7 papers
BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: a-priori error estimates
Michele Aldé, Dirk Praetorius, Michael Feischl
We consider the Landau-Lifshitz-Gilbert equation (LLG), which models time-dependent micromagnetic phenomena. We analyze a fully discrete scheme that combines first-order finite ele…
Optimal Time-Adaptivity for Parabolic Problems
Michael Feischl, Fernando HenrÃquez, David Niederkofler
Since the first optimality proofs for adaptive mesh refinement algorithms in the early 2000s, the theory of optimal mesh refinement for PDEs was inherently limited to stationary pr…
Regularized dynamical parametric approximation
Michael Feischl, Caroline Lasser, Christian Lubich +1
This paper studies the numerical approximation of evolution equations by nonlinear parametrizations $u(t)=Φ(\param(t))$ with time-dependent parameters $\param(t)$, which are to be…
A Reduced Basis Method for the Stochastic Landau-Lifshitz-Gilbert Equation
Andrea Scaglioni, Michael Feischl, Fernando HenrÃquez
In this work, we consider the construction of efficient surrogates for the stochastic version of the Landau-Lifshitz-Gilbert (LLG) equation using model order reduction techniques,…
Optimal adaptive implicit time stepping
Michael Feischl, David Niederkofler
We revisit adaptive time stepping, one of the classical topics of numerical analysis and computational engineering. While widely used in application and subject of many theoretical…
Computational Math with Neural Networks is Hard
Michael Feischl, Fabian Zehetgruber
We show that under some widely believed assumptions, there are no higher-order algorithms for basic tasks in computational mathematics such as: Computing integrals with neural netw…