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## Main Question or Discussion Point

Hi all, I am looking for ways to solve the following system of equations for [itex]\vec{B}[/itex]:

[tex]

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

[/tex]

[tex]

\left( \nabla \times \vec{B} \right) \cdot \nabla f = 0

[/tex]

[tex]

\nabla \cdot \vec{B} = 0

[/tex]

and [itex]f[/itex] is a known scalar function. I think we can assume there is a solution since we have 3 equations and 3 unknown components of [itex]\vec{B}[/itex].

I don't think there is an analytic solution here, but could someone give some pointers on how one would solve this system numerically?

[tex]

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

[/tex]

[tex]

\left( \nabla \times \vec{B} \right) \cdot \nabla f = 0

[/tex]

[tex]

\nabla \cdot \vec{B} = 0

[/tex]

and [itex]f[/itex] is a known scalar function. I think we can assume there is a solution since we have 3 equations and 3 unknown components of [itex]\vec{B}[/itex].

I don't think there is an analytic solution here, but could someone give some pointers on how one would solve this system numerically?