Analysis of the operator \(\Delta^{-1}\text{div}\) arising in magnetic models

DOI10.4171/ZAA/1212zbMath1137.35342OpenAlexW2058213353MaRDI QIDQ879696

Dirk Praetorius

Publication date: 14 May 2007

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/1212

zbMATH Keywords

integral representationLaplace equationmicromagneticsCalderón-Zygmund kernelhierarchical matricesmagnetic potentialpanel clustering

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Integral representations of solutions to PDEs (35C15) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Integral representations, integral operators, integral equations methods in two dimensions (31A10) Statistical mechanics of magnetic materials (82D40)

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Spin-polarized transport in ferromagnetic multilayers: an unconditionally convergent FEM integrator ⋮ Micromagnetics of thin films in the presence of Dzyaloshinskii–Moriya interaction ⋮ The mass-lumped midpoint scheme for computational micromagnetics: Newton linearization and application to magnetic skyrmion dynamics ⋮ Curved thin-film limits of chiral Dirichlet energies ⋮ Variational Principles of Micromagnetics Revisited ⋮ Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics ⋮ Boundary regularity for minimizers of the micromagnetic energy functional ⋮ Convergence of an implicit-explicit midpoint scheme for computational micromagnetics ⋮ Applications of \(\mathcal H\)-matrix techniques in micromagnetics ⋮ Effective simulation of a macroscopic model for stationary micromagnetics ⋮ On stabilized models in micromagnetics ⋮ Micromagnetics of curved thin films ⋮ Spin-diffusion model for micromagnetics in the limit of long times

Cites Work

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• Applications of \(\mathcal H\)-matrix techniques in micromagnetics
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• Analysis of the Finite Element Approximation of Microstructure in Micromagnetics
• Elliptic Partial Differential Equations of Second Order
• A Posteriori Error Control in Adaptive Qualocation Boundary Element Analysis for a Logarithmic-Kernel Integral Equation of the First Kind
• Numerical Analysis for a Macroscopic Model in Micromagnetics

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