10 papers
Finite element exponential integration for rough solutions of nonlinear wave equations. Part II: Dynamic boundary conditions on curved domains
Jiachuan Cao, Benjamin Dörich, Buyang Li
We study nonlinear wave equations with dynamic boundary conditions on smooth bounded domains and analyze a fully discrete approximation in the low-regularity regime. The method com…
Finite element exponential integration for rough solutions of nonlinear wave equations. Part I: Dirichlet boundary conditions on polygonal and polyhedral domains
Jiachuan Cao, Benjamin Dörich, Marlis Hochbruck +1
We study a fully discrete scheme for nonlinear wave equations on general bounded polygonal/polyhedral domains with initial data , $0<γ\le…
GLENN: Neural network-enhanced computation of Ginzburg-Landau energy minimizers
Michael Crocoll, Christian Döding, Benjamin Dörich +1
In this work, we propose a neural network-enhanced finite element strategy to compute the minimizer of the Ginzburg-Landau energy based on an unsupervised deep Ritz-type strategy.…
Complexity bounds on neural networks for the solution of structured linear systems of equations
Benjamin Dörich, Roland Maier, Lukas Ullmer
We derive upper bounds on the complexity of ReLU neural networks approximating the solution of a linear system given the matrix and the right-hand side. We focus on matrices which…
A multiscale approach to the stationary Ginzburg-Landau equations of superconductivity
Christian Döding, Benjamin Dörich, Patrick Henning
In this work, we study the numerical approximation of minimizers of the Ginzburg-Landau free energy, a common model to describe the behavior of superconductors under magnetic field…
Gautschi-type and implicit-explicit integrators for constrained wave equations
R. Altmann, B. Dörich, C. Zimmer
This paper deals with the construction and analysis of two integrators for (semi-linear) second-order partial differential-algebraic equations of semi-explicit type. More precisely…