Flame sheet problems are on the natural route to the numerical solution of detailed chemistry, laminar diffusion flames, which, in turn, are important in many engineering applications. In order to model the flame structure more accurately, we use the vorticity-velocity formulation of the fluid flow equations instead of the more traditional stream function-vorticity approach. The numerical solution of the resulting nonlinear coupled elliptic partial differential equations involves damped Newton iterations, adaptive grid procedures, and multigrid methods. We focus on nonlinear damped Newton multigrid, using either one way or correction schemes. Results on serial and parallel processors are presented.