96 citations · 123 across the 12 of their papers we have counts for
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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…