8 citations · 25 across the 13 of their papers we have counts for
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Three Dimensional Optimization of Scaffold Porosities for Bone Tissue Engineering
Patrick Dondl, Marius Zeinhofer
We consider the scaffold design optimization problem associated to the three dimensional, time dependent model for scaffold mediated bone regeneration considered in Dondl et al. (2…
Regularity for Reaction-Diffusion Equations with Non-smooth Data
Patrick Dondl, Marius Zeinhofer
We prove an regularity result for a reaction-diffusion equation with mixed boundary conditions, symmetric coefficients and an initial conditio…
Uniform Convergence Guarantees for the Deep Ritz Method for Nonlinear Problems
Patrick Dondl, Johannes Müller, Marius Zeinhofer
We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover non-linear variational problems such as the -Laplace equation or…
A parameter study on optimal scaffolds in a simple model for bone regeneration
Patrick Dondl, Marius Zeinhofer
We propose a simple model for scaffold aided bone regeneration. In this model, only macroscopic quantities, e.g., locally averaged osteoblast densities, are considered. This allows…
Notes on Exact Boundary Values in Residual Minimisation
Johannes Müller, Marius Zeinhofer
We analyse the difference in convergence mode using exact versus penalised boundary values for the residual minimisation of PDEs with neural network type ansatz functions, as is co…
Error Estimates for the Deep Ritz Method with Boundary Penalty
Johannes Müller, Marius Zeinhofer
We estimate the error of the Deep Ritz Method for linear elliptic equations. For Dirichlet boundary conditions, we estimate the error when the boundary values are imposed through t…
An Efficient Model for Scaffold-Mediated Bone Regeneration
Patrick Dondl, Patrina S. P. Poh, Marius Zeinhofer
We present a three dimensional, time dependent model for bone regeneration in the presence of porous scaffolds to bridge critical size bone defects. Our approach uses homogenized q…