This book focuses on mesh (grid) enhancement techniques - specifically, the use of selected elliptic methods for both structured and unstructured meshes associated with computational physics applications. Mesh enhancement is the process in which an existing mesh is modified to better meet the requirements of the physics application. To provide the reader with sufficient background information, seven of the nine chapters contain a summary of the numerical simulation process, basic background on mesh terminology and generation approaches, computational geometry, discretization of differential equations, methods of solving linear and nonlinear algebraic systems, geometry of surfaces in Euclidean space, and general elliptic methods for mesh enhancement. Furthermore, these chapters use the concept of harmonic coordinates to develop a unifying framework, the Laplace-Beltrami system, which is the governing principle of the book. The final two chapters apply this scheme, along with other selected elliptic methods, to various structured and unstructured example problems.
Basic Concepts; Computational Geometry and Geometric Data Structures; Discretization Methods for Differential Equations; Solving the Mesh Enhancement Algebraic Equation System; The Geometry of Surfaces in Euclidean Space; Special Coordinate Systems; Elliptic Mesh Enhancement Equation Systems; Structured Mesh Smoothing and Enhancement; Mesh Enhancement Methods for Unstructured Meshes