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07/27/2023
DNN-MG: A Hybrid Neural Network/Finite Element Method with Applications to 3D Simulations of the Navier-Stokes Equations
We extend and analyze the deep neural network multigrid solver (DNN-MG) ...
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07/23/2023
A monolithic space-time temporal multirate finite element framework for interface and volume coupled problems
In this work, we propose and computationally investigate a monolithic sp...
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07/18/2023
Quasi-Random Discrete Ordinates Method to Radiative Transfer Equation with Linear Anisotropic Scattering
The quasi-random discrete ordinates method (QRDOM) is here proposed for ...
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07/18/2023
Quasi-Random Discrete Ordinates Method for Transport Problems
The quasi-random discrete ordinates method (QRDOM) is here proposed for ...
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07/03/2023
A hybrid finite element/neural network solver and its application to the Poisson problem
We analyze a hybrid method that enriches coarse grid finite element solu...
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06/30/2023
Color Learning for Image Compression
Deep learning based image compression has gained a lot of momentum in re...
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11/10/2021
Error Estimate for the Heat Equation on a Coupled Moving Domain in a Fully Eulerian Framework
We introduce an unfitted finite element method with Lagrange-multipliers...
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07/23/2021
Error Estimates for Neural Network Solutions of Partial Differential Equations
We develop an error estimator for neural network approximations of PDEs....
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06/17/2021
On temporal homogenization in the numerical simulation of atherosclerotic plaque growth
A temporal homogenization approach for the numerical simulation of ather...
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06/14/2021
Deep neural networks for geometric multigrid methods
We investigate scaling and efficiency of the deep neural network multigr...
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02/23/2021
Using a deep neural network to predict the motion of under-resolved triangular rigid bodies in an incompressible flow
We consider non-spherical rigid body particles in an incompressible flui...
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12/09/2020
Structure Preservation for the Deep Neural Network Multigrid Solver
The simulation of partial differential equations is a central subject of...
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11/17/2020
Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data
We evaluate a number of different finite element approaches for fluid-st...
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08/26/2020
A neural network multigrid solver for the Navier-Stokes equations
We present a deep neural network multigrid solver (DNN-MG) that we devel...
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08/24/2020
A Low-rank Method for Parameter-dependent Fluid-structure Interaction Discretizations With Hyperelasticity
In aerospace engineering and boat building, fluid-structure interaction ...
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07/27/2020
A locally modified second-order finite element method for interface problems
The locally modified finite element method, which is introduced in [Frei...
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07/10/2020
Adaptive time-step control for a monolithic multirate scheme coupling the heat and wave equation
We consider the dynamics of a parabolic and a hyperbolic equation couple...
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06/09/2020
Error estimation and adaptivity for differential equations with multiple scales in time
We consider systems of ordinary differential equations with multiple sca...
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02/22/2020
The candy wrapper problem – a temporal multiscale approach for pde/pde systems
We describe a temporal multiscale approach for the simulation of long-te...
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02/11/2020
A goal oriented error estimator and mesh adaptivity for sea ice simulations
For the first time we introduce an error estimator for the numerical app...
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02/06/2020
An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains
We analyse a Eulerian Finite Element method, combining a Eulerian time-s...
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11/19/2019
A Low-rank Approach for Nonlinear Parameter-dependent Fluid-structure Interaction Problems
Parameter-dependent discretizations of linear fluid-structure interactio...
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11/10/2019
Second order pressure estimates for the Crank-Nicolson discretization of the incompressible Navier-Stokes Equations
We provide optimal order pressure error estimates for the Crank-Nicolson...
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08/13/2019
Numerical benchmarking of fluid-rigid body interactions
We propose a fluid-rigid body interaction benchmark problem, consisting ...
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07/03/2019
Industrial DevOps
The visions and ideas of Industry 4.0 require a profound interconnection...
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07/02/2019
Parallel time-stepping for fluid-structure interactions
We present a parallel time-stepping method for fluid-structure interacti...
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11/30/2017