Prof. Dr. Helmut Harbrecht

Direktor BEZ

helmut.harbrecht-at-unibas.ch

Büro 05.007

Telefon
+41 (0)61 207 39 92
Fax
+41 (0)61 207 26 95

http://www.math.unibas.ch/~harbrech

Teaching in HS 17:

Research interests:

Recent Publications:

  • M. Dambrine, H. Harbrecht, and B. Puig.Incorporating knowledge on the measurement noise in electrical impedance tomography. Preprint 2017-14, Fachbereich Mathematik, Universität Basel, Switzerland, 2017.
  • R. Brügger, R. Croce, and H. Harbrecht. Solving a free boundary problem with non-constant coefficients. Preprint 2017-13, Fachbereich Mathematik, Universität Basel, Switzerland, 2017.
  • J. Dölz, H. Harbrecht, S. Kurz, S. Schöps, and F. Wolf. A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems. Preprint 2017-11, Fachbereich Mathematik, Universität Basel, Switzerland, 2017.
  • M. Griebel and H. Harbrecht. Singular value decomposition versus sparse grids. Refined complexity estimates. Preprint 2017-08, Fachbereich Mathematik, Universität Basel, Switzerland, 2017.
  • H. Harbrecht and M. Schmidlin. Multilevel methods for uncertainty quantification of elliptic PDEs with random anisotropic diffusion. Preprint 2017-07, Fachbereich Mathematik, Universität Basel, Switzerland, 2017.
  • J. Dölz and H. Harbrecht. Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains. Preprint 2017-05, Fachbereich Mathematik, Universität Basel, Switzerland, 2017.
  • J. Dölz and T. Gerig, M. Lüthi, H. Harbrecht and T. Vetter. Efficient computation of low-rank Gaussian process models for surface and image registration. Preprint 2017-01, Fachbereich Mathematik, Universität Basel, Switzerland, 2017.
  • Ch. Bürli, H. Harbrecht, P. Odermatt, S. Sayasone, and N. Chitnis. Mathematical Analysis of the Transmission Dynamics of the Liver Fluke, Opisthorchis viverrini, Preprint 2016-34, Fachbereich Mathematik, Universität Basel, Switzerland, 2016.
  • H. Harbrecht and J. Tausch. A fast sparse grid based space-time boundary element method for the nonstationary heat equation. Preprint 2016-32, Fachbereich Mathematik, Universität Basel, Switzerland, 2016.
  • M. Dambrine, H. Harbrecht, M. Peters, and B. Puig. On Bernoulli's free boundary problem with a random boundary. Int. J. Uncertain. Quantif., 7(4):335-353, 2017.
  • S. Dahlke, H. Harbrecht, M. Utzinger, and M. Weimar. Adaptive Wavelet BEM for boundary integral equations. Theory and numerical experiments. Preprint 2016-20, Fachbereich Mathematik, Universität Basel, Switzerland, 2016 (to appear in Numer. Funct. Anal. Optim.).
  • H. Harbrecht, M. Peters, and M. Schmidlin. Uncertainty quantification for PDEs with anisotropic random diffusion. SIAM J. Numer. Anal., 55(2):1002-1023, 2017.
  • M. Dambrine, I. Greff, H. Harbrecht, and B. Puig. Numerical solution of the homogeneous Neumann boundary value problem on domains with a thin layer of random thickness. J. Comput. Phys., 330:943–959, 2017.
  • H. Harbrecht and R. Schneider. A note on multilevel based error estimation. Comput. Methods Appl. Math., 16(3):447-458, 2016. 
  • H. Harbrecht and M. Utzinger. On adaptive wavelet boundary element methods. J. Comput. Math., 36(1):90-109, 2018.
  • H. Harbrecht, W.L. Wendland, and N. Zorii. Minimal energy problems for strongly singular Riesz kernels. Preprint 2015-41, Mathematisches Institut, Universität Basel, Switzerland, 2015 (to appear in Math. Nachr.).
  • H. Harbrecht and M. Peters. The second order perturbation approach for PDEs on random domains. Preprint 2015-40, Mathematisches Institut, Universität Basel, Switzerland, 2015.
  • J. Dölz, H. Harbrecht, and M. Peters. H-matrix based second moment analysis for rough random fields and finite element discretizations. SIAM J. Sci. Comput., 39(4):B618-B639, 2017.
  • M. Griebel, H. Harbrecht, and M. Peters. Multilevel quadrature for elliptic parametric partial differential equations on non-nested meshes. Preprint 2015-29, Mathematisches Institut, Universität Basel, Switzerland, 2015.
  • A.-L. Haji-Ali, H. Harbrecht, M. Peters, and M. Siebenmorgen. Novel results for the anisotropic sparse quadrature and their impact on random diffusion problems. Preprint 2015-27, Mathematisches Institut, Universität Basel, Switzerland, 2015.
  • 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.
  • M. Bugeanu, R. Di Remigio, K. Mozgawa, S. Reine, H. Harbrecht, and L. Frediani. Wavelet formulation of the polarizable continuum model. II. Use of piecewise bilinear boundary elements. Phys. Chem. Chem. Phys., 17:31566-31581, 2015. 
