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

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9789048184842: Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers (Scientific Computation)

This book explains how to solve partial differential equations numerically using single and multidomain spectral methods. It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.

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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.

About the Author:

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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David A. Kopriva
Published by Springer, Netherlands (2010)
ISBN 10: 9048184843 ISBN 13: 9789048184842
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Book Description Springer, Netherlands, 2010. Paperback. Book Condition: New. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. 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,b ut2Daswell,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. Softcover reprint of hardcover 1st ed. 2009. Bookseller Inventory # LIE9789048184842

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Book Description Springer, Netherlands, 2010. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****.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. Softcover reprint of hardcover 1st ed. 2009. Bookseller Inventory # AAV9789048184842

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Book Description Springer, Netherlands, 2010. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****. 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. Softcover reprint of hardcover 1st ed. 2009. Bookseller Inventory # AAV9789048184842

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