Have you ever simulated a dipole antenna in MATLAB, for example, using PDETOOL?

I am trying to achieve this, but I reach to non-accurate solutions when I set non-canonical phantoms in the environment of the dipole, comparing the results with comercial softwares.

This is because I just solve the Helmholtz equation

Laplacian of E + k^2 * E = 0

with k=2*pi*f*sqrt(mu*epsilon_c), and epsilon_c=epsilon_0*(epsilon_-j*epsilon__), and epsilon__=sigma/(2*pi*f*epsilon_0)

PDETOOL solve this equation using assempde pretty good when I set also some boundary conditions, and I set Neumann boundary conditions, using the gradient of the electric field radiated by a dipole in free-space, taking the analytical equation from Balanis - Antenna Theory.

But in this process, I do not set the dipole in the simulation domain.

Now I am trying to do this, taking into account J (current density), but I am not able to achieve any good result. I fail even in achieve the result for the electric field in free space.

I have attacked the problem calculating the inhomogeneous Helmholtz equation

Laplacian of E + k^2 * E = -j*2*pi*f*mu0*J

with J=Im*sin(k*(h-abs(y))), being h the semi-length of the dipole, and the dipole oriented in the y axis, and Im equal to the maximum current.

Also, I tried to calculate the electric potential vector, A, solving

Laplacian of A + k^2 * A = -mu0*J

and I also failed.

Note that I just simulate the dipole in free-space to validate the calculation method, but I need this method later for more complicated problems, not just the E field in free-space, solve in Modeling Antennas using MATLAB.

Any ideas?

Thanks in advance.