David A. Kopriva, “Implementing Spectral Methods

for Partial Differential Equations: Algorithms for Scientists and

Engineers (Scientific Computation)”

Publisher: S—er | ISBN 31: 9169396963 | 3131 | PDF | 636 pages | 6.9 MB

This book offers a systematic and self-contained approach to solve

partial differential equations numerically using single and multidomain

spectral methods. It contains detailed algorithms in pseudocode for the

application of spectral approximations to both one and two dimensional

PDEs of mathematical physics describing potentials, transport, and wave

propagation. David Kopriva, a well-known researcher in the field with

extensive practical experience, shows how only a few fundamental

algorithms form the building blocks of any spectral code, even for

problems with complex geometries. The book addresses computational and

applications scientists, as it emphasizes the practical derivation and

implementation of spectral methods over abstract mathematics. It is

divided into two parts: First comes a primer on spectral approximation

and the basic algorithms, including FFT algorithms, Gauss quadrature

algorithms, and how to approximate derivatives. The second part shows

how to use those algorithms to solve steady and time dependent PDEs in

one and two space dimensions. Exercises and questions at the end of each

chapter encourage the reader to experiment with the algorithms.

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