./jacobi2d <input filename> <# of timesteps> <size_X> <size_Y>
        

For the sample file above, size_X = size_Y = 512. The number of processes the program will run on is specified as part of the mpirun command with the -np argument.

        mpirun -np <# of processes> ./jacobi2d <input filename> <# of timesteps> <size_X> <size_Y>
        

Serial Computation

At each timestep, the value in each cell (array element) is updated by averaging the values of its four neighbors and itself.

      A[i, j] = (A[i, j] + A[i-1, j] + A[i+1, j] + A[i, j-1] + A[i, j+1]) * 0.2
      

You can assume periodic boundary conditions so the array elements at the edges will exchange data with elements on the opposite edge.

Output

Your program should write a single file called <size_X>x<size_Y>.<#-processes>-output.csv (from one designated rank) that contains comma separated values (up to three decimal points) of the 2D array. Each line in the file should correspond to one row of the array starting with i=0, j=0. This is the correct output file for the sample input file above after 100 timesteps. The only print from your program to standard output should be from process 0 that looks like this:

      TIME: Min: 25.389 s Avg: 27.452 s Max: 41.672 s
      

where Min, Avg and Max time (in seconds) are calculated using MPI reduction operations over the individual time measurements of the "main" for loop (over timesteps) on different processes for the sample 512x512 input file.

Parallel Version

Use a 2D decomposition (both rows and columns) to parallelize the program. You can assume that size_X and size_Y will be powers of 2 as will be the number of processes you will be running on. You can also assume that you will be running the program on a minimum of 4 processes and size_X and size_Y are much larger than the number of processes.

Other sample inputs and outputs after 100 timesteps:

• Input 1 Output 1 size_X = 32, size_Y = 32, timesteps = 100
• Input 2 Output 2 size_X = 64, size_Y = 128, timesteps = 100
• Input 3 Output 3 size_X = 128, size_Y = 256, timesteps = 100
• Input 4 Output 4 size_X = 1024, size_Y = 1024, timesteps = 500

What to Submit

You must submit the following files and no other files:

• jacobi2d.[c,C]: your parallel implementation
• Makefile that will compile your code successfully on zaratan when using mpicc or mpicxx. You can see a sample Makefile here. Make sure that the executable name is jacobi2d and do not include the executable in the tarball.
• You must also submit a short report (pdf) with performance results (a line plot). The line plot should present the execution times to run the parallel version on the sample 1024x1024 input file (for 4, 8, 16, 32, and 64 processes) for 500 iterations. Since the cluster you run on has 128 cores per node, you will only run on 1 node so will not be using the Infiniband network.

You should put the code, Makefile and report in a single directory (named LastName-assign1), compress it to .tar.gz (LastName-assign1.tar.gz) and upload that to ELMS.

Tips

• Quick zaratan primer.
• Use -g while debugging but -O2 when collecting performance numbers.
• MPI_Wtime example
• You can use this Python script to visualize the output csv at any timestep.

Grading

The project will be graded as follows:

Component	Percentage
Runs correctly on 4 processes	10
Runs correctly on 64 processes	40
Performance using 4 processes	20
Speedup with 64 processes	20
Writeup	10

NOTE: If your program does not run correctly, you do NOT get any points for performance/speedup.