mm

Michael Multerer

Università della Svizzera italiana

http://usi.to/3ps

Publications


Journal articles

  1. H. Harbrecht, M. Peters, and R. Schneider. On the low-rank approximation by the pivoted Cholesky decomposition. Appl. Numer. Math., 62:28-440, 2012.
  2. H. Harbrecht and M. Peters. Comparison of fast boundary element methods on parametric surfaces. Comput. Methods Appl. Mech. Engrg., 261-262:39–55, 2013.
  3. 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.
  4. 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.
  5. H. Harbrecht, M. Peters, and M. Siebenmorgen. Efficient approximation of random fields for numerical applications. Numer. Linear Algebra Appl., 22(4):596–617, 2015.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. H. Harbrecht and M. D. Peters. The second order perturbation approach for PDEs on random domains. Appl. Numer. Math., 125:159–171, 2018.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. M. D. Multerer. A note on the domain mapping method with rough coefficients. Appl. Numer. Math., 145:283-296, 2019.
  21. 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.
  22. 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.
  23. 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.
  24. H. Harbrecht and M. Multerer. A fast direct solver for nonlocal operators in wavelet coordinates. J. Comput. Phys., 428:110056, 2021.
  25. 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.
  26. 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.
  27. 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.
  28. W. Huang and M. Multerer. Isogeometric analysis of diffusion problems on random surfaces. Appl. Numer. Math., 179:50-65, 2022.
  29. H. Harbrecht and M. Multerer. Samplets: Construction and scattered data compression. J. Comput. Phys. 471:111616, 2022.
  30. 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.
  31. 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.
  32. H. Harbrecht, M. Multerer, O. Schenk, and C. Schwab. Multiresolution kernel matrix algebra. Numer. Math., 156(3):1085–1114, 2024.
  33. M. Multerer, P. Schneider, and R. Sen. Fast empirical scenarios. J. Comput. Math. Data Sci., 12:100099, 2024.

Peer-reviewed book chapters

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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

  1. H. Harbrecht and M. Multerer. Algorithmische Mathematik. Springer Spektrum, Berlin, Heidelberg, 2022.

Theses

  1. M. Peters. Numerische Lösung von Eigenwertproblemen kompakter, symmetrischer Integraloperatoren. Diploma thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, 2010. Link
  2. M. Peters. Numerical methods for boundary value problems on random domains. PhD thesis, Universität Basel, 2014. Link