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Parallel Spectral Numerical Methods
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  • Title Parallel Spectral Numerical Methods
  • Author(s) Gong Chen, Brandon Cloutier, Ning Li, Benson Muite and Paul Rigge, et al
  • Publisher: Open Michigan (University of Michigan)
  • License(s): CC BY 3.0
  • Hardcover/Paperback N/A
  • eBook HTML and PDF (348 pages)
  • Language: English
  • ISBN-10: N/A
  • ISBN-13: N/A
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Book Description

This book teaches the principals of Fourier spectral methods, their utility in solving partial differential equation and how to implement them in code. Performance considerations for several Fourier spectral implementations are discussed and methods for effective scaling on parallel computers are explained.

It starts by taking a quick look at finite precision arithmetic. It then discusses how to solve ordinary differential equations (ODE) and partial differential equations (PDE) using separation of variables. Next, it introduces numerical time-stepping schemes that can be used to solve ODEs and PDEs. This is followed by an introduction to pseudo spectral methods through an overview of the discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT) algorithm that is used to quickly calculate the DFT. Finally it will combine all of these to solve a couple of different PDEs first in a serial setting and then in a parallel setting.

The programs will use Matlab1 and Fortran. A Python2 implementation of some of the Matlab programs is also provided.

About the Authors
  • Gong Chen is an undergraduate student in School of Mathematics, University of Minnesota- Twin Cities. His mathematical interests are analysis, differential equations and mathematical physics.
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