323 citations · 565 across the 31 of their papers we have counts for
32 papers
Accuracy Controlled Schemes for the Eigenvalue Problem of the Radiative Transfer Equation
Wolfgang Dahmen, Olga Mula
The criticality problem in nuclear engineering asks for the principal eigenpair of a Boltzmann operator describing neutron transport in a reactor core. Being able to reliably desig…
Reduced order modeling for elliptic problems with high contrast diffusion coefficients
Albert Cohen, Matthieu Dolbeault, Agustin Somacal +1
We consider the parametric elliptic PDE on a spatial domain , with a scalar piecewise constant diffusion coefficient taking any positive val…
Solving PDEs with Incomplete Information
Peter Binev, Andrea Bonito, Albert Cohen +3
We consider the problem of numerically approximating the solutions to a partial differential equation (PDE) when there is insufficient information to determine a unique solution. O…
Least squares solvers for ill-posed PDEs that are conditionally stable
Wolfgang Dahmen, Harald Monsuur, Rob Stevenson
This paper is concerned with the design and analysis of least squares solvers for ill-posed PDEs that are conditionally stable. The norms and the regularization term used in the le…
Compositional Sparsity, Approximation Classes, and Parametric Transport Equations
Wolfgang Dahmen
Approximating functions of a large number of variables poses particular challenges often subsumed under the term ``Curse of Dimensionality'' (CoD). Unless the approximated function…
Nonlinear Reduced DNN Models for State Estimation
Wolfgang Dahmen, Min Wang, Zhu Wang
We propose in this paper a data driven state estimation scheme for generating nonlinear reduced models for parametric families of PDEs, directly providing data-to-state maps, repre…