Publications in Scientific Journals:

N. Mauser, C.-M. Pfeiler, D. Praetorius, M. Ruggeri:
"Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics";
Applied Numerical Mathematics, 180 (2022), 33 - 54.

English abstract:
Recently, Kim & Wilkening (Convergence of a mass-lumped finite element method for the
Landau-Lifshitz equation, Quart. Appl. Math., 76, 383-405, 2018) proposed two novel
predictor-corrector methods for the Landau-Lifshitz-Gilbert equation (LLG) in micromagnetics,
which models the dynamics of the magnetization in ferromagnetic materials. Both integrators
are based on the so-called Landau-Lifshitz form of LLG, use mass-lumped variational
formulations discretized by first-order finite elements, and only require the solution of linear
systems, despite the nonlinearity of LLG. The first(-order in time) method combines a linear
update with an explicit projection of an intermediate approximation onto the unit sphere in order
to fulfill the LLG-inherent unit-length constraint at the discrete level. In the second(-order in
time) integrator, the projection step is replaced by a linear constraint-preserving variational
formulation. In this paper, we extend the analysis of the integrators by proving unconditional
wellposedness and by establishing a close connection of the methods with other approaches
available in the literature. Moreover, the new analysis also provides a well-posed integrator for
the Schrödinger map equation (which is the limit case of LLG for vanishing damping). Finally, we
design an implicit-explicit strategy for the treatment of the lower-order field contributions,
which significantly reduces the computational cost of the schemes, while preserving their
theoretical properties.

"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)

Created from the Publication Database of the Vienna University of Technology.