Tuesday, 23 May 2017, 5 p.m. (sharp),
Dr. Michele Ruggeri, TU Vienna,
at the conference room of IMATI-CNR in Pavia, will give a lecture titled:
MATHEMATICAL CHALLENGES IN COMPUTATIONAL MICROMAGNETICS
as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).
At the end a refreshment will be organized.
The understanding of the magnetization dynamics plays an essential
role in the design of many technological applications, e.g., magnetic
sensors, actuators, and storage devices. The availability of reliable
numerical tools to perform large-scale micromagnetic simulations of
magnetic systems is therefore of fundamental importance.
Time-dependent micromagnetic phenomena are usually described by the
Landau--Lifshitz--Gilbert (LLG) equation. The numerical integration of
the LLG equation poses several challenges: strong nonlinearities, a
nonconvex pointwise constraint, an intrinsic energy law, which
combines conservative and dissipative effects, as well as the presence
of nonlocal field contributions, which prescribe the coupling with
other partial differential equations.
In this talk, we consider the numerical analysis of a class of tangent
plane integrators for the LLG equation.
The methods are based on equivalent reformulations of the equation in
the tangent space, which are discretized by first-order finite
elements and only require the solution of one linear system per
The pointwise constraint is enforced at the discrete level by applying
the nodal projection mapping to the computed solution at each
time-step. Under appropriate assumptions, the convergence towards a
weak solution of the problem is unconditional, i.e., the numerical
analysis does not require to impose any CFL-type condition on the
time-step size and the spatial mesh size. Numerical experiments
support our theoretical findings and demonstrate the applicability of
the method for the simulation of practically relevant problem sizes.
This is joint work with Dirk Praetorius, Bernhard Stiftner (TU Wien),
Claas Abert, and Dieter Suess (University of Vienna).