3D Structured Grid
 

I am writing a code to generate a 3D structured mesh using differential equations for x, y and z. I used SOR method to solve these equations, it works fine, but too slow. As I want to use this grid generator for flow with deforming boundaries (grid will be updated each time step), I need a fast process for generating the grid.

I tried to use multigrid techniques to solve the equations. Although multigrid works, but it is still too slow, and it needs many iterations to reach to a converged solution. It is more critical, if I use control functions and stretch the grid lines close to the boundaries. I used GS smoother in the multigrid. I also used linewise smoothing in the high stretching direction, but still I can't get a fast convergence.

Is there any method to accelerate this process in multigrid? Is there any method/algorithm (other than multigrid) which can solve these equations in a fast way?

Thanks
Nabi