Overview

This book is aimed to be both a textbook for graduate students and a starting point for applicationsscientists. It is designedto show how to implementspectral methods to approximate the solutions of partial differential equations. It presents a syst- atic development of the fundamental algorithms needed to write spectral methods codes to solve basic problems of mathematical physics, including steady potentials, transport, and wave propagation. As such, it is meant to supplement, not replace, more general monographs on spectral methods like the recently updated ""Spectral Methods: Fundamentals in Single Domains"" and ""Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics"" by Canuto, Hussaini, Quarteroni and Zang, which provide detailed surveys of the variety of methods, their performance and theory. I was motivated by comments that I have heard over the years that spectral me- ods are ""too hard to implement."" I hope to dispel this view-or at least to remove the ""too"". Although it is true that a spectral code is harder to hack together than a s- ple ?nite difference code (at least a low order ?nite difference method on a square domain), I show that only a few fundamental algorithms for interpolation, differen- ation, FFT and quadrature-the subjects of basic numerical methods courses-form the building blocks of any spectral code, even for problems in complex geometries. Ipresentthealgorithmsnotonlytosolveproblemsin1D,but2Daswell,toshowthe ?exibility of spectral methods and to make as straightforward as possible the tr- sition from simple, exploratory programs that illustrate the behavior of the methods to application programs.

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9789048184842

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Reviews

From the reviews: This book focuses on the implementation aspects of spectral methods. ... serve as a textbook for graduate students and applied mathematics researchers who seek a practical way to implement spectral algorithms. The presentation is pedagogical, moving from algorithms that are easy to understand to ones that are more complex and involved. ... It is a very recommendable book for a graduate course on spectral methods, and covers more practical subjects that are not usually treated in detail in other monographs on spectral methods. (Javier de Frutos, Mathematical Reviews, Issue 2010 j)

From the reviews: This book focuses on the implementation aspects of spectral methods. ... serve as a textbook for graduate students and applied mathematics researchers who seek a practical way to implement spectral algorithms. The presentation is pedagogical, moving from algorithms that are easy to understand to ones that are more complex and involved. ... It is a very recommendable book for a graduate course on spectral methods, and covers more practical subjects that are not usually treated in detail in other monographs on spectral methods. --- (Javier de Frutos, Mathematical Reviews, Issue 2010 j)

From the reviews: This book focuses on the implementation aspects of spectral methods. ! serve as a textbook for graduate students and applied mathematics researchers who seek a practical way to implement spectral algorithms. The presentation is pedagogical, moving from algorithms that are easy to understand to ones that are more complex and involved. ! It is a very recommendable book for a graduate course on spectral methods, and covers more practical subjects that are not usually treated in detail in other monographs on spectral methods. (Javier de Frutos, Mathematical Reviews, Issue 2010 j)

Author Information

David Kopriva is Professor of Mathematics at the Florida State University, where he has taught since 1985. He is an expert in the development, implementation and application of high order spectral multi-domain methods for time dependent problems. In 1986 he developed the first multi-domain spectral method for hyperbolic systems, which was applied to the Euler equations of gas dynamics.

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