1. Amir Torjeman Nitay Shiran
Parallel Processing Final Project Parallel FFT using to solve Poisson’s Equation
Amir Torjeman
Nitay Shiran

2. Poisson’s Equation
The Fourier coefficients for function Φ:

3. Solving the Equation by DFT
Perform 2D DFT on both sides of the equation becomes:

4. The DFT The problem: huge number of calculations: O(N^2)
The solution: FFT: Fast DFT algorithm

5. FFT: Decimation in time: RADIX2
Assume: N=2^d
Use: Recursive formula:
1- divide series into 2 series: fodd,feven
2- perform FFT to each serie.(recursive part)
3- F= Feven+Fodd*exp(-2πi k/N) *(-1)^kd-1

6. FFT: cont.
The Butterfly:

7. 2D DFT 2 dimensional transform: Transform each row
Replace each row with its transform
Transform each column
Replace each column with its transform

8. 2D DFT example
FFT
sinc
Square cube

9. Parallel 2D DFT: Step 1: transform rows: Divide rows to num of process.

10. Parallel 2D DFT: cont. Step 2: transform columns:
Divide columns to num
of process
Process 0 
Process 1 
Process 2 
Process 3  .

11. Our Work
Syntsize the source function f(x,y) in Matlab, and save in file.
Perform 2D parallel FFT in MPI on the source file.
Find the solution to Poisson’s equation.
save solution in file.
3) Load file in MATLAB and display solution.
Syntsize
MATLAB
Parallel Computing
MPI
Display

12. 2D FFT example:
Before:
After:

13. THANK YOU!
ANY QUESTIONS?