Faculty of Informatics
Via Giuseppe Buffi 13
Michael D. Multerer
- Bayesian inference and data assimilation
- Fast methods for non-local operators
- Finite elements and boundary elements
- Numerical linear algebra
- Partial differential equations with random data
- Sparse quadrature
- Supervised and unsupervised learning
- J. Dölz, H. Harbrecht, and M.D. Multerer. On the best approximation of the hierarchical matrix product. Preprint 2018-10, Fachbereich Mathematik, Universität Basel, Switzerland, 2018 (to appear in SIAM J. Matrix Anal. Appl.).
- 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.
- R. N. Gantner, M. D. Peters. Higher order quasi-Monte Carlo for Baysian shape inversion. SIAM/ASA J. Uncertain. Quantif., 6(2):707-736, 2018.
- H. Harbrecht and M. D. Peters. The second order perturbation approach for PDEs on random domains. Appl. Numer. Math., 125:159-171, 2018.
- 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.
- 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.
- 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.
- H. Harbrecht, M. D. Peters and S. Schmidlin. Uncertainty quantification for PDEs with anisotropic random diffusion. SIAM J. Numer. Anal., 55(2):1002-1023, 2017.
- 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.
- 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.
- 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.
- 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.
- H. Harbrecht and M. D. Peters. Solution of free boundary problems in the presence of geometric uncertainties. In M. Bergounioux et al., editors, Topological Optimization and Optimal Transport in the Applied Sciences, pages 20-39, de Gruyter, Berlin-Bosten, 2017.
- H. Harbrecht and M. Peters. Combination technique based second moment analysis for PDEs on random domains. In J. Garcke and D. Pflüger, editors, Sparse grids and applications - Stuttgart 2014, volume 109 of Lecture Notes in Computational Science and Engineering, pages 51-77, Springer International Publishing, Switzerland, 2016.
- H. Harbrecht, M. Peters, and M. Siebenmorgen. Efficient approximation of random fields for numerical applications. Numer. Linear Algebra Appl. 22(4):596-617, 2015.
- 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.
- H. Harbrecht and M. Peters. Comparison of fast boundary element methods on parametric surfaces. Comput. Methods Appl. Mech. Engrg., 261-262:39-55, 2013.
- H. Harbrecht, M. Peters, and M. Siebenmorgen. Combination technique based k-th moment analysis of elliptic problems with random diffusion. J. Comput. Phys., 252:128-141, 2013.
- 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.
- H. Harbrecht, M. Peters, and R. Schneider. On the low-rank approximation by the pivoted Cholesky decomposition. Appl. Numer. Math., 62(4):428-440, 2012.
- D. Barac, M. D. Multerer, and D. Iber. Global optimization using Gaussian Processes to estimate biological parameters from image data. arXiv:1807.10180, 2018.
- H. Harbrecht, N. Ilić, and M.D. Multerer. Acoustic scattering in case of random obstacles. Preprint 2018-12, Fachbereich Mathematik, Universität Basel, Switzerland, 2018.
- M. D. Peters. A note on the domain mapping method with rough coefficients. arXiv:1805.02889, 2018.
- M. Griebel, H. Harbrecht, and M. D. Peters. Multilevel quadrature for elliptic parametric partial differential equations on non-nested meshes. Preprint 2015-29, Mathematisches Institut, Universität Basel, Switzerland, 2015.
BEM-Based Engineering Library (Bembel)
Bembel is a Boundary Element Method Based Engineering Library written in C and C++ to solve boundary value problems governed by the Laplace, Helmholtz or electric wave equation. It was written as part of a cooperation between the TU Darmstadt and the University of Basel, coordinated by H. Harbrecht, S. Kurz and S. Schöps. It is based on the Laplace BEM of J. Dölz, H. Harbrecht and M. Multerer as well as the spline and geometry framework of F. Wolf. We plan to release the code in early 2019.
Realizes a high precision implementation of the Halton Set in arbitrary dimensions using a simple sieve for the prime generation and an explicit storage of their b-adic representation. In order to achieve high accuracy, the radical inverse is formed by the Horner scheme.
SParse Quadrature Routines (SPQR)
A Package which implements the anisotropic sparse grid quadrature for arbitrary downward closed index sets. To provide maximum flexibility, the underlying univariate quadrature rules as well as the criterion for the sparse index set can be defined by the user. Optimised versions of the total degree index set and the hyperbolic cross index set are provided by default. Currently, the package comes with a simple Matlab interface.