Overview

Mesh enhancement is best defined as the set of operations designed to improve a mesh. Improvement of a mesh means different things to different people and it involves a variety of numerical algorithms and depends on the target application that the mesh will support. Improving a mesh may mean making the mesh cells or elements as nearly uniform in volume as possible. It might also mean packing mesh cells near a particular boundary according to a specified rule in order to capture a given physical phenomenon. It might mean that variations in cell volume are smooth over the domain; that the mesh is free of isolated large or small cells surrounded by cells of approximately uniform volume.

Historically, mesh improvement has been referred to as grid generation. In this monograph, the phrase mesh enhancement is used instead, leaving grid generation to mean the operations performed on the given geometry to produce an initial mesh. It is the initial mesh that is to be enhanced through the elliptic methods described herein. The mesh improvement process is also, at times, called mesh smoothing. In addition, as the reader has already seen, the terms mesh and grid are used interchangeably to mean the set of cells, faces, and/or nodes that represent the discretization of physical space contained and defined by geometrical surfaces, etc. for use by an approximate numerical algorithm for the purpose of simulating a physical process.

Ultimately, the intent of mesh enhancement is to...