Dear Madame/sir,
Currently I am studying the Helmholtz equation. From the theory of electromagnetic waves I understand that the imaginary part of the complex wavevector causes damping in the system. This complex part is based on the material through which the wave propagates. In Comsol Multiphysics I modelled a 3d rectangular cavity excited by an antenna in the frequency domain. I used the default solver settings. This is a stationary solver with the Fully coupled subnode and a FGMRES iterative solver. I dont fully understand the functionality of the fully coupled subnode. Here one can choose the option for specifying the damping factor (can be either automatic Newton or constant Newton). I thought the Helmholtz equation was linear so why is there Newton method commonly used for non linear cases?
The main confusion follows from the damping factor in this subnode. How does this damping factor relate to the damping of an electromagnetic wave with a non-zero imaginary wavevector? If one decreases the damping factor, it takes more iterations to converge. If one makes it too big, it might not converge at all. If the input damping factor is directly related to the damping factor of the wavevector is it then not changing the equations and thereby the solutions?
Also why does it take less iterations to converge if you consider a room filled with a non-zero conductivity material with respect to a room filled with a material with zero conductivity?
Some explanation to clear up the confusion would be a great help! Thanks in advance. Yours sincerely, Gijs Mast