Are you looking for CAD to solve a problem or a mathematical description of the method?

I am looking for mathematical description of the method that I could implement, but if there is a program that already do this job it would be very helpful.

COMSOL, Ansys HFSS...are either of these options for you?

Do they show the vectorial solution?

Yes, COMSOL and HFSS provide the vector solution.

Unless you have a specific reason for finite element, you may also consider using the finite-difference method to obtain your vector solution. If you want to see what this might be light, take a look at Lectures 10-12 here:

http://emlab.utep.edu/ee5390cem.htm

I have since improved the description of the finite-difference method. See Topics 6b, 6c, and 7 here:

http://emlab.utep.edu/ee4386_5301_CompMethEE.htm

Both of the above courses have lecture notes and video recordings of the lectures.

Agree with Raymond Rumpf ...