Implementing Spectral Methods for Partial ...

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Beschreibung

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 ¿toö. 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.

Über den Autor

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.

Zusammenfassung

First book to cover multidomain spectral methods for the numerical solution of time-dependent 1D and 2D partial differential equations

Presented without too much abstract mathematics and minutae

Contains a set of basic examples as building blocks for solving complex PDEs in realistic geometries

With exercises and questions at the end of each chapter

Both an introduction for graduate students and a reference for computational scientists working on numerical solutions of PDEs

Includes supplementary material: [...]

Inhaltsverzeichnis

Approximating Functions, Derivatives and Integrals.- Spectral Approximation.- Algorithms for Periodic Functions.- Algorithms for Non-Periodic Functions.- Approximating Solutions of PDEs.- Survey of Spectral Approximations.- Spectral Approximation on the Square.- Transformation Methods from Square to Non-Square Geometries.- Spectral Methods in Non-Square Geometries.- Spectral Element Methods.- Erratum.- Erratum.

Erscheinungsjahr:	2010
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xviii 397 S.
ISBN-13:	9789048184842
ISBN-10:	9048184843
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Kopriva, David A.
Auflage:	Softcover reprint of hardcover 1st edition 2009
Hersteller:	Springer Netherland Springer Netherlands
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 23 mm
Von/Mit:	David A. Kopriva
Erscheinungsdatum:	19.10.2010
Gewicht:	0,622 kg

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