An adaptive step implicit midpoint rule for the time integration of Newton's linearisations of non-linear problems with applications in micromagnetics

DOI10.1007/s10915-019-00965-8zbMath1477.65162OpenAlexW2945156329WikidataQ127844477 ScholiaQ127844477MaRDI QIDQ2316256

Matthias Heil, James Miles, Milan D. Mihajlović, David Shepherd

Publication date: 26 July 2019

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-019-00965-8

zbMATH Keywords

initial value problemsRunge-Kutta methodspredictor-corrector methodsLandau-Lifshitz-Gilbert equationmicromagneticsadaptive time integration

Mathematics Subject Classification ID

Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Uses Software

• SymPy
• hlib
• ode45
• oomph-lib
• GitHub
• sym-bdf3.py

Cites Work

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• Geometrical integration of Landau-Lifshitz-Gilbert equation based on the mid-point rule
• Finite Elements and Fast Iterative Solvers
• Adaptive Time-Stepping for Incompressible Flow Part II: Navier–Stokes Equations
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• On conservative finite element formulations of the inviscid Boussinesq equations
• A New Stabilization of Adaptive Step Trapezoid Rule Based on Finite Difference Interrupts
• Adaptive Time-Stepping for Incompressible Flow Part I: Scalar Advection-Diffusion
• Finite element formalism for micromagnetism
• Convergence of an Implicit Finite Element Method for the Landau–Lifshitz–Gilbert Equation

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