Posted by Precise Simulation on
URL: http://forum.featool.com/Vector-Poisson-Equation-for-a-3D-Current-Source-tp338p358.html

So if I understand correctly you want to solve the system $\frac{\partial^2 Ax_i}{\partial x^2} + \frac{\partial^2 Ax_i}{\partial y^2} + \frac{\partial^2 Ax_i}{\partial z^2} = -\mu_0 Jx_i$ for $x_i = x,\ y,\ z$ in this case the corresponding FEATool equation form would read:

    A1x_x + A1y_y + A1z_z = -mu0*J1
    A2x_x + A2y_y + A2z_z = -mu0*J2
    A3x_x + A3y_y + A3z_z = -mu0*J3

where Ax = A1, Jx = J1, ... etc for clarity. You can set up this system by either using 3 custom equations, or by using a single custom equation and entering A1 A2 A3 in the "Dependent Variable Names" edit field.

custom_equation_3D_magnetostatics.fes

Note that even though you might use A1-3 to represent a vector field, these are technically three uncoupled scalar equations. (P.S. you can now use Latex/MathJax to enter equations.)