49 citations · 104 across the 12 of their papers we have counts for
4 papers · 1 filter
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…