Numerical study of multigrid methods with various smoothersfor the elliptic grid generation

A robust solver for the elliptic grid generation equations is sought via a numerical study. The system of PDEs is discretized with nite diierences and multigrid methods are applied to the resulting nonlinear algebraic equations. Multigrid iterations are compared with respect to the robustness and eeciency. Diierent smoothers are tried to improve the convergence of iterations. The methods are applied to four 2D grid generation problems over a wide range of grid distortions. The results of the study help to select smoothing schemes and the overall multigrid procedures for elliptic grid generation.