Matthias Bollhöfer. A modified adaptive-order rational Arnoldi method for model order reduction.
Proceedings in Applied Mathematics and Mechanics 13(1):415-416, 2013. ISSN: 1617-7061. DOI:10.1002/pamm.201310203

2012

1
J.I. Aliaga, M. Bollhöfer, A. Martin and E. Quintana-Orti. ILUPACK, Invited Book Chapter in Springer Encyclopedia of Parallel Computing, David Padua (Ed.), Springer, pp. 917-926, 2012. ISBN: 978-0-387-09765-7 DOI:10.1007/978-0-387-09766-4

2
J.I. Aliaga, M. Bollhöfer, A. Martin and E. Quintana-Orti. Parallelization of Multilevel ILU Preconditioners on Distributed-Memory Multiprocessors.
Applied Parallel and Scientific Computing ,10th International Conference, PARA 2010, Reykjavik, Iceland, June 6-9, 2010, Revised Selected Papers, Part I, Lecture Notes in Computer Science 7133 (K. Jonasson ed.), pp. 162-172, 2012.ISBN 978-3-642-28150-1. DOI:10.1007/978-3-642-28151-8

3
Matthias Bollhöfer and Stephane Lanteri. Block preconditioning strategies for high order finite element discretization of the time-harmonic Maxwell equations. Scientific Computing in Electrical Engineering SCEE 2010, Mathematics in Industry, Vol. 16, B. Michielsen, J.-R. Poirier (eds), p.25-34, 2012. ISBN 978-3-642-22452-2. DOI:10.1007/978-3-642-22453-9

4
Aldo Bonfiglioli, Sergio Campobasso, Bruno Carpentieri, and Matthias Bollhöfer.
A parallel 3D unstructured implicit RANS solver for compressible and incompressible CFD simulations.
Parallel Processing and Applied Mathematics, Part II, Lecture Notes in Computer Science 7204 (R. Wyrzykowski et al. eds.), pp. 313-322, 2012. ISBN 978-3-642-31499-5. DOI:10.1007/978-3-642-31500-8

5
B. Carpentieri, M. Bollhöfer. Symmetric Inverse-Based Multilevel ILU Preconditioning for Solving Dense Complex Non-Hermitian Systems in Electromagnetics Progress In Electromagnetics Research 128:55-74, 2012. ISSN: 1070-4698. DOI:10.2528/PIER12041006

6
A. Eppler, M. Bollhöfer. Structure-preserving GMRES methods for solving large Lyapunov equations. Progress in Industrial Mathematics at ECMI 2010, Mathematics in Industry, Vol. 17, Günther, M.; Bartel, A.; Brunk, M.; Schoeps, S.; Striebel, M. (eds.), pp.131-136, 2012. ISBN 978-3-642-25099-6. DOI:10.1007/978-3-642-25100-9

2011

1
J.I. Aliaga, M. Bollhöfer, A. Martin and E. Quintana-Orti.
Exploiting Thread-Level Parallelism in the Iterative Solution of Sparse Linear Systems.
Parallel Computing 37(3):183-202, 2011. ISSN: 0167-8191. DOI:10.1016/j.parco.2010.11.002.

2010

1
A. Eppler, M. Bollhöfer. An alternative way of solving large Lyapunov equations. Proceedings in Applied Mathematics and Mechanics 10(1):547-548, 2010. ISSN: 1617-7061. DOI:10.1002/pamm.201010266
2
Amin Rafiei, Matthias Bollhöfer.
Robust incomplete factorization for nonsymmetric matrices . Numerische Mathematik, 118(2):247-269, 2010. DOI:10.1007/s00211-010-0336-1

2009

1
J.I. Aliaga, M. Bollhöfer, A. Martin and E. Quintana-Orti.
Evaluation of Parallel Sparse Matrix Partitioning Software for Parallel Multilevel ILU Preconditioning on Shared-Memory Multiprocessors.
`Parallel Computing: From Multicores and GPUs to Petascale'. B. Chapman et al. eds. p.125-132, 2009. ISBN 978-1-60750-529-7. DOI:10.3233/978-1-60750-530-3-125

2
J.I. Aliaga, M. Bollhöfer, A. Martin and E. Quintana-Orti.
Recent advances in the parallel iterative solution of large-scale sparse linear systems Proceedings of the 2009 International Conference on Computational and Mathematical Methods in Science and Engineering. J. Vigo-Aguiar et al. eds. p.68-72. ISBN: 978-84-612-9727-6.

