Parallel Spectral Numerical Methods



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Chapter Contents

 * 1) Acknowledgments
 * 2) Overview
 * 3) Finite Precision Arithmetic
 * 4) Separation of Variables
 * 5) Motivation for Numerical Methods
 * 6) Timestepping
 * 7) One-Dimensional Discrete Fourier Transforms
 * 8) Finding Derivatives using Fourier Spectral Methods
 * 9) Examples in Matlab and Python
 * 10) Nonlinear Ordinary Differential Equations and Iteration
 * 11) Fortran Programs and Getting Started on Windows
 * 12) Introduction to Parallel Programming
 * 13) The Cubic Nonlinear Schrodinger Equation
 * 14) The Two- and Three-Dimensional Navier-Stokes Equations
 * 15) The Klein-Gordon Equation
 * 16) /Gray Scott/
 * 17) /Maxwell's Equations/
 * 18) Incompressible Magnetohydrodynamics
 * 19) GPU programs for Fourier pseudospectral simulations of the Navier-Stokes, Cubic Nonlinear Schrodinger and sine Gordon equations
 * 20) Visualization with ParaView CoProcessing


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Programming Languages

 * 1) Matlab
 * 2) Python
 * 3) Fortran


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