96 citations · 123 across the 12 of their papers we have counts for
12 papers
A Comparison Of Direct Solvers In FROSch Applied To Chemo-Mechanics
Alexander Heinlein, Bjoern Kiefer, Stefan Prüger +2
Sparse direct linear solvers are at the computational core of domain decomposition preconditioners and therefore have a strong impact on their performance. In this paper, we consid…
Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks
Viktor Grimm, Alexander Heinlein, Axel Klawonn
In recent years, the concept of introducing physics to machine learning has become widely popular. Most physics-inclusive ML-techniques however are still limited to a single geomet…
A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods
Daniel Balzani, Alexander Heinlein, Axel Klawonn +5
A computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial…
Multilevel domain decomposition-based architectures for physics-informed neural networks
Victorita Dolean, Alexander Heinlein, Siddhartha Mishra +1
Physics-informed neural networks (PINNs) are a powerful approach for solving problems involving differential equations, yet they often struggle to solve problems with high frequenc…
Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data
Svenja Ehlers, Marco Klein, Alexander Heinlein +4
Accurate short-term predictions of phase-resolved water wave conditions are crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wa…
An Experimental Study of Two-Level Schwarz Domain Decomposition Preconditioners on GPUs
Ichitaro Yamazaki, Alexander Heinlein, Sivasankaran Rajamanickam
The generalized Dryja--Smith--Widlund (GDSW) preconditioner is a two-level overlapping Schwarz domain decomposition (DD) preconditioner that couples a classical one-level overlappi…
An extension of the approximate component mode synthesis method to the heterogeneous Helmholtz equation
Elena Giammatteo, Alexander Heinlein, Matthias Schlottbom
In this work we propose and analyze an extension of the approximate component mode synthesis (ACMS) method to the heterogeneous Helmholtz equation. The ACMS method has originally b…
Finite basis physics-informed neural networks as a Schwarz domain decomposition method
Victorita Dolean, Alexander Heinlein, Siddhartha Mishra +1
Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neura…
A fully algebraic and robust two-level Schwarz method based on optimal local approximation spaces
Alexander Heinlein, Kathrin Smetana
Two-level domain decomposition preconditioners lead to fast convergence and scalability of iterative solvers. However, for highly heterogeneous problems, where the coefficient func…
Efficient coarse correction for parallel time-stepping in plaque growth simulations
Stefan Frei, Alexander Heinlein
In order to make the numerical simulation of atherosclerotic plaque growth feasible, a temporal homogenization approach is employed. The resulting macro-scale problem for the plaqu…
Towards parallel time-stepping for the numerical simulation of atherosclerotic plaque growth
Stefan Frei, Alexander Heinlein
The numerical simulation of atherosclerotic plaque growth is computationally prohibitive, since it involves a complex cardiovascular fluid-structure interaction (FSI) problem with…
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…