3
M. Bollhöfer and M. Grote and O. Schenk.
Algebraic Multilevel Preconditioner for the Helmholtz Equation in Heterogeous Media
SIAM J. Sci. Comput. 31(5):3781-3805, 2009. ISSN: 1064-8275. DOI:10.1137/080725702

2008

1
J.I. Aliaga, M. Bollhöfer, A. Martin and E. Quintana-Orti.
Scheduling Strategies for Parallel Sparse Backward/Forward Substitution.
Proceedings of the PARA 2008, 9th International Workshop on State-of-the-Art in Scientific and Parallel Computing, 2008. To appear in Lecture Notes in Computer Science Vol. 6126-6127

2
J.I. Aliaga, M. Bollhöfer, A. Martin and E. Quintana-Orti.
Design, Tuning and Evaluation of Parallel Multilevel ILU Preconditioners
High Performance Computing for Computational Science - VECPAR 2008, Lecture Notes in Computer Science 5336 (J. Palma et al. eds.), pp. 314-327, 2008. ISBN 978-3-540-92858-4. DOI:10.1007/978-3-540-92859-1_28

3
S.-M. Hong, C. Jungemann and M. Bollhöfer.
A Deterministic Boltzmann Equation Solver for Two-Dimensional Semiconductor Devices.
Simulation of Semiconductor Processes and Devices, 2008. SISPAD 2008. International Conference on, Hakone (Japan), pp.293-296, 2008. DOI:10.1109/SISPAD.2008.4648295

4
O. Schenk and M. Bollhöfer and R.A. Römer.
Selected SIGEST paper: On Large Scale Diagonalization Techniques for the Anderson Model of Localization.
SIAM Review, 50(1):91-112, 2008. ISSN: 0036-1445. SIGEST Introduction by the Editors. DOI:10.1137/070707002

2007

1
J. I. Aliaga, M. Bollhöfer, A. F. Martin and E. S. Quintana-Orti.
Parallelization of Multilevel Preconditioners Constructed from Inverse-Based ILUs on Shared-Memory Multiprocessors.
In `Parallel Computing: Architectures, Algorithms and Applications'. C. Bischof et al. eds. p.287-294. 2007. ISBN 978-3-9810843-4-4.

2
M. Bollhöfer, Y. Notay.
JADAMILU: a code for computing selected eigenvalues of large sparse symmetric matrices.
Comput. Phys. Commun. 177(12):951-964, 2007. ISSN: 0010-4655. DOI:10.1016/j.cpc.2007.08.004

3
Olaf Schenk, Matthias Bollhöfer and Rudolf A. Römer
On large-scale diagonalization techniques for the Anderson model of localization.
PAMM, 7(1):1021003-1021004, 2007. ISSN: 1617-7061. DOI: 10.1002/pamm.200700768
4
Peter Stange, Andreas Griewank, Matthias Bollhöfer
On the Efficient Update of Rectangular LU Factorizations subject to Low Rank Modifications.
ETNA, 26:161-177, 2007. ISSN: 1068-9613.

2006

1
M. Bollhöfer and Y. Saad.
Multilevel preconditioners constructed from inverse-based ILUs.
SIAM J. Sci. Comput., 27(5):1627-1650, 2006. ISSN: 1064-8275. DOI:10.1137/040608374

2
Matthias Bollhöfer, Olaf Schenk.
Combinatorial Aspects in Sparse Elimination Methods
GAMM Mitteilungen, Themenheft "Applied and Numerical Linear Algebra'', Part II, 29(2):342-367, 2006.
3
L. Horesh, M. Schweiger, M. Bollhöfer, A. Douiri, D.S. Holder and S.R. Arridge.
Multilevel preconditioning for 3D large-scale soft-field medical applications modelling.
Int. J. of Information and Systems Sciences, 2(4):532-556, 2006. ISSN: 1708-296X.

4
L. Horesh, M. Schweiger, M. Bollhöfer, A. Douiri, S.R. Arridge and D.S. Holder.
Novel Large-Scale 3D Electrical Impedance Tomography Modeling of the Human Head.
World Congress on Medical Physics and Biomedical Engineering, IFMBE Proceedings 14(27):3858-3861, 2006. DOI:10.1007/978-3-540-36841-0_976

5
Christoph Jungemann, A.T. Pham, Bernd Meinerzhagen, C. Ringhofer, Matthias Bollhöfer.
Stable discretization of the Boltzmann equation based on spherical harmonics, box integration, and a maximum entropy dissipation principle.
Journal of Applied Physics, 100(024502):1-13, 2006. ISSN: 0021-8979. DOI:10.1063/1.2212207

6
O. Schenk, M. Bollhöfer, M. Grote.
Algebraic Multilevel Preconditioning for Helmholtz Equations.
Proceedings of the ECCOMAS CFD 2006 Conference, 05.09.-08.09.2006, Egmond aan Zee, The Netherlands.

