49 citations · 137 across the 15 of their papers we have counts for
16 papers
DEIM vs. leverage scores for time-parallel construction of problem-adapted basis functions
Julia Schleuß, Kathrin Smetana
To tackle heterogeneous time-dependent problems, an algorithm that constructs problem-adapted basis functions in an embarrassingly parallel and local manner in time has recently be…
A fully algebraic and robust two-level Schwarz method based on optimal local approximation spaces
Alexander Heinlein, Kathrin Smetana
Two-level domain decomposition preconditioners lead to fast convergence and scalability of iterative solvers. However, for highly heterogeneous problems, where the coefficient func…
Randomized quasi-optimal local approximation spaces in time
Julia Schleuß, Kathrin Smetana, Lukas ter Maat
We target time-dependent partial differential equations (PDEs) with heterogeneous coefficients in space and time. To tackle these problems, we construct reduced basis/ multiscale a…
Localized model reduction for nonlinear elliptic partial differential equations: localized training, partition of unity, and adaptive enrichment
Kathrin Smetana, Tommaso Taddei
We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized {nonlinear} elliptic partial differential equations (PDEs). CB-pMOR is desig…
Optimal local approximation spaces for parabolic problems
Julia Schleuß, Kathrin Smetana
We propose local space-time approximation spaces for parabolic problems that are optimal in the sense of Kolmogorov and may be employed in multiscale and domain decomposition metho…
Stable and efficient Petrov-Galerkin methods for a kinetic Fokker-Planck equation
Julia Brunken, Kathrin Smetana
We propose a stable Petrov-Galerkin discretization of a kinetic Fokker-Planck equation constructed in such a way that uniform inf-sup stability can be inferred directly from the va…
Randomized residual-based error estimators for the Proper Generalized Decomposition approximation of parametrized problems
Kathrin Smetana, Olivier Zahm
This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It buil…
Localized model reduction for parameterized problems
Andreas Buhr, Laura Iapichino, Mario Ohlberger +3
In this contribution we present a survey of concepts in localized model order reduction methods for parameterized partial differential equations. The key concept of localized model…
Static condensation optimal port/interface reduction and error estimation for structural health monitoring
Kathrin Smetana
Having the application in structural health monitoring in mind, we propose reduced port spaces that exhibit an exponential convergence for static condensation procedures on structu…
Randomized residual-based error estimators for parametrized equations
Kathrin Smetana, Olivier Zahm, Anthony T Patera
We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important pr…
(Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods
Julia Brunken, Kathrin Smetana, Karsten Urban
We consider ultraweak variational formulations for (parametrized) linear first order transport equations in time and/or space. Computationally feasible pairs of optimally stable tr…
Randomized Local Model Order Reduction
Andreas Buhr, Kathrin Smetana
In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed…
Problem adapted Hierarchical Model Reduction for the Fokker-Planck equation
Julia Brunken, Tobias Leibner, Mario Ohlberger +1
In this paper we introduce a new hierarchical model reduction framework for the Fokker-Planck equation. We reduce the dimension of the equation by a truncated basis expansion in th…
Approximation of skewed interfaces with tensor-based model reduction procedures: application to the reduced basis hierarchical model reduction approach
Mario Ohlberger, Kathrin Smetana
In this article we introduce a procedure, which allows to recover the potentially very good approximation properties of tensor-based model reduction procedures for the solution of…
Hierarchical model reduction of nonlinear partial differential equations based on the adaptive empirical projection method and reduced basis techniques
Kathrin Smetana, Mario Ohlberger
In this paper we extend the hierarchical model reduction framework based on reduced basis techniques for the application to nonlinear partial differential equations. The major new…
Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions
Heiko Berninger, Mario Ohlberger, Oliver Sander +1
We analytically and numerically analyze groundwater flow in a homogeneous soil described by the Richards equation, coupled to surface water represented by a set of ordinary differe…