I am new to the field of magnetostatics. I wish to write a 2d finite element code for obtaining the magnetic field inside a solenoid coil. I have started with a 2d xy code and have followed the method as described in the book by J.Bastos and N Sadowski. I managed to get the solutions and validated it from FEMM. I have also built the code for 2d axisymmetric problem using the method described in the book by Nathan Ida. However when i am trying to validate my code using FEMM, I am not able to match the results.
The problem I am trying is a square domain with side =60mm. A small square at the centre with 20mm side carries a current density of 10^6 A/m2. All the edges of the square boundaries are at A=0 where A is the vector potential. The material of the inner square with current density is one with relative per of 1 and the outer square has a rel. perm of 10.
My questions are
1. I have been stuck on this for a while. Is there any paper or book which has a validation problem for the same which clearly brings out the method?
2. Is there a open source code for axisymmetric case that i can refer to? Or any experts that can help me in the algorithm for axisymmetric FEM for magnetic vector potential?
Hello Shekhar,
I have not worked with FEMM, but I use COMSOL and I can suggest you this link:
https://www.comsol.it/support/learning-center/article/Modeling-Electromagnetic-Coils-8381/112
it is an entire course on modelling coils in 2D and 3D. The interface is not the same of FEMM, but the concepts should apply.
I have not tried your simulation, but I believe that the problem is related to the fact that you are forcing all the boundaries of your geometry to be at A=0. You should try to add an air volume around the solenoid and use different boundaries conditions.
I think Matlab has a FEM solver for the magnetostatics problem. You can look for it.
Hi Shekhar,
The main changes in the axisymmetric coordinate system are different forms of the differential operators, see https://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates .
Usually a change of variable for the potential A
Thank you everyone for your replies. As you rightly mentioned, Léo Friedrich the change of variable worked. Also I referred the following books where different methods are mentioned. The one by Ida is the one I used.
Book Electromagnetics and Calculation of Fields
https://www.wiley.com/en-us/The+Finite+Element+Method+in+Electromagnetics%2C+3rd+Edition-p-9781118571361
Both methods work well