Concluding Remarks

Coordinate systems generated using the approach advocated by Liseikin (2004) offer significant improvements in overall mesh smoothness. Accordingly, they should be good underlying meshes on which to numerical compute PDE solutions. Importantly, because the numerical solution process splits into finite differences along single coordinate directions, this approach easily extends to 3-D meshing or projecting 2-D surfaces into 3-D volumes. The results for this paper were generated using fairly basic monitor functions. Further work is required to better understand how other choices would potentially impact geophysical meshing solutions.