49 citations · 104 across the 12 of their papers we have counts for
12 papers
A robust and stable hybrid neural network/finite element method for 2D flows that generalizes to different geometries
Robert Jendersie, Nils Margenberg, Christian Lessig +1
The deep neural network multigrid solver (DNN-MG) combines a coarse-grid finite element simulation with a deep neural network that corrects the solution on finer grid levels, there…
A Hybrid Neural Network-Finite Element Method for the Viscous-Plastic Sea-Ice Model
Nils Margenberg, Carolin Mehlmann
We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations…
The Biot-Allard poro-elasticity system: equivalent forms and well-posedness
Jakob S. Stokke, Markus Bause, Nils Margenberg +1
We consider the fully dynamic Biot-Allard model, which includes memory effects. Convolution integrals in time model the history of the porous medium. We use a series representation…
Optimal Dirichlet Boundary Control by Fourier Neural Operators Applied to Nonlinear Optics
Nils Margenberg, Franz X. Kärtner, Markus Bause
We present an approach for solving optimal Dirichlet boundary control problems of nonlinear optics by using deep learning. For computing high resolution approximations of the solut…
Benchmark computations of dynamic poroelasticity
Mathias Anselmann, Markus Bause, Nils Margenberg +1
We present benchmark computations of dynamic poroelasticity modeling fluid flow in deformable porous media by a coupled hyperbolic-parabolic system of partial differential equation…
DNN-MG: A Hybrid Neural Network/Finite Element Method with Applications to 3D Simulations of the Navier-Stokes Equations
Nils Margenberg, Robert Jendersie, Christian Lessig +1
We extend and analyze the deep neural network multigrid solver (DNN-MG) for the Navier-Stokes equations in three dimensions. The idea of the method is to augment a finite element s…
An energy-efficient GMRES-Multigrid solver for space-time finite element computation of dynamic poro- and thermoelasticity
Mathias Anselmann, Markus Bause, Nils Margenberg +1
We present families of space-time finite element methods (STFEMs) for a coupled hyperbolic-parabolic system of poro- or thermoelasticity. Well-posedness of the discrete problems is…
Accurate simulation of THz generation with Finite-Element Time Domain methods
Nils Margenberg, Franz X. Kärtner, Markus Bause
We investigate the accurate full broadband simulation of complex nonlinear optical processes. A mathematical model and numerical simulation techniques in the time domain are develo…
Deep neural networks for geometric multigrid methods
Nils Margenberg, Robert Jendersie, Thomas Richter +1
We investigate scaling and efficiency of the deep neural network multigrid method (DNN-MG). DNN-MG is a novel neural network-based technique for the simulation of the Navier-Stokes…
Structure Preservation for the Deep Neural Network Multigrid Solver
Nils Margenberg, Christian Lessig, Thomas Richter
The simulation of partial differential equations is a central subject of numerical analysis and an indispensable tool in science, engineering and related fields. Existing approache…
A neural network multigrid solver for the Navier-Stokes equations
Nils Margenberg, Dirk Hartmann, Christian Lessig +1
We present the deep neural network multigrid solver (DNN-MG) that we develop for the instationary Navier-Stokes equations. DNN-MG improves computational efficiency using a judiciou…
Parallel time-stepping for fluid-structure interactions
Nils Margenberg, Thomas Richter
We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulat…