6 papers
BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: unconditional weak convergence to weak solutions
Michele Aldé, Michael Feischl, Dirk Praetorius
We consider the Landau-Lifshitz-Gilbert equation (LLG) that models time-dependent micromagnetic phenomena. We propose a full discretization that employs first-order finite elements…
Adaptive mesh refinement for the Landau-Lifshitz-Gilbert equation
Jan Bohn, Willy Dörfler, Michael Feischl +1
We propose a new adaptive algorithm for the approximation of the Landau-Lifshitz-Gilbert equation via a higher-order tangent plane scheme. We show that the adaptive approximation s…
Convergence of adaptive stochastic collocation with finite elements
Michael Feischl, Andrea Scaglioni
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element…
Sparse grid approximation of nonlinear SPDEs: The Landau--Lifshitz--Gilbert equation
Xin An, Josef Dick, Michael Feischl +2
We show convergence rates for a sparse grid approximation of the distribution of solutions of the stochastic Landau-Lifshitz-Gilbert equation. Beyond being a frequently studied equ…
Towards optimal hierarchical training of neural networks
Michael Feischl, Alexander Rieder, Fabian Zehetgruber
We propose a hierarchical training algorithm for standard feed-forward neural networks that adaptively extends the network architecture as soon as the optimization reaches a statio…
On full linear convergence and optimal complexity of adaptive FEM with inexact solver
Philipp Bringmann, Michael Feischl, Ani Miraci +2
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time.…