Spectral Element Methods

Chapter 8 introduces multidomain methods to compute problems in geometries that are more complex than a quadrilateral with curved sides. In multidomain spectral methods, and spectral element methods in particular, the domain of interest is subdivided into smaller subdomains that are mapped individually onto the square, allowing problems in truly complex geometries to be solved. Spectral element methods are introduced for one space dimension then generalized to two. Benchmark solutions include steady temperatures in a long cylindrical rod, propagation of a circular sound wave in a disk, and transmission and reflection of a plane wave at a material interface.