Transformation Methods from Square to Non-Square Geometries

Abstract

The first step to extend spectral methods to approximate the solutions of PDEs in complex geometries is to derive methods for quadrilateral domains with curved sides. Chapter 6 introduces the most commonly used approach, which creates a mapping from the square to the domain on which the solution is desired. The chapter then shows how to transform the equations when a mapping is used. The end of the chapter shows how to approximate and compute the geometric quantities needed to approximate the solutions of PDEs in quadrilateral domains.