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This scheme is proved to be positive under a suitable time step constraint.
The use of a different chemically controlled time step constraint in both calculations induces some inconsistencies into the validation tests.
One of the main difficulties in micromagnetics simulation is the severe time step constraint introduced by the exchange field.
Furthermore, by applying the positivity-preserving limiter, our fully discretized scheme produces non-negative solutions for all cases under a time step constraint.
Normal-mode analyses are performed to indicate the stability of the proposed scheme and the associated time step constraint for a stable computation.
We use the relaxation system formulation [28] for describing the XMHD model, and solve the equations using a split level implicit explicit time advance scheme, stepping over the time step constraint imposed by the stiff source terms.
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Actually the stability condition may imply very tight time step constraints.
Explicit methods for their solution are easy to implement but have very restrictive time step constraints.
The time step constraints were also re-evaluated to account for the change resulting from mesh refinement.
It is suitable for very short lines where the travelling wave models cannot be used, due to time step constraints.
In a second step, constraints and potential of buried pipe systems are analyzed for the case of a typical Central European climate, for which the constraint between climate and comfort threshold induces a fundamental asymmetry between preheating and cooling potential.
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