Nonzero Dirichlet boundary condition for 2D Poisson's equation

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Another methodology for solving Poisson’s Equations (and honestly I think easier) is to take the Fourier Transform. Specifically, I got it to work using Discrete Sine Transform type I. If you use the Discrete Fourier Transform regularly, in my experience I had to use an odd extension each time and then transform which is equivalent to if I had taken the DST-I of the unmodified dataset.

LudwigHorsecock