Introduction to Parallel Computing (CMSC498X/CMSC818X)

Assignment 1: MPI

Due: Monday October 5, 2020 @ 11:59 PM Anywhere on Earth (AoE)

The purpose of this programming assignment is to gain experience in parallel programming on a cluster and MPI. For this assignment you have to write a parallel implementation of an iterative stencil computation.

        ./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>-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

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 deepthought2 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 512x512 input file (for 4, 8, 16 and 32 processes) for 100 iterations. Since the cluster you run on has 20 cores per node, you must time your code running on two different numbers of cores per node (--ntasks-per-node=8 and 16) to see the performance effects. In total, you will be running the program 8 times for 4 process counts X 2 cores/node settings.

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 deepthought2 primer.
• Use -g while debugging but -O3 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 16 processes	40
Performance using 4 processes	20
Speedup with 16 processes	20
Writeup	10

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