  • M. Dambrine, C. Dapogny, and H. Harbrecht. Shape optimization for quadratic functionals and states with random right-hand sides. SIAM J. Control Optim., 53(5):3081-3103, 2015. 
  • H. Harbrecht and M. 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.
  • Radon Series on Computational and Applied Mathematics, de Gruyter).
  • 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.
  • M. Dambrine, I. Greff, H. Harbrecht, and B. Puig. Solution of the Poisson equation with a thin layer of random thickness. SIAM J. Numer. Anal., 54(2):921–941, 2016.
  • M. Bugeanu and H. Harbrecht. A second order convergent trial method for a free boundary problem in three dimensions. Interfaces Free Bound. 17(4):517-537, 2015.
  • M. Dambrine, H. Harbrecht, and B. Puig. Computing quantities of interest for random domains with second order shape sensitivity analysis. ESIAM Math. Model. Numer. Anal., 49(5):1285-1302, 2015.
  • J. Dölz, H. Harbrecht, and C. Schwab. Covariance regularity and H-matrix approximation for rough random fields. Numer. Math., 135(4):1045-1071, 2017.
  • H. Harbrecht, W.L. Wendland, and N. Zorii. Rapid solution of minimal Riesz energy problems. Numer. Methods Partial Differential Equations, 32(6):1535-1552, 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.
  • 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, M. Peters, and M. Siebenmorgen. Efficient approximation of random fields for numerical applications. Numer. Linear Algebra Appl., 22(4):596-617, 2015.
  • H. Harbrecht and G. Mitrou. Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data. Math. Meth. Appl. Sci., 38(13):2850-2863, 2015.
  • 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 J. Tausch. On shape optimization with parabolic state equation.  In G. Leugering et al., editors, Trends in PDE Constrained Optimization, volume 165 of International Series of Numerical Mathematics, pages 213-229, Birkhäuser, Basel, 2014.
  • H. Harbrecht and G. Mitrou. Improved trial methods for a class of generalized Bernoulli problems. J. Math. Anal. Appl., 420:177-194, 2014.
  • 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. 
  • D. Alm, H. Harbrecht, and U. Krämer. The -wavelet method. J. Comput. Appl. Math., 267:131-159, 2014.
  • H. Harbrecht and F. Loos. Optimization of current carrying multicables. Comput. Optim. Appl., 63(1):237-271, 2016. 
  • J. Fender, L. Graff, H. Harbrecht, and M. Zimmermann. Identifying key parameters for design improvement in high-dimensional systems with uncertainty. J. Mech. Design, 136:041007, 2014.
  • M. Griebel and H. Harbrecht. On the convergence of the combination technique. In J. Garcke and D. Pflüger, editors, Sparse grids and applications - Munich 2012, volume 97 of Lecture Notes in Computational Science and Engineering, pages 55-74, Springer, Berlin-Heidelberg, 2014.
  • H. Harbrecht and M. Peters. Comparison of fast boundary element methods on parametric surfaces. Comput. Methods Appl. Mech. Engrg., 261-262:39-55, 2013. 
  • L. Graff, H. Harbrecht, and M. Zimmermann. On the computation of solution spaces in high dimensions. Struct. Multidiscip. Optim., 54(4):811-829, 2016.
  • H. Harbrecht. Second moment analysis for Robin boundary value problems on random domains. In M. Griebel, editor, Singular Phenomena and Scaling in Mathematical Models, pages 261-282, Springer, Berlin-Heidelberg, 2014.
  • A. Buffa, H. Harbrecht, A. Kunoth, and G. Sangalli. BPX-preconditioning for isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 265:63-70, 2013.
  • M. Griebel and H. Harbrecht. A note on the construction of L-fold sparse tensor product spaces. Constr. Approx., 38(2):235-251, 2013. 
  • H. Harbrecht, W.L. Wendland, and N. Zorii. Riesz minimal energy problems on Ck1,1-manifolds. Math. Nachr., 287(1):48-69, 2014.
  • H. Harbrecht. Preconditioning of wavelet BEM by the incomplete Cholesky factorization. Comput. Vis. Sci., 15(6):319-329, 2012.
  • 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 and J. Tausch. On the numerical solution of a shape optimization problem for the heat equation. SIAM J. Sci. Comput., 35(1):A104-A121, 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.
  • M. Griebel and H. Harbrecht. On the construction of sparse tensor product spaces. Math. Comput., 82(282):975-994, 2013.
  • H. Harbrecht and J. Li. A fast deterministic method for stochastic elliptic interface problems based on low-rank approximation. ESAIM Math. Model. Numer. Anal., 47(5):1533-1552, 2013. 
  • H. Harbrecht. On analytical derivatives for geometry optimization in the polarizable continuum model. J. Math. Chem., 49(9):1928-1936, 2011.