Solving Poisson’s Equation with the FFT II
So solution of Poisson’s equation involves the following steps
1) Find the Fourier coefficients fjk of f(x,y) by performing integral
2) Form the Fourier coefficients of ? by ?jk = fjk / (-p2j2 - p2k2)
3) Construct the solution by performing sum ?(x,y)
There is another version of this (Discrete Fourier Transform) which deals with functions defined at grid points and not directly the continuous integral
- Also the simplest (mathematically) transform uses exp(-2pijx) not sin(p jx)
- Let us first consider 1D discrete version of this case
- PDE case normally deals with discretized functions as these needed for other parts of problem