Expressing magnetostatic equation as a partial differential equation

[stephenx_86]

Hi,

I am trying to model the magnetic field from two permanent magnets using Matlab, although my particular problem here relates to the physics/maths involved (though if someone could also give me advice on how to implement this particular problem in Matlab that would be awesome!). My system consists of two square magnetic regions (each of side length 5mm and gap between magnets of 1mm - although this is variable), which I have successfully modeled (although at a too low mesh density) using other PDE/FEM software using the equation:

curl(curl(A)-Br)/mu[0]) + J = 0

Where Br is the remnant magnetisation, mu[0] is the permeability of free space and J is the free charge density, which is zero in this case. I know Br is 1.24T and is parallel to the axis that runs through both magnet centres.

However, I really want to be able to use Matlab, but this requires that I express the equation above in what I presume is the standard PDE format. This is something like:

-div(c*grad(u))+ a*u = f

Where u is the variable to be solved and a and f are constants. (There are other types of PDE, but they all seem to be of the same general form)

Does anyone know how I can express my equation, in which 'A' is the thing to be solved for in the form of the second equation. I've spent absolutely hours on this and have no idea how to do it, so any help would be greatly appreciated.

Thanks in advance
Stephen

 

[eljose79]

Hi Stephen,

Thank you for reaching out for help with your problem. It sounds like you have a good understanding of the physics behind your system and have already successfully modeled it using other software. As for implementing it in Matlab, I would suggest breaking down your equation into smaller parts and then writing a script to solve for each part individually.

For example, you could start by defining your constants (mu[0], Br, and J) and then writing a script to solve for the curl of A. From there, you could solve for the curl of the curl of A and then add in the other terms (mu[0] and J) as needed. This approach may take some trial and error, but breaking it down into smaller steps can help make the problem more manageable.

Additionally, you may find it helpful to consult with other experts in the Matlab community or reach out to the Matlab support team for guidance on how to express your equation in the standard PDE format. They may have suggestions or resources that can help you better understand the format and how to apply it to your specific problem.

I hope this helps and good luck with your modeling! Don't hesitate to reach out for further assistance if needed.