Time Periodic
Whenever a problem is time periodic, the fields are functions of the phase ϕ as well as periodic with the period 2π. The difference compared to the Frequency Domain is that the dependence is not necessarily harmonic here. A generic periodic phase function is allowed and affects
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Dependent variables, such as the out-of-plane component of the magnetic vector potential AZ(ϕ) in The Magnetic Machinery, Rotating, Time Periodic Interface in 2D.
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Derived quantities, such as the magnetic flux density B(ϕ) =∇ × (AZ(ϕ)eZ) in The Magnetic Machinery, Rotating, Time Periodic Interface in 2D.
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External sources defined through user inputs, such as the out-of-plane component of the external current density JeZ(ϕ) in The Magnetic Machinery, Rotating, Time Periodic Interface in 2D.
The frequency of the time periodic signal is typically referred to as fTP and is a physics variable, which may be inherited from the study. The phase is related to this frequency by the usual relation ϕ = 2πfTPt. It follows that time derivatives in time periodic problems can conveniently be computed as derivatives with respect to phase through the relation
The phase dependence is typically mapped on evenly distributed points and phase derivatives at a given phase value are computed as a ratio between the variable values at the closest phase values.
Averages, root mean squares, standard deviations, and Fourier transform coefficients derived from time periodic variables are available in result evaluation. For The Magnetic Machinery, Rotating, Time Periodic Interface, more details can be found in Feature Specific Variables and Accessing the Solution at Different Phases.