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I am working on a optimization problem involving vector fields. In order to define a objective function I need a measure (scalar quantity) of some properties of the vector field. The vector field comes from a finite element analysis, that is the vector field is calculated on a discretized domain. If possible I want to exclude the time domain.

The properties I am intrested in are the path/direction of the vector field. Due to the geometry and material properties the vector field (or flux) travels in an unwanted path.

Until now I have used a 1-dimensional measure( flux through a surface), calculated the fourier transform and total harmonic distortion to describe the problem. But I feel this is not a good enough description of the behavior.

I have tried searching for a better solution but having difficulties finding the proper solution. From all the math class I have had up until now I dont recall a method having such a function. I have thought of a 2D fourier transform but i lack the knowledge of analyzing the results. In essence I need a scalar quantity in the end. I dont know if one can describe the vector field by harmonic content as with the 1D case.

I dont need a actual unit on the measure, but a quantity who describe the field and how the field changes when the geometry of the domain is changed.

I would be very happy if any of you guys and girls could guide me in the right direction and suggest some methods I can look into.

Thanks,

SirAskalot

(if this thread fits better in another sub-category, let me know)

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# Analysis of vector fields, fourier and harmonics

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