# Computation of resistance with arbitrary local resistivity rho(x,y,z)

Bonjour,

I need to numerically compute the net electrical resistance of a given geometry.

I know the shape of my object, it is relatively simple. It's close to this: http://2.imimg.com/data2/QX/UC/IMFCP-3019296/i-shape-big-1-250x250.jpg
Actually my shape is even simpler because it's a parallelepiped flanked by two trapezoids.

As data, I have many points coordinates x,y,z and the corresponding resistivity which is unusually dependant of the position.

my data table looks like that:

x1 y1 z1 rho1
x2 y2 z2 rho2
x3 y3 z3 rho3
x4 y4 z4 rho4
...
ect...
...
xn yn zn rhon

n is my number of point in my geometry.

Naturally, since the electrical current will preferentially go to the low resistivity domain. I cannot use the R=rho*l/S formula.

I probably have to solve J=sigma*E for every point with sigma(x,y,z)=1/rho(x,y,z)

Does someone have any idea of algorithm that can compute the resistance?

Thank you very much

Pierre