Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers (Scientific Computation)

This book offers a systematic and self-contained approach to solvepartial differential equations numerically using single and multidomain spectralmethods. It contains detailed algorithms in pseudocode for the applicationof spectral approximations to both one and two dimensional PDEsof mathematical physics describing potentials,transport, and wave propagation. David Kopriva, a well-known researcherin the field with extensive practical experience, shows how only a fewfundamental algorithms form the building blocks of any spectral code, evenfor problems with complex geometries. The book addresses computationaland applications scientists, as it emphasizes thepractical derivation and implementation of spectral methods over abstract mathematics. It is divided into two parts: First comes a primer on spectralapproximation and the basic algorithms, including FFT algorithms, Gaussquadrature algorithms, and how to approximate derivatives. The secondpart shows how to use those algorithms to solve steady and time dependent PDEs in one and two space dimensions. Exercises and questions at theend of each chapter encourage the reader to experiment with thealgorithms.