The Eddy Current--LLG Equations: FEM-BEM Coupling and A Priori Error Estimates

DOI10.1137/16M1065161zbMath1378.35291arXiv1602.00745MaRDI QIDQ4976110

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Publication date: 27 July 2017

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.00745

zbMATH Keywords

finite elementLandau-Lifshitz-Gilbert equationferromagnetismcouplingboundary elementa priori error estimateeddy current

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with optics and electromagnetic theory (35Q60) A priori estimates in context of PDEs (35B45) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Boundary element methods applied to problems in optics and electromagnetic theory (78M15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Electro- and magnetostatics (78A30)

Related Items (13)

Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics ⋮ Temporal convergence of extrapolated BDF-2 scheme for the Maxwell-Landau-Lifshitz equations ⋮ Existence of Regular Solutions of the Landau--Lifshitz--Gilbert Equation in 3D with Natural Boundary Conditions ⋮ FEM-BEM coupling for the Maxwell-Landau-Lifshitz-Gilbert equations via convolution quadrature: weak form and numerical approximation ⋮ The mass-lumped midpoint scheme for computational micromagnetics: Newton linearization and application to magnetic skyrmion dynamics ⋮ Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps ⋮ Computational micromagnetics with Commics ⋮ Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics ⋮ Convergence of an implicit-explicit midpoint scheme for computational micromagnetics ⋮ Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics ⋮ Convergence analysis of a second-order semi-implicit projection method for Landau-Lifshitz equation ⋮ Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation ⋮ Numerical analysis of the Landau–Lifshitz–Gilbert equation with inertial effects

Uses Software

• FEniCS
• SyFi
• BEM++

Cites Work

• A convergent finite element approximation for the quasi-static Maxwell-Landau-Lifshitz-Gilbert equations
• A convergent and precise finite element scheme for Landau-Lifschitz-Gilbert equation
• Automated solution of differential equations by the finite element method. The FEniCS book
• A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equations
• A survey on the numerics and computations for the Landau-Lifshitz equation of micromagnetism
• A new finite element scheme for Landau-Lifschitz equations
• Existence, regularity and local uniqueness of the solutions to the Maxwell-Landau-Lifshitz system in three dimensions
• Time average in micromagnetism
• Spin-polarized transport in ferromagnetic multilayers: an unconditionally convergent FEM integrator
• On traces for functional spaces related to Maxwell's equations Part I: An integration by parts formula in Lipschitz polyhedra
• Projection-free approximation of geometrically constrained partial differential equations
• Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems
• Recent Developments in the Modeling, Analysis, and Numerics of Ferromagnetism
• A Convergent Implicit Finite Element Discretization of the Maxwell–Landau–Lifshitz–Gilbert Equation
• On global weak solutions for Landau-Lifshitz equations: Existence and nonuniqueness
• On Landau-Lifshitz’ equations for ferromagnetism
• Finite Element Methods for Maxwell's Equations
• On a decoupled linear FEM integrator for eddy-current-LLG
• Solving Boundary Integral Problems with BEM++
• Differential Forms, Galerkin Duality, and Sparse Inverse Approximations in Finite Element Solutions of Maxwell Equations
• Numerical analysis of an explicit approximation scheme for the Landau-Lifshitz-Gilbert equation
• Convergence of an Implicit Finite Element Method for the Landau–Lifshitz–Gilbert Equation
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