MATLAB Boundary conditions in the resolution of a PDE with the FFT method

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SUMMARY

This discussion focuses on imposing boundary conditions when solving partial differential equations (PDEs) using the Fast Fourier Transform (FFT) method. It establishes that discrete Fourier transforms are inherently suited for periodic domains. For non-periodic domains, the use of discrete sine or cosine transforms is applicable, but the recommended approach for general cases is to utilize a discrete Chebyshev transform to effectively leverage FFT-based algorithms.

PREREQUISITES
  • Understanding of partial differential equations (PDEs)
  • Familiarity with Fast Fourier Transform (FFT) techniques
  • Knowledge of discrete Fourier transforms and their applications
  • Experience with Chebyshev transforms in numerical analysis
NEXT STEPS
  • Research the implementation of discrete Chebyshev transforms in numerical PDE solutions
  • Explore the differences between discrete sine and cosine transforms for boundary conditions
  • Learn about the application of FFT in solving non-periodic PDEs
  • Investigate advanced techniques for imposing boundary conditions in numerical simulations
USEFUL FOR

Mathematicians, numerical analysts, and engineers working on solving partial differential equations, particularly those interested in applying FFT methods to various boundary condition scenarios.

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How to impose boundary conditions when solving a PDE with fft? For example here:
If I copy this code I get periodic boundary conditions. Thank you
 
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Well, yes. Discrete Fourier transforms are for periodic domains. If you have a non-periodic domain then depending on the boundary conditions you might be able to use a discrete sine or cosine transform, but in the general case you should use a discrete Chebyshev transform if you want access to an FFT based algorithm.
 

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