Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers

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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