20 citations · 30 across the 9 of their papers we have counts for
9 papers
A Discontinuous Galerkin discretization for the sea ice dynamics
Emma Lagracie, Thomas Richter
Sea ice dynamics plays a crucial role in the Earth's climate system, making it an important component of weather and climate prediction models. Its numerical simulation remains cha…
Goal oriented error estimation for adaptive sampling of PINNS
Medard Govoeyi, Thomas Richter
Physics-Informed Neural Networks (PINNs) are mesh-free approaches for the numerical approximation of partial differential equations, where a neural network is trained by minimizing…
Application of a Temporal Multiscale Method for Efficient Simulation of Degradation in PEM Water Electrolysis under Dynamic Operation
Dayron Chang Dominguez, An Phuc Dam, Thomas Richter +2
Hydrogen is vital for sectors like chemicals and others, driven by the need to reduce carbon emissions. Proton Electrolyte Membrane Water Electrolysis (PEMWE) is a key technology f…
Error analysis of a pressure correction method with explicit time stepping
Utku Kaya, Thomas Richter
The pressure-correction method is a well established approach for simulating unsteady, incompressible fluids. It is well-known that implicit discretization of the time derivative i…
An adaptive finite element multigrid solver using GPU acceleration
Manuel Liebchen, Robert Jendersie, Utku Kaya +2
Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Ye…
Towards a GPU-Parallelization of the neXtSIM-DG Dynamical Core
Robert Jendersie, Christian Lessig, Thomas Richter
The cryosphere plays a significant role in Earth's climate system. Therefore, an accurate simulation of sea ice is of great importance to improve climate projections. To enable hig…
Error analysis for hybrid finite element/neural network discretizations
Uladzislau Kapustsin, Utku Kaya, Johannes Pfefferer +1
We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine sca…
A hybrid finite element/neural network solver and its application to the Poisson problem
Uladzislau Kapustsin, Utku Kaya, Thomas Richter
We analyze a hybrid method that enriches coarse grid finite element solutions with fine scale fluctuations obtained from a neural network. The idea stems from the Deep Neural Netwo…
A priori and a posteriori error estimates for the Deep Ritz method applied to the Laplace and Stokes problem
Piotr Minakowski, Thomas Richter
We analyze neural network solutions to partial differential equations obtained with Physics Informed Neural Networks. In particular, we apply tools of classical finite element erro…