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…
Accuracy controlled data assimilation for parabolic problems
Wolfgang Dahmen, Rob Stevenson, Jan Westerdiep
This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylin…
Nonlinear reduced models for state and parameter estimation
Albert Cohen, Wolfgang Dahmen, Olga Mula +1
State estimation aims at approximately reconstructing the solution to a parametrized partial differential equation from linear measurements, when the parameter vector i…
State Estimation -- The Role of Reduced Models
Albert Cohen, Wolfgang Dahmen, Ron DeVore
The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a fa…
Adaptive Low-Rank Approximations for Operator Equations: Accuracy Control and Computational Complexity
Markus Bachmayr, Wolfgang Dahmen
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do no…
Optimal reduced model algorithms for data-based state estimation
Albert Cohen, Wolfgang Dahmen, Ron DeVore +3
Reduced model spaces, such as reduced basis and polynomial chaos, are linear spaces of finite dimension which are designed for the efficient approximation of families par…
Reduced Basis Greedy Selection Using Random Training Sets
Albert Cohen, Wolfgang Dahmen, Ronald DeVore
Reduced bases have been introduced for the approximation of parametrized PDEs in applications where many online queries are required. Their numerical efficiency for such problems h…
An Adaptive Nested Source Term Iteration for Radiative Transfer Equations
Wolfgang Dahmen, Felix Gruber, Olga Mula
We propose a new approach to the numerical solution of radiative transfer equations with certified a posteriori error bounds. A key role is played by stable Petrov--Galerkin type v…
Adaptive Strategies for Transport Equations
W. Dahmen, R. P. Stevenson
This paper is concerned with a posteriori error bounds for linear transport equations and related questions of contriving corresponding adaptive solution strategies in the context…
Parametric PDEs: Sparse or Low-Rank Approximations?
Markus Bachmayr, Albert Cohen, Wolfgang Dahmen
We consider adaptive approximations of the parameter-to-solution map for elliptic operator equations depending on a large or infinite number of parameters, comparing approximation…
Adaptive Anisotropic Petrov-Galerkin Methods for First Order Transport Equations
W. Dahmen, G. Kutyniok, W. -Q Lim +2
This paper builds on recent developments of adaptive methods for linear transport equations based on certain stable variational formulations of Petrov-Galerkin type. The variationa…
On the stability of DPG formulations of transport equations
D. Broersen, W. Dahmen, R. P. Stevenson
In this paper we formulate and analyze a Discontinuous Petrov Galerkin formulation of linear transport equations with variable convection fields. We show that a corresponding {\em…
Orthogonal Matching Pursuit under the Restricted Isometry Property
Albert Cohen, Wolfgang Dahmen, Ronald DeVore
This paper is concerned with the performance of Orthogonal Matching Pursuit (OMP) algorithms applied to a dictionary in a Hilbert space . Given an elemen…
Data Assimilation in Reduced Modeling
Peter Binev, Albert Cohen, Wolfgang Dahmen +3
We consider the problem of optimal recovery of an element of a Hilbert space from measurements obtained through known linear functionals on . Pro…
How to best sample a solution manifold?
Wolfgang Dahmen
Model reduction attempts to guarantee a desired "model quality", e.g. given in terms of accuracy requirements, with as small a model size as possible. This article highlights some…
Classification algorithms using adaptive partitioning
Peter Binev, Albert Cohen, Wolfgang Dahmen +1
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementat…
Efficient Resolution of Anisotropic Structures
Wolfgang Dahmen, Chunyan Huang, Gitta Kutyniok +3
We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in…
Tensor-Sparsity of Solutions to High-Dimensional Elliptic Partial Differential Equations
Wolfgang Dahmen, Ronald DeVore, Lars Grasedyck +1
A recurring theme in attempts to break the curse of dimensionality in the numerical approximations of solutions to high-dimensional partial differential equations (PDEs) is to empl…
Adaptive Low-Rank Methods: Problems on Sobolev Spaces
Markus Bachmayr, Wolfgang Dahmen
This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats…