6 papers
Optimization-Based Identification of Effective Coefficients for Wave Equations in Spatio-Temporal Metamaterials
Christian Döding, Vishnu Raveendran, Barbara Verfürth
We study the identification of effective coefficients for wave equations in heterogeneous media. Such equations arise in the modeling of spatio-temporal metamaterials, where the un…
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.…
On second-order optimality in the high- regime of the Ginzburg-Landau model
Christian Döding
We study energy minimizers of the Ginzburg-Landau (GL) free energy, a fundamental model of superconductivity. We address the high- regime, the regime of a large GL parameter, in…
The Ginzburg-Landau equations: Vortex states and numerical multiscale approximations
Christian Döding, Patrick Henning
In this review article, we provide an overview of recent advances in the numerical approximation of minimizers of the Ginzburg-Landau energy in multiscale spaces. Such minimizers r…
Vortex-capturing multiscale spaces for the Ginzburg-Landau equation
Maria Blum, Christian Döding, Patrick Henning
This paper considers minimizers of the Ginzburg-Landau energy functional in special multiscale spaces that are based on finite elements. The spaces are constructed by localized ort…
Localized Orthogonal Decomposition Methods vs. Classical FEM for the Gross-Pitaevskii Equation
Christian Döding
The time-dependent Gross-Pitaevksii equation (GPE) is a nonlinear Schrödinger equation which is used in quantum physics to model the dynamics of Bose-Einstein condensates. In this…