Publications
Journal articles
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J. Dölz, W. Huang, and M. Multerer.
p-Multilevel Monte Carlo for acoustic scattering from large deviation
rough random surfaces.
SIAM/ASA J. Uncertain. Quantif., 13(4):1950–1971, 2025.
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S. Avesani, R. Kempf, M. Multerer, and H. Wendland.
Multiscale scattered data analysis in samplet coordinates.
SIAM J. Sci. Comput., 47(5):A3038–A3063, 2025.
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H. Harbrecht, M. Multerer, and J. Quizi.
The dimension weighted fast multipole method for scattered data
approximation. J. Comput. Phys., 532:113956, 2025.
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W. Huang, M. Valsecchi, and M. Multerer.
Anisotropic multiresolution analyses for deepfake detection.
Pattern Recognit., 164:111551, 2025.
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H. Harbrecht, R. Kempf, and M. Multerer.
Construction of quasi-localized dual bases in reproducing kernel
Hilbert spaces.
J. Comput. Appl. Math., 465:116545, 2025.
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D. Filipovic, M. Multerer, and P. Schneider.
Adaptive joint distribution learning.
SIAM J. Math. Data Sci., 7:28–54, 2025.
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J. Dölz, H. Harbrecht, and M. Multerer.
Solving acoustic scattering problems by the isogeometric boundary
element method. Eng. Comput., 40:3651–3661, 2024.
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M. Multerer, P. Schneider, and R. Sen. Fast empirical scenarios.
J. Comput. Math. Data Sci., 12:100099, 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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D. Baroli, H. Harbrecht, and M. Multerer.
Samplet basis pursuit: Multiresolution scattered data approximation
with sparsity constraints.
IEEE Trans. Signal Process., 72:1813–1823, 2024.
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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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H. Harbrecht and M. Multerer. Samplets: Construction and scattered
data compression. J. Comput. Phys., 471:111616, 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, 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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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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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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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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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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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. 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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M. D. Multerer. A note on the domain mapping method with rough
coefficients. Appl. Numer. Math., 145:283–296, 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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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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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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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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R. N. Gantner and M. D. Peters. Higher order quasi-Monte Carlo for
Bayesian shape inversion.
SIAM/ASA J. Uncertain. Quantif., 6(2):707–736, 2018.
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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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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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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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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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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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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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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. 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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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. Efficient approximation
of random fields for numerical applications. Numer. Linear Algebra Appl.,
22(4):596–617, 2015.
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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. Combination technique
based k-th moment analysis of elliptic problems with random diffusion.
J. Comp. Phys., 252:128–141, 2013.
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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 R. Schneider.
On the low-rank approximation by the pivoted Cholesky decomposition.
Appl. Numer. Math., 62:28–440, 2012.
Peer-reviewed book chapters
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V. Ghidini, M. Multerer, J. Quizi, and R. Sen.
Observation-specific explanations through scattered data
approximation. In Explainable Artificial Intelligence,
xAI 2024 Conference Proceedings, pages 335–345,
Springer, Cham, 2024.
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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.
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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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H. Harbrecht and M. Peters. Solution of free boundary problems in
the presence of geometric uncertainties.
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–Boston, 2017.
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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, Cham, 2016.
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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.
Books
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H. Harbrecht and M. Multerer. Algorithmische Mathematik.
Springer Spektrum, Berlin, Heidelberg, 2022.
Theses
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M. Peters. Numerical methods for boundary value problems on random
domains. PhD thesis, Universität Basel, 2014.
Link
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M. Peters. Numerische Lösung von Eigenwertproblemen kompakter,
symmetrischer Integraloperatoren. Diploma thesis, Rheinische
Friedrich-Wilhelms-Universität Bonn, 2010.
Link