Publications
Journal articles
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H. Harbrecht, M. Peters, and R. Schneider.
On the low-rank approximation by the pivoted Cholesky decomposition.
Appl. Numer. Math., 62:28-440, 2012.
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H. Harbrecht and M. Peters. Comparison of fast boundary element
methods on parametric surfaces. Comput. Methods Appl. Mech. Engrg.,
261-262:39–55, 2013.
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H. Harbrecht, M. Peters, and M. Siebenmorgen. Combination technique
based k-th moment analysis of elliptic problems with random diffusion.
J. Comp. Phys., 252:128–141, 2013.
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J. Dölz, H. Harbrecht, and M. Peters. H-matrix accelerated second
moment analysis for potentials with rough correlation. J. Sci. Comput.,
65(1):387–410, 2015.
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H. Harbrecht, M. Peters, and M. Siebenmorgen. Efficient approximation
of random fields for numerical applications. Numer. Linear Algebra Appl.,
22(4):596–617, 2015.
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H. Harbrecht, M. Peters, and M. Siebenmorgen. Analysis of the domain
mapping method for elliptic diffusion problems on random domains.
Numer. Math., 134(4):823–856, 2016.
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H. Harbrecht, M. Peters, and M. Siebenmorgen. Multilevel accelerated
quadrature for PDEs with log-normally distributed random coefficient.
SIAM/ASA J. Uncertain. Quantif., 4(1):520–551, 2016.
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J. Dölz, H. Harbrecht, and M. Peters. An interpolation-based fast
multipole method for higher order boundary elements on parametric surfaces.
Int. J. Numer. Meth. Eng., 108(13):1705–1728, 2016.
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H. Harbrecht, M. Peters, and M. Siebenmorgen. On the quasi-Monte Carlo
quadrature with Halton points for elliptic PDEs with log-normal diffusion.
Math. Comput., 86:771–797, 2017.
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H. Harbrecht, M. D. Peters, and M. Schmidlin. Uncertainty
quantification for PDEs with anisotropic random diffusion. SIAM J. Numer. Anal.,
55(2):1002–1023, 2017.
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J. Ballani, D. Kressner, and M. D. Peters. Multilevel tensor
approximation of PDEs with random data. Stoch. Partial Differ. Equ. Anal. Comput.,
5(3):400–427, 2017.
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J. Dölz, H. Harbrecht, and M. D. Peters. H-matrix based second
moment analysis for rough random fields and finite element discretizations.
SIAM J. Sci. Comput., 39(4):B618–B639, 2017.
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M. Dambrine, H. Harbrecht, M. D. Peters, and B. Puig. On Bernoulli's free boundary
problem with a random boundary. Int. J. Uncertain. Quantif., 7(4):335–353, 2017.
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H. Harbrecht and M. D. Peters. The second order perturbation approach for PDEs on
random domains. Appl. Numer. Math., 125:159–171, 2018.
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R. N. Gantner and M. D. Peters. Higher order quasi-Monte Carlo for
Baysian shape inversion. SIAM/ASA J. on Uncertain. Quantif., 6(2):707-736, 2018.
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A.-L. Haji-Ali, H. Harbrecht, M. D. Peters, and M. Siebenmorgen. Novel results for the
anisotropic sparse grid quadrature. J. Complexity, 47:62-85, 2018.
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D. Barac, M. D. Multerer, and D. Iber. Global optimization using Gaussian processes to
estimate biological parameters from image data. J. Theor. Biol., 481:233-248, 2019.
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J. Dölz, H. Harbrecht, and M. D. Multerer. On the best approximation of the hierarchical
matrix product. SIAM J. Matrix Anal. Appl., 40(1):147–174, 2019.
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H. Harbrecht, N. Ilic, and M. D. Multerer. Rapid computation of far-field statistics for
random obstacle scattering. Eng. Anal. Bound. Elem., 101:243–251, 2019.
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M. D. Multerer. A note on the domain mapping method with rough coefficients. Appl.
Numer. Math., 145:283-296, 2019.
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M. Griebel, H. Harbrecht, and M. D. Multerer. Multilevel quadrature for elliptic parametric
partial differential equations in case of polygonal approximations of curved domains. SIAM
J. Numer. Anal. 58(1):684-705, 2020.
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J. Dölz, H. Harbrecht, S. Kurz, M. Multerer, S. Schöps, and F. Wolf. Bembel: The fast
isogeometric boundary element C++ library for Laplace, Helmholtz, and electric wave
equation. SoftwareX, 11:100476, 2020.
