Parallel Spectral Numerical Methods

Table of Contents

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

Programming Languages

  1. Matlab
  2. Python
  3. Fortran

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