99 citations · 117 across the 7 of their papers we have counts for
11 papers
Fredholm integral equations for function approximation and the training of neural networks
Patrick Gelß, Aizhan Issagali, Ralf Kornhuber
We present a novel and mathematically transparent approach to function approximation and the training of large, high-dimensional neural networks, based on the approximate least-squ…
Numerical simulation of multiscale fault systems with rate- and state-dependent friction
Carsten Gräser, Ralf Kornhuber, Joscha Podlesny
We consider the deformation of a geological structure with non-intersecting faults that can be represented by a layered system of viscoelastic bodies satisfying rate- and state-dep…
Free energy computation of particles with membrane-mediated interactions via Langevin dynamics
Tobias Kies, Carsten Gräser, Luigi Delle Site +1
We apply well-established concepts of Langevin sampling to derive a new class of algorithms for the efficient computation of free energy differences of fluctuating particles embedd…
Numerical Homogenization of Fractal Interface Problems
Ralf Kornhuber, Joscha Podlesny, Harry Yserentant
We consider the numerical homogenization of a class of fractal elliptic interface problems inspired by related mechanical contact problems from the geosciences. A particular featur…
Fractal homogenization of multiscale interface problems
Martin Heida, Ralf Kornhuber, Joscha Podlesny
Inspired by continuum mechanical contact problems with geological fault networks, we consider elliptic second order differential equations with jump conditions on a sequence of mul…
A globally convergent filter-trust-region method for large deformation contact problems
Jonathan Youett, Oliver Sander, Ralf Kornhuber
We present a globally convergent method for the solution of frictionless large deformation contact problems for hyperelastic materials. The discretisation uses the mortar method wh…
Evolving surface finite element methods for random advection-diffusion equations
Ana Djurdjevac, Charles M. Elliott, Ralf Kornhuber +1
In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After statin…
Adaptive Multilevel Monte Carlo Methods for Stochastic Variational Inequalities
Ralf Kornhuber, Evgenia Youett
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spa…
An analysis of a class of variational multiscale methods based on subspace decomposition
Ralf Kornhuber, Daniel Peterseim, Harry Yserentant
Numerical homogenization tries to approximate the solutions of elliptic partial differential equations with strongly oscillating coefficients by functions from modified finite elem…
Numerical approximation of multi-phase Penrose-Fife systems
Carsten Gräser, Max Kahnt, Ralf Kornhuber
We consider a non-isothermal multi-phase field model. We subsequently discretize implicitly in time and with linear finite elements. The arising algebraic problem is formulated in…
A Variational Approach to Particles in Lipid Membranes
Charles M. Elliott, Carsten Gräser, Graham Hobbs +2
A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspecti…