A generalized length strategy for direct optimization in planar grid generation

We consider an alternative to conventional grid generation strategies based on the length functional. These conventional strategies include using an inverse mapping (the famous Winslow generator), or augmenting length with other functionals that promote unicity. Both strategies have the drawback that the resulting minimization problem becomes complicated and expensive. As an alternative, we propose a generalized strategy for length which does not use inverse mappings or auxiliary functionals. The strategy, based largely on reference mappings, provides flexibility in controlling grid quality, and its minimization problems can be solved using a simple multigrid algorithm, yielding a grid generation scheme with optimal complexity.