Controlled Elliptic Grid Generation

The numerical solution to the quasi-linear elliptic grid generation equation usually procedds in a staggered iterative manner. In an outer loop the control functions and the coefficients containg first order derivatives are updated. Then the linearized equation with known control functions is solved in an inner loop. This article shows that one may equally well disregard the control functions altogether and obtain the solution to the equivalent grid generation equation directly from a suitable average of the line-wise specified target central points, thus saving one of the afore-mentioned iterative loops