Codd, AndreaManteuffel, TMcCormick, SRuge, J2015-12-132015-12-130036-1429http://hdl.handle.net/1885/76847A new fully variational approach is studied for elliptic grid generation (EGG). It is based on a general algorithm developed in a companion paper [A. L. Codd, T. A. Manteuffel, and S. F. McCormick, SIAM J. Numer. Anal., 41 (2003), pp. 2197-2209] that involves using Newton's method to linearize an appropriate equivalent first-order system, first-order system least squares (FOSLS) to formulate and discretize the Newton step, and algebraic multigrid (AMG) to solve the resulting matrix equation. The approach is coupled with nested iteration to provide an accurate initial guess for finer levels using coarse-level computation. The present paper verifies the assumptions of the companion work and confirms the overall efficiency of the scheme with numerical experiments.Keywords: Elliptic grid generation; Least-squares discretization; Multigrid; Nonlinear elliptic boundary value problems; Approximation theory; Boundary value problems; Error analysis; Iterative methods; Mathematical transformations; Matrix algebra; Numerical analys Least-squares discretization; Multigrid; Nonlinear elliptic boundary value problems200310.1137/S00361429024044182015-12-11