Magneto-Fluid Dynamics Seminar

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The mimetic finite difference method and the mass-lumped finite element method for the Landau-Lifshitz equation

Speaker: Eugenia Kim, University of California, Berkeley

Location: Warren Weaver Hall 905

Date: Tuesday, October 17, 2017, 11 a.m.

Synopsis:

Micromagnetics studies magnetic behavior of ferromagnetic materials at sub-micrometer
length scales. The dynamics of the magnetic distribution in a ferromagnetic material are
governed by the Landau-Lifshitz equation. This equation is highly nonlinear, has a non-
convex constraint, has several equivalent forms, and involves solving an auxiliary problem
in the infinite domain, all of which pose interesting challenges in developing numerical
methods. We introduce numerical methods that preserve the properties of the underlying
PDE. First, we discuss the explicit and implicit mimetic finite difference method for the
Landau-Lifshitz equation, which is a new spatial discretization method which works on
arbitrary polygonal and polyhedral meshes. These schemes provide enormous flexibility
in modeling magnetic devices of various shapes. We present convergence tests for the
schemes on general meshes such as distorted and randomized meshes. We also provide
numerical experiments for the NIST standard problem #4 and formation of domain wall
structures in a thin film. We further present a high-order mimetic finite difference method
for the Landau-Lifshitz equation and compare the efficiencies of the low and high order
mimetic finite difference method using skyrmion simulation. Lastly, we present a new
class of convergent mass-lumped finite element method for the Landau-Lifshitz equation
that deals with weak solutions. This is a joint work with Konstantin Lipnikov and Jon
Wilkening.