The approach of layer-damping coordinate transformations to treat singularly perturbed equations is a relatively new, and fast growing area in the field of applied mathematics. This monograph aims to present a clear, concise, and easily understandable description of the qualitative properties of solutions to singularly perturbed problems as well as of the essential elements, methods and codes of the technology adjusted to numerical solutions of equations with singularities by applying layer-damping coordinate transformations and corresponding layer-resolving grids. The first part of the book deals with an analytical study of estimates of the solutions and their derivatives in layers of singularities as well as suitable techniques for obtaining results. In the second part, a technique for building the coordinate transformations eliminating boundary and interior layers, is presented. Numerical algorithms based on the technique which is developed for generating layer-damping coordinate transformations and their corresponding layer-resolving meshes are presented in the final part of this volume. This book will be of value and interest to researchers in computational and applied mathematics.

The process of breaking up a physical domain into smaller sub-domains, known as meshing, facilitates the numerical solution of partial differential equations used to simulate physical systems. In an updated and expanded Second Edition, this monograph gives a detailed treatment based on the numerical solution of inverted Beltramian and diffusion equations with respect to monitor metrics for generating both structured and unstructured grids in domains and on surfaces.

This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.

The process of breaking up a physical domain into smaller sub-domains, known as meshing, facilitates the numerical solution of partial differential equations used to simulate physical systems. In an updated and expanded Second Edition, this monograph gives a detailed treatment based on the numerical solution of inverted Beltramian and diffusion equations with respect to monitor metrics for generating both structured and unstructured grids in domains and on surfaces.