49 citations · 324 across the 34 of their papers we have counts for
37 papers
Quasi-Random Discrete Ordinates Method to Radiative Transfer Equation with Linear Anisotropic Scattering
Pedro H. A. Konzen, Leonardo F. Guidi, Thomas Richter
The quasi-random discrete ordinates method (QRDOM) is here proposed for the approximation of transport problems. Its central idea is to explore a quasi Monte Carlo integration with…
Quasi-Random Discrete Ordinates Method for Transport Problems
Pedro H. A. Konzen, Leonardo F. Guidi, Thomas Richter
The quasi-random discrete ordinates method (QRDOM) is here proposed for the approximation of transport problems. Its central idea is to explore a quasi Monte Carlo integration with…
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…
A monolithic space-time temporal multirate finite element framework for interface and volume coupled problems
Julian Roth, Martyna Soszyńska, Thomas Richter +1
In this work, we propose and computationally investigate a monolithic space-time multirate scheme for coupled problems. The novelty lies in the monolithic formulation of the multir…
Adjacency-based, Non-intrusive Reduced-order Modeling for Fluid-Structure Interactions
Leonidas Gkimisis, Thomas Richter, Peter Benner
Non-intrusive model reduction is a promising solution to system dynamics prediction, especially in cases where data are collected from experimental campaigns or proprietary softwar…
Adjacency-based, non-intrusive model reduction for Vortex-Induced Vibrations
Leonidas Gkimisis, Thomas Richter, Peter Benner
Vortex-induced vibrations (VIV) pose computationally expensive problems of high practical interest to several engineering fields. In this work we develop a non-intrusive, reduced-o…
Error analysis for a parabolic PDE model problem on a coupled moving domain in a fully Eulerian framework
Henry von Wahl, Thomas Richter
We introduce an unfitted finite element method with Lagrange-multipliers to study an Eulerian time stepping scheme for moving domain problems applied to a model problem where the d…
Steady azimuthal flow field induced by a rotating sphere near a rigid disk or inside a gap between two coaxially positioned rigid disks
Abdallah Daddi-Moussa-Ider, Alexander R. Sprenger, Thomas Richter +2
Geometric confinements play an important role in many physical and biological processes and significantly affect the rheology and behavior of colloidal suspensions at low Reynolds…
On temporal homogenization in the numerical simulation of atherosclerotic plaque growth
Stefan Frei, Alexander Heinlein, Thomas Richter
A temporal homogenization approach for the numerical simulation of atherosclerotic plaque growth is extended to fully coupled fluid-structure interaction (FSI) simulations. The num…
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…
Using a deep neural network to predict the motion of under-resolved triangular rigid bodies in an incompressible flow
Henry von Wahl, Thomas Richter
We consider non-spherical rigid body particles in an incompressible fluid in the regime where the particles are too large to assume that they are simply transported with the fluid…
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…
Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data
Henry von Wahl, Thomas Richter, Stefan Frei +1
We evaluate a number of different finite element approaches for fluid-structure (contact) interaction problems against data from physical experiments. For this we take the data fro…
A finite element / neural network framework for modeling suspensions of non-spherical particles. Concepts and medical applications
Martyna Minakowska, Thomas Richter, Sebastian Sager
An accurate prediction of the translational and rotational motion of particles suspended in a fluid is only possible if a complete set of correlations for the force coefficients of…
Settling of spherical particles in the transitional regime
Thomas Hagemeier, Dominique Thévenin, Thomas Richter
The settling process and wall impact of large spherical particles in a stagnant, highly viscous fluid has been observed by means of high-speed shadow imaging. The particles include…
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…
A Low-rank Method for Parameter-dependent Fluid-structure Interaction Discretizations With Hyperelasticity
Peter Benner, Thomas Richter, Roman Weinhandl
Fluid-structure interaction models are used to study how a material interacts with different fluids at different Reynolds numbers. Examining the same model not only for different f…
Adaptive time-step control for a monolithic multirate scheme coupling the heat and wave equation
Martyna Soszynska, Thomas Richter
We consider the dynamics of a parabolic and a hyperbolic equation coupled on a common interface and develop time-stepping schemes that can use different time-step sizes for each of…
A locally modified second-order finite element method for interface problems and its implementation in 2 dimensions
Stefan Frei, Gozel Judakova, Thomas Richter
The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve w…
Axisymmetric Stokes flow due to a point-force singularity acting between two coaxially positioned rigid no-slip disks
Abdallah Daddi-Moussa-Ider, Alexander Sprenger, Yacine Amarouchene +5
We investigate theoretically on the basis of the steady Stokes equations for a viscous incompressible fluid the flow induced by a Stokeslet located on the centre axis of two coaxia…
Error estimation and adaptivity for differential equations with multiple scales in time
Leopold Lautsch, Thomas Richter
We consider systems of ordinary differential equations with multiple scales in time. In general, we are interested in the long time horizon of a slow variable that is coupled to so…
A Newton multigrid framework for optimal control of fluid-structure interactions
L. Failer, T. Richter
In this paper we consider optimal control of nonlinear time-dependent fluid structure interactions. To determine a time-dependent control variable a BFGS algorithm is used, whereby…
On the Impact of Fluid Structure Interaction in Blood Flow Simulations: Stenotic Coronary Artery Benchmark
Lukas Failer, Piotr Minakowski, Thomas Richter
We study the impact of using fluid-structure interactions (FSI) to simulate blood flow in a large stenosed artery. We compare typical flow configurations using Navier-Stokes in a r…
The candy wrapper problem -- a temporal multiscale approach for pde/pde systems
Thomas Richter, Jeremi Mizerski
We describe a temporal multiscale approach for the simulation of long-term processes with short-term influences involving partial differential equations. The specific problem under…