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Optimization with Particle Tracing Module

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Hi everyone,

As mentioned, I would like to use COMSOL's optimization module to apply to Particle Tracing for Fluid Flow physics interface. The model refers to "Acoustic Levitator" of the model libraries. The model solves the Pressure Acoustics, Frequency Domain to calculate the pressure p, then apply this interface on Particle Tracing for Fluid Flow to trace the trajectories of the particles. Two studies are used included: Study 1 for Frequency Domain (calculate pressure in Acoustic Pressure, Frequency Domain interface), Study 2 for Time Dependent (trace the particle's position in Particle Tracing for Fluid Flow).

The optimization is maximizing Laplacian of acoustophoretic potential energy (in Particle Tracing Module) at a specific point. To do that, I've used the probe objective with the expression d(d(fpt.Urad),x),x)+d(d(fpt.Urad),y),y) with a random probe coordinates. I've also used the Global Control Variable to define the phase of the transducer (initial value= 60[deg]; bound range from -180[deg] to 180[deg]). However, when computing, it is said the "Only the BDF solver support analytic gradient". Therefore, I try "BDF" and "Initialization only" in the "Time-Dependent Solver" but none of them works.
I' ve tried to plot the particle trajectories with the above expression and the plot works well. I suspect the problem is because of the mathematical expression of potential energy contains two terms that are in the form of realdot(a,conj(a)) but I'm not so sure.

I would very much appreciate if anyone could help me. The attached below are some settings in the model.

Sincerely,
Quoc

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