# 2D axisymmetric Magnetostatics Finite Element Method solver

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 code and have followed the method as described in the book by J.Bastos and N Sadowski. I managed to get the solutions and verified it from FEMM (a open source software package for magnetics and electrostatics). 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 verify my code using FEMM (as there are no validation problems in the book), I am not able to match the results.

The axisymmetric problem I am trying is a square domain with side =60mm.The axis of symmetry is the bottom side of the square. A small square at the centre with 20mm side carries a current density of $$10^6$$ $$A/m^2$$. All the edges of the outer square boundaries are at A=0 where A is the magnetic vector potential. The material of the inner square with current density is one with $$\mu_r$$= 1 and the outer square has a $$\mu_r$$= 10.I am solving for the vector potential inside the bigger square.The equations I am solving are

$$\vec{\nabla} \times \vec{H}=\vec{J}$$

$$\vec{\nabla}\cdot\vec{B}=0$$

$$\vec{B}=\mu \vec{H}$$

I am solving for the magnetic vector potential $$A$$ where

$$\vec{\nabla} \times \vec{A}=\vec{B}$$

My questions are

1. I have been stuck on this for a while. Is there any paper or book which has a verification 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?

P.S.: I am not sure if I have explained the problem clearly. Let me know if any clarifications are required

• I think that you are referring to verification and not validation. Having said that, I'd trust FEMM since it is specialized in electromagnetics. If you are in need for verification you could try with analytical solutions and using the method of Manufactured solutions. If you write some of the equations more people might be able to give you suggestions. Oct 31 '21 at 21:34
• Also, it is a good idea to add the complete bibliographic information of the books. Oct 31 '21 at 21:39
• @nicoguaro you are right. What I am looking for is a verification problem for my code. I will edit the question and add the bibliographic information. Also I will add the relevant equations Nov 3 '21 at 14:41