Averaging in frequency domain vs averaging in time dependent study

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Hello all,

I am a novice in COMSOL and CFD in general. I have a pretty basic question regarding how frequency domain studies can be translated to time dependent studies. I am trying to simulate a 2D electric field between two electrodes with a dielectric in between. One of the electrodes is supplied with an alternating sinusoidal voltage, while the other electrode is set as the ground. In the time-dependant study, when I evaluate a surface average of normE in the dielectric, I get an average value for each time step. In comparision, when I evaluate the same in a frequency domain study, I am only getting a single average value for the particular frequency of the voltage waveform, regardless of the phase I set. My question is, is the average obtained from the frequency domain study equivalent to a time-averaged surface average normE in the time-dependent study over several periods?

Thank you


3 Replies Last Post Jun 13, 2024, 12:22 a.m. EDT
Robert Koslover Certified Consultant

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Posted: 5 months ago Jun 12, 2024, 11:06 a.m. EDT
Updated: 5 months ago Jun 12, 2024, 11:10 a.m. EDT

In a time domain study, fields do not have to exhibit a sinusoidal dependence on time. Frequency domain studies are a special case in which the time dependence is known to be sinusoidal, so a simpler approach becomes possible. Phase information is managed by treating E as complex. In the frequency domain, emw.normE is the local value of the (phase independent) magnitude of the E vector. If you want phase information, you can examine the real and imaginary parts of individual field components, or you can apply the arg function to them. In time-domain, temw.normE is the local value of the time-dependent magnitude of the E-vector. Since there is no a priori' reason for the software to assume that E will oscillate sinusoidally in a generic time domain model, no default time-averaging is performed for you (although you could set up your own operations to do something like that, if you wanted). Note: Since your specific problem has a sinusoidal dependence in time, you are better off using the frequency-domain model, which is more efficient for that purpose.

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Scientific Applications & Research Associates (SARA) Inc.
www.comsol.com/partners-consultants/certified-consultants/sara
In a time domain study, fields do not have to exhibit a sinusoidal dependence on time. Frequency domain studies are a special case in which the time dependence is known to be sinusoidal, so a simpler approach becomes possible. Phase information is managed by treating E as *complex*. In the frequency domain, emw.normE is the local value of the (phase independent) *magnitude* of the E vector. If you want phase information, you can examine the *real* and *imaginary* parts of individual field components, or you can apply the *arg* function to them. In time-domain, temw.normE is the local value of the time-dependent magnitude of the E-vector. Since there is no a priori' reason for the software to assume that E will oscillate sinusoidally in a generic time domain model, no default time-averaging is performed for you (although you could set up your own operations to do something like that, if you wanted). Note: Since your specific problem has a sinusoidal dependence in time, you are better off using the frequency-domain model, which is more efficient for that purpose.

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Posted: 5 months ago Jun 12, 2024, 5:22 p.m. EDT

Hi Robert, thank you for the detailed response. Just to follow up, if I want to find the average value of the electric field magnitude (at a point or surface) over one or more cycles in a frequency domain study, how should I proceed? I was under the assumption that it would be just equal to the phase-independant emw.normE. Thank you.

Hi Robert, thank you for the detailed response. Just to follow up, if I want to find the average value of the electric field magnitude (at a point or surface) over one or more cycles in a frequency domain study, how should I proceed? I was under the assumption that it would be just equal to the phase-independant emw.normE. Thank you.

Robert Koslover Certified Consultant

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Posted: 5 months ago Jun 13, 2024, 12:22 a.m. EDT

Again, in frequency domain, there is no averaging over cycles of the direct field quantities. You can average over space if you want to. Any temporal sinusoidally-varying scalar quantity (such any particular vector component of a sinusoidally varying field quantity) has a peak value. It also has a root mean square (rms) value, which is (for a sinusoid) 1/sqrt(2) of the peak value. Is that, perhaps, the "average" of interest to you? The true average over a cycle of any particular vector component of any sinusoidally varying field quantity is zero. After all, the average of a sine (or cosine) function over a cycle is zero. Hence, there is no need to compute it (since it is zero). You can form spatial averages of anything that you enter into operators (like Comsol's probes and post-processing integration operators) that can compute spatial averages.

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Scientific Applications & Research Associates (SARA) Inc.
www.comsol.com/partners-consultants/certified-consultants/sara
Again, in frequency domain, there is no *averaging* over cycles of the direct field quantities. You can average over space if you want to. Any temporal sinusoidally-varying scalar quantity (such any particular vector *component* of a sinusoidally varying field quantity) has a peak value. It also has a root mean square (rms) value, which is (for a sinusoid) 1/sqrt(2) of the peak value. Is that, perhaps, the "average" of interest to you? The true *average over a cycle* of any particular vector *component* of any sinusoidally varying field quantity is zero. After all, the average of a sine (or cosine) function over a cycle is zero. Hence, there is no need to compute it (since it is zero). You can form spatial averages of anything that you enter into operators (like Comsol's probes and post-processing integration operators) that can compute spatial averages.

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