Grid Generation Methods and Techniques In Partial Differential Equation |
The simplest place to start an exposition of the basicphilosophy behind the use of an adapted, irregular grid is in one dimension.The most widely used method is the equidistributed mesh. The principles of themethod were later applied to generating efficient computational grids for thenumerical solution of steady PDEs. For example White used a transformation toarc-length coordinates to generate equidistributing meshes for the numericalsolution of two-point boundary value problems. In another approach where theone-dimensional mesh was iterated by trying to reduce the truncation error ofthe solution of the underlying PDE after each iteration. This is a convenientpoint at which to formally introduce and dene the equidistribution principle.