I'm trying to simulate by finite elements method Maxwell equations for a current carrying wire. My 3d geometry consists of a cylinder and a box containing it. I will use a mixed formulation and Nedelec's elements introducing a vector potential. I'm in a magnetostatic regime. At the end of the simulation I would like to plot the lines of the magnetic field around the wire (the cylinder) and probably compute forces and see that the numerics method agrees with classical results. My troubles concern the boundary conditions I have to impose on the surfaces of the cylinder (side, top and bottom) and on the box. I think I will use a value of permittivity of $\mu_0$ for the box and a copper relative one for the wire. I hope someone of you can help me seeing that my physics background is not so good.
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2$\begingroup$ Maybe better suited to be posted in Computational Science $\endgroup$– John AlexiouFeb 27, 2014 at 13:42
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1$\begingroup$ @ja72 I think this topic is fine for Physics SE. $\endgroup$– DanielSankMay 23, 2017 at 0:29
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3$\begingroup$ The way this site works is that you ask a question and other users answer. This post does not seem to ask a question. Phrase edit it. $\endgroup$– DanielSankMay 23, 2017 at 0:30
2 Answers
Some updates....I found out I will have to impose boundary conditions like: $$\mu^{-1}curl \textbf{A} \times \textbf{n} =\textbf{0}$$ in the outer boundary and in the interface. Those corresponds to the Neumann natural conditions of my weak formulation and those imply that in the two boundary pieces $\textbf{H} \times \textbf{n} = \textbf{0}$. Furthermore I need to impose $$ \textbf{B} \cdot \textbf{n} =0 $$ just at the interface and this in terms of the vector potential formulation corresponds to $\textbf{A} \times \textbf{n} = \textbf{0}$. This last corresponds to a Dirichlet boundary condition.
Can someone confirm what I said? The problem is that even if is true I don't know how to implement the Dirichlet boundary conditions with freefem++...
It is easier to answer if you have a sketch of the problem you want to solve.
I think that good results can be obtained only by setting the outer space section large enough and giving no boundary conditions at the outer boundary (which is equivalent to giving $\bf{n}\times\bf{H}=\bf{0}$ at the outer boundary).
[Edit #1]
A similar problem was solved numerically. Centered cubic iron (assumed linear material having relative permeability 1500) and circular coil. Boundary conditions ($\vec{n}\times \vec{A}=0$) are applied to the x=0 and y=0 planes to meet symmetry.
Numerically calculated magnetic B fields and vector A potentials are shown.
