Discussion Forum

Hi,

I'm working with RF-transient module and tried to deduce the governing equation used by COMSOL (wave equation of the magnetic vector potential). I came to a similar equation, however on the right side I have the "grad (div A)." Someone could explain why the Comsol considers grad (div A) = 0 in the RF-transient module (also called temw)?

Using the condition of Lorenz Gauge, classically the wave equation of the magnetic vector potential is written in the form (people.ucalgary.ca/~aknigh/fea/sys/wave.html) :

Laplacian A - u*sigma*(dA/dt) - u*eps*(d²A/dt²) = 0 (1)

Using the following identity:

curl curl A = grad(div A)- laplacian A
laplacian A = grad(div A) - (curl curl A) (2)

and substituting (2) in (1), we have:

grad(div A) - (curl curl A) - u*sigma*(dA/dt) - u*eps*(d²A/dt²) = 0
(curl curl A) + u*sigma*(dA/dt) + u*eps*(d²A/dt²) = grad(div A)
(curl curl A) + (ur*u0)*sigma*(dA/dt) + (ur*u0)*(epsr*eps0)*(d²A/dt²) = grad(div A)
(curl curl A)/ur + u0*sigma*(dA/dt) + u0*(epsr*eps0)*(d²A/dt²) = ur*grad(div A) (3)
"where ur and u0 are relative and vacuum permeability. And "u" absolute permeability."

Note that the last equation (3) is the same as the governing equation of Comsol except for the right term "ur*grad(div A)". The governing equation of RF-transient module is:

(curl curl A)/ur + u0*sigma*(dA/dt) + u0*(epsr*eps0)*(d²A/dt²) = 0

Why Comsol considers "grad(div A) = 0" ???

Thanks