5 papers
Projection-based low-rank assembly in IgA
Tom-Christian Riemer, Martin Stoll
Isogeometric Analysis (IgA) uses the same spline functions to represent the computational domain and to approximate the solution. This allows exact geometry descriptions, but the r…
Adaptive Krylov Methods for Low-Rank Exponential Integrators
Rico Weigel, Tom-Christian Riemer, Martin Stoll
Differential equations arise in numerous applications, particularly within scientific and technical contexts. Systems of stiff, time-dependent ordinary differential equations const…
A Low-Rank tensor framework for THB-Splines
Tom-Christian Riemer, Martin Stoll
We introduce a low-rank framework for adaptive isogeometric analysis with truncated hierarchical B-splines (THB-splines) that targets the main bottleneck of local refinement: memor…
Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation and parameter identification
Jan Blechschmidt, Tom-Christian Riemer, Max Winkler +2
We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a…
A comparison of PINN approaches for drift-diffusion equations on metric graphs
Jan Blechschmidt, Jan-Frederik Pietschman, Tom-Christian Riemer +2
In this paper we focus on comparing machine learning approaches for quantum graphs, which are metric graphs, i.e., graphs with dedicated edge lengths, and an associated differentia…