Pérez García, Victor M.. 

We discuss how to obtain numerical solutions of the Maxwell-Bloch equations on a mesh of processors. A full multigrid method (the FMVJ method) is used to solve the systems of equations arising at each temporal step when an implicit numerical scheme is employed to study this mathematical model from laser physics. This work has been done as an interdisciplinary collaboration between various departments at Complutense University: Optics (experimental), Theoretical Physics (modellization) and Computer Sciences (implementation) together with applied matematicians from other universities (Castilla-La Mancha University in Spain and Shangai University in China) and has involved some feedback with the industry concerning the problems appearing in real CO$_2$ industrial lasers used for material processing.