7
Olaf Schenk, Matthias Bollhöfer, Rudolf A. Römer
On Large Scale Diagonalization Techniques For The Anderson Model Of Localization
SIAM J. Scientific Computing (28) 2006:963-983. ISSN: 1064-8275. DOI:10.1137/050637649

2005

1
Christoph Jungemann, Bernd Meinerzhagen, Matthias Bollhöfer
Convergence of the Legendre Polynomial Expansion of the Boltzmann Equation for Nanoscale Devices
Proccedings of the 35-th ESSDERC, pp. 341-344, Grenoble (France), 2005 DOI:10.1109/ESSDER.2005.1546655

2
Olaf Schenk, Matthias Bollhöfer, Rudolf A. Römer
On Large Scale Diagonalization Techniques For The Anderson Model Of Localization
Preprint 15-2005, Institute of Mathematics, Technische Universität Berlin, 2005

2004

1
Matthias Bollhöfer.
A robust and efficient ILU that incorporates the growth of the inverse triangular factors.
SIAM J. Sci. Comput., 25(1):86-103, 2004. ISSN: 1064-8275. DOI:10.1137/S1064827502403411

2
M. Bollhöfer and V. Mehrmann.
Numerische Mathematik - Eine projektorientierte Einführung für Ingenieure, Mathematiker und Naturwissenschaftler.
Vieweg Wiesbaden, Dezember 2004. ISBN: 978-3-528-03220-3 Webseite mit Musteraufgaben.

2003

1
Matthias Bollhöfer.
Preconditioning Techniques for Unstructured Systems and Algebraic Multigrid Preconditioners.
Habilitation thesis, Technische Universität Berlin, Institut für Mathematik, Juni 2003.
2
Matthias Bollhöfer , V. Mehrmann.
Some convergence estimates for algebraic multilevel preconditioners.
In V. Olshevsky, editor, Fast Algorithms for Structured Matrices: Theory and Applications, 323:293-312. AMS, SIAM, 2003. ISBN-13: 978-0898715439

2002

1
Matthias Bollhöfer.
Adapted Sparse Approximate Inverse Smoothers in Algebraic Multilevel Methods .
Preprint 759-2002, Institute of Mathematics, Technische Universität Berlin, 2002.
2
Matthias Bollhöfer, Volker Mehrmann
Algebraic Multilevel Methods and Sparse Approximate Inverses.
SIAM J. Matrix Anal. Appl., 24(1):191-218, 2002. ISSN: 0895-4798. DOI:10.1137/S0895479899364441

3
Matthias Bollhöfer, Youcef Saad.
On the relations between ILUs and factored approximate inverses.
SIAM J. Matrix Anal. Appl., 24(1):219--237, 2002. ISSN: 0895-4798. DOI:10.1137/S0895479800372110

2001

1
Matthias Bollhöfer.
A Robust ILU Based on Monitoring the Growth of the Inverse Factors.
Linear Algebra Appl., 338(1-3):201-218, 2001. ISSN: 0024-3795. DOI:10.1016/S0024-3795(01)00385-8

2
Matthias Bollhöfer .
Geometrische und Algebraische Mehrgitterverfahren - Eine Einführung
Kursmaterial zum Kompaktkurs Iterative Gleichungssystemlöser und parallele Algorithmen, Uni Hamburg, 19.-23. Februar 2001. Vortragsfolien als PDF und PostScript
3
Matthias Bollhöfer , Youcef Saad.
A Factored Approximate Inverse Preconditioner with Pivoting
SIAM J. Matrix Anal. Appl., 23(3):692-705, 2001. ISSN: 0895-4798. DOI:10.1137/S0895479800372122

2000

1
Matthias Bollhöfer , Youcef Saad.
ILUs and Factorized Approximate Inverses are Strongly Related: Part 1: Overview of Results
University of Minnesota Supercomputing Institute Research Report UMSI 2000/39.

1999

1
Matthias Bollhöfer, Volker Mehrmann.
A New Approach to Algebraic Multilevel Methods Based on Sparse Approximate Inverses .
SFB 393 `Numerische Simulation auf massiv parallelen Rechnern' in Chemnitz, SFB393/99-22, 1999.

1998

1
Matthias Bollhöfer.
Algebraic Domain Decomposition
PhD Thesis of the Department of Mathematics, Chemnitz University of Technology, 1998.
2
Matthias Bollhöfer, Volker Mehrmann.
Nested divide and conquer methods for the solution of large sparse linear systems
SFB 393 `Numerische Simulation auf massiv parallelen Rechnern' in Chemnitz, SFB393/98-05, 1998.