Multigrid Methods for Mesh Relaxation

When generating a mesh for the initial conditions for a computer simulation, you want the mesh to be as smooth as possible. A common practice is to use equipotential mesh relaxation to smooth out a distorted computational mesh. Typically a Laplace-like equation is set up for the mesh coordinates and then one or more Jacobi iterations are performed to relax the mesh. As the zone count gets really large, the Jacobi iteration becomes less and less effective and we are stuck with our original unrelaxed mesh. This type of iteration can only damp high frequency errors and the smooth errors remain. When the zone count is large, almost everything looks smooth so relaxation cannot solve the problem. In this paper we examine a multigrid technique which effectively smooths out the mesh, independent of the number of zones