74 citations · 525 across the 47 of their papers we have counts for
12 papers · 1 filter
Construction of Grid Operators for Multilevel Solvers: a Neural Network Approach
Claudio Tomasi, Rolf Krause
In this paper, we investigate the combination of multigrid methods and neural networks, starting from a Finite Element discretization of an elliptic PDE. Multigrid methods use inte…
Training of deep residual networks with stochastic MG/OPT
Cyrill von Planta, Alena Kopanicakova, Rolf Krause
We train deep residual networks with a stochastic variant of the nonlinear multigrid method MG/OPT. To build the multilevel hierarchy, we use the dynamical systems viewpoint specif…
Globally Convergent Multilevel Training of Deep Residual Networks
Alena Kopaničáková, Rolf Krause
We propose a globally convergent multilevel training method for deep residual networks (ResNets). The devised method can be seen as a novel variant of the recursive multilevel trus…
A Generalized Multigrid Method for Solving Contact Problems in Lagrange Multiplier based Unfitted Finite Element Method
Hardik Kothari, Rolf Krause
Internal interfaces in a domain could exist as a material defect or they can appear due to propagations of cracks. Discretization of such geometries and solution of the contact pro…
Patch-Smoother and Multigrid for the Dual Formulation for Linear Elasticity
Gabriele Rovi, Rolf Krause
The dual formulation for linear elasticity, in contrast to the primal formulation, is not affected by locking, as it is based on the stresses as main unknowns. Thus it is quite att…
Space-time multilevel quadrature methods and their application for cardiac electrophysiology
Seif Ben Bader, Helmut Harbrecht, Rolf Krause +3
We present a novel approach which aims at high-performance uncertainty quantification for cardiac electrophysiology simulations. Employing the monodomain equation to model the tran…
On the Globalization of ASPIN Employing Trust-Region Control Strategies -- Convergence Analysis and Numerical Examples
Christian Gross, Rolf Krause
The parallel solution of large scale non-linear programming problems, which arise for example from the discretization of non-linear partial differential equations, is a highly dema…
Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization
Alena Kopaničáková, Rolf Krause
We introduce a novel variant of the recursive multilevel trust-region (RMTR) method, called MASTR. The method is designed for solving non-convex bound-constrained minimization prob…
A Multigrid Preconditioner for Jacobian-free Newton-Krylov Methods
Hardik Kothari, Alena Kopaničáková, Rolf Krause
In this work, we propose a multigrid preconditioner for Jacobian-free Newton-Krylov (JFNK) methods. Our multigrid method does not require knowledge of the Jacobian at any level of…
Multigrid and saddle-point preconditioners for unfitted finite element modelling of inclusions
Hardik Kothari, Rolf Krause
In this work, we consider the modeling of inclusions in the material using an unfitted finite element method. In the unfitted methods, structured background meshes are used and onl…
Learning atrial fiber orientations and conductivity tensors from intracardiac maps using physics-informed neural networks
Thomas Grandits, Simone Pezzuto, Francisco Sahli Costabal +4
Electroanatomical maps are a key tool in the diagnosis and treatment of atrial fibrillation. Current approaches focus on the activation times recorded. However, more information ca…
GEASI: Geodesic-based Earliest Activation Sites Identification in cardiac models
Thomas Grandits, Alexander Effland, Thomas Pock +3
The identification of the initial ventricular activation sequence is a critical step for the correct personalization of patient-specific cardiac models. In healthy conditions, the…