Thesis
Numerical analysis and simulation of magnetoelastic, antiferromagnetic, and ultrafast magnetic materials
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2026
- Thesis identifier
- T17693
- Person Identifier (Local)
- 202268973
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- For modern technological applications, magnetic materials and their underlying magnetization dynamics are of great interest for data storage, spintronic devices, and various magnetic sensors. The dynamics of magnetization are typically modelled by the Landau–Lifshitz–Gilbert (LLG) equation, which is a highly nonlinear, time-dependent partial differential equation, subject to a non-convex unit length constraint, and governed by an intrinsic dissipative energy law. The LLG equation is often extended to include additional effects, such as magnetoelastic coupling, where the magnetic and elastic behaviour of the material are coupled through the conservation of momentum equation, antiferromagnetic/ferrimagnetic interactions where multiple LLG equations are coupled together, and ultrafast dynamics where the LLG equation includes a higher derivative term in time yielding high frequency nutation behaviour on short time-scales. Each of these extensions introduces additional complications to the analysis and efficient numerical simulation of the respective models. In this thesis, we develop finite element numerical schemes based upon a projection-free tangent plane scheme, with first-order finite elements for the spatial discretization where the LLG equation is reformulated in its tangent space, and the unit length constraint is not enforced via a nodal projection to the sphere. Despite this, the schemes are fully linear, decoupled, unconditionally stable, and, under suitable assumptions, convergent to weak solutions. Importantly, we do not require restrictive geometric conditions on the meshes used in the numerical schemes. Particular attention is paid to the energetic behaviour of the discrete schemes, with a focus on mimicking the energy law satisfied by the continuous problem at the discrete level. Numerical experiments are provided to demonstrate the performance of the schemes and to support our theoretical findings.
- Advisor / supervisor
- Barrenechea, Gabriel R.
- Ruggeri, Michele
- Resource Type
- DOI
- Funder
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PDF of thesis T17693 | 2026-04-15 | Public | Download |