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M. Eigel, M. Marschall, and M. Multerer. An adaptive stochastic Galerkin tensor train
discretization for randomly perturbed domains. SIAM/ASA J. Uncertain. Quantif.,
8(3):1189-1214, 2020.
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H. Harbrecht and M. Multerer. A fast direct solver for nonlocal operators in wavelet
coordinates. J. Comput. Phys., 428:110056, 2021.
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L. Gander, R. Krause, M. Multerer, and S. Pezzuto. Space-time shape uncertainties in
the forward and inverse problem of electrocardiography. Int. J. Numer. Methods Biomed.
Eng., 37(10):e3522, 2021.
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J. Dölz, H. Harbrecht, C. Jerez-Hanckes, and M. Multerer. Isogeometric multilevel
quadrature for forward and inverse random acoustic scattering Comput. Methods Appl.
Mech. Eng., 388:114242, 2022.
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H. Harbrecht, M. Multerer, and R. von Rickenbach. Isogeometric shape optimization of
periodic structures in three dimensions. Comput. Methods Appl. Mech. Eng., 391:114552,
2022.
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W. Huang and M. Multerer. Isogeometric analysis of diffusion problems on random
surfaces. Appl. Numer. Math., 179:50-65, 2022.
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H. Harbrecht and M. Multerer. Samplets: Construction and scattered data compression.
J. Comput. Phys. 471:111616, 2022.
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S. Ben Bader, H. Harbrecht, R. Krause, M. Multerer, A. Quaglino, and M. Schmidlin.
Space-time multilevel quadrature methods and their application for cardiac
electrophysiology. SIAM/ASA J. Uncertain. Quantif., 11(4):1329–1356, 2023.
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D. Baroli, H. Harbrecht, and M. Multerer. Samplet basis pursuit: Multiresolution
scattered data approximation with sparsity constraints.
IEEE Trans. Sign. Proc., 72:1813-1823, 2024.
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H. Harbrecht, M. Multerer, O. Schenk, and C. Schwab. Multiresolution kernel matrix
algebra. Numer. Math., 156(3):1085–1114, 2024.
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M. Multerer, P. Schneider, and R. Sen. Fast empirical scenarios.
J. Comput. Math. Data Sci., 12:100099, 2024.
Peer-reviewed book chapters
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H. Harbrecht, M. Peters, and M. Siebenmorgen. On multilevel quadrature for elliptic
stochastic partial differential equations. In J. Garcke and M.
Griebel, editors, Sparse grids and applications, volume 88 of
Lecture Notes in Computational Science and Engineering,
pages 161–179, Springer, Berlin-Heidelberg, 2013.
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H. Harbrecht and M. Peters. Combination technique based second moment analysis for
elliptic PDEs on random domains. In J. Garcke and D. Pflüger, editors, Sparse Grids and
Applications, volume 109 of Lecture Notes in Computational Science and Engineering,
pages 51–77, Springer International Publishing, Cham, 2016.
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H. Harbrecht and M. Peters. Solution of free boundary problems in the presence of geometric
uncertainties. In: In Bergounioux, M., Oudet, E., Rumpf, M., Carlier, G., Champion,
T., and Santambrogio, F., editors, Topological Optimization and Optimal Transport in the
Applied Sciences, pages 20–39, de Gruyter, Berlin-Bosten, 2017.
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M. D. Multerer, L. D. Wittwer, A. Stopka, D. Barac, C. Lang, and D. Iber. Simulation of
morphogen and tissue dynamics. In J. Dubrulle, editor, Morphogen Gradients: Methods
and Protocols, pages 223–250, Humana Press, New York, 2018.
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M. Multerer and S. Pezzuto. Fast and accurate uncertainty quantification for the ECG with
random electrodes location. In D. B. Ennis, L. E. Perotti, V. Y. Wang, editors, Functional
Imaging and Modeling of the Heart. FIMH 2021, pages 561–572, Springer, Cham, 2021.
Books
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H. Harbrecht and M. Multerer. Algorithmische Mathematik. Springer
Spektrum, Berlin, Heidelberg, 2022.
Theses
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M. Peters. Numerische Lösung von Eigenwertproblemen kompakter,
symmetrischer Integraloperatoren. Diploma thesis, Rheinische
Friedrich-Wilhelms-Universität Bonn, 2010.
Link
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M. Peters. Numerical methods for boundary value problems on random
domains. PhD thesis, Universität Basel, 2014.
Link