Partitioned implicit Runge-Kutta timesteppers for micromagnetics with eddy currents

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2018-08

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Abstract

Our research concerns the numerical solution of the Landau-Lifschitz-Gilbert Equation coupled with the Eddy Currents Equation. We construct a partitioned implicit Runge-Kutta timestepper with one component being L-stable and the other being quadratic invariant-preserving. Mixed (Nedelec, Vector Lagrange) finite elements are employed for spatial discretization. We discuss using the resulting scheme for simulations as well as validation tests and error estimates. Remarks on software implementation are provided.


Errata added 09/2022. Please refer to it in addition to the original dissertation.

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Keywords

Implicit Runge-Kutta, Timestepper, Finite elements, Nedelec, Vector Lagrange, Eddy currents, Landau-Lifschitz-Gilbert, Validation test, L-stable, Quadratic invariant

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