61 citations · 89 across the 20 of their papers we have counts for
32 papers
Two-norm discrepancy and convergence of the stochastic gradient method with application to shape optimization
Marc Dambrine, Caroline Geiersbach, Helmut Harbrecht
The present article is dedicated to proving convergence of the stochastic gradient method in case of random shape optimization problems. To that end, we consider Bernoulli's exteri…
The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs
Helmut Harbrecht, Marc Schmidlin, Christoph Schwab
This article is concerned with a regularity analysis of parametric operator equations with a perspective on uncertainty quantification. We study the regularity of mappings between…
Solving acoustic scattering problems by the isogeometric boundary element method
Jürgen Dölz, Helmut Harbrecht, Michael Multerer
We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equatio…
Samplet basis pursuit: Multiresolution scattered data approximation with sparsity constraints
Davide Baroli, Helmut Harbrecht, Michael Multerer
We consider scattered data approximation in samplet coordinates with -regularization. The application of an -regularization term enforces sparsity of the coefficien…
Multiresolution kernel matrix algebra
H. Harbrecht, M. Multerer, O. Schenk +1
We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets pro…
Uncertainty quantification for random domains using periodic random variables
Harri Hakula, Helmut Harbrecht, Vesa Kaarnioja +2
We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random domain, we use the model recently in…