Link to this document's Jupyter Notebook

In order to successfully complete this assignment you need to participate both individually and in groups during class. If you attend class in-person then have one of the instructors check your notebook and sign you out before leaving class on Wednesday February 24. If you are attending asynchronously, turn in your assignment using D2L no later than 11:59pm on Wednesday February 24.

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In-Class Assignment: Practice using Wave Equation example

Image from: https://commons.wikimedia.org/wiki/File:2D_Wave_Function_resize.gif

Agenda for today's class (70 minutes)

1. (20 minutes) Pre class Review
2. (20 minutes) Practice using OpenMP loop Wave Equation
3. (30 minutes) 2D Wave Equation

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1. Pre class Review

0223--OMP_Data_pre-class-assignment

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2. Practice using OpenMP 1D Wave Equation

The rest of class we will try to help each other out so that everyone gets a parallel OpenMP version of the Pi-code working. We will use breakout rooms for smaller groups so you can help each other out. Lets see how far we get doing the following:

• If you are stuck or confused, raise your hand and ask for help.
• If you get stuck review code in the Google document.
• Help your neighbors
• If you have your basic code working, share it on the Google document.
• Once you have a parallel code working, do a scaling study and very the number of cores. Plot the results and share your plot on the Google document.
• Conduct the scaling study on different development nodes and generate different plots. Share them on the Google document.
• Write a submission script and run the scaling study using the SLURM scheduler.
• Share all of your solutions with each other using the following Google Document.
• Review the Google Document and learn from each other's solutions.

Group Google Document

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3. 2D Wave Equation

Consider the following example program. See if you can get the serial version running. Benchmark it and then get it working faster using OpenMP

%%writefile 2d_wave.c

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "png_util.h"
#define min(X,Y) ((X) < (Y) ? (X) : (Y))
#define max(X,Y) ((X) > (Y) ? (X) : (Y))

int main(int argc, char ** argv) {
    int nx = 500;
    int ny = 500;
    int nt = 10000; 
    int frame=0;
    //int nt = 1000000;
    int r,c,it;
    double dx,dy,dt;
    double max,min;
    double tmax;
    double dx2inv, dy2inv;
    char filename[sizeof "./images/file00000.png"];

    image_size_t sz; 
    sz.width=nx;
    sz.height=ny;

    //make mesh
    double * h_z = (double *) malloc(nx*ny*sizeof(double));
    double ** z = malloc(ny * sizeof(double*));
    for (r=0; r<ny; r++)
    	z[r] = &h_z[r*nx];

    //Velocity
    double * h_v = (double *) malloc(nx*ny*sizeof(double));
    double ** v = malloc(ny * sizeof(double*));
    for (r=0; r<ny; r++)
        v[r] = &h_v[r*nx];

    //Accelleration
    double * h_a = (double *) malloc(nx*ny*sizeof(double));
    double ** a = malloc(ny * sizeof(double*));
    for (r=0; r<ny; r++)
        a[r] = &h_a[r*nx];

    //output image
    char * o_img = (char *) malloc(sz.width*sz.height*sizeof(char));
    char **output = malloc(sz.height * sizeof(char*));
    for (int r=0; r<sz.height; r++)
        output[r] = &o_img[r*sz.width];

    max=10.0;
    min=0.0;
    dx = (max-min)/(double)(nx-1);
    dy = (max-min)/(double)(ny-1);
    
    tmax=20.0;
    dt= (tmax-0.0)/(double)(nt-1);

    double x,y; 
    for (r=0;r<ny;r++)  {
    	for (c=0;c<nx;c++)  {
		x = min+(double)c*dx;
		y = min+(double)r*dy;
        	z[r][c] = exp(-(sqrt((x-5.0)*(x-5.0)+(y-5.0)*(y-5.0))));
        	v[r][c] = 0.0;
	        a[r][c] = 0.0;
    	}
    }
    
    dx2inv=1.0/(dx*dx);
    dy2inv=1.0/(dy*dy);

    for(it=0;it<nt-1;it++) {
	//printf("%d\n",it);
        for (r=1;r<ny-1;r++)  
    	    for (c=1;c<nx-1;c++)  {
		double ax = (z[r+1][c]+z[r-1][c]-2.0*z[r][c])*dx2inv;
		double ay = (z[r][c+1]+z[r][c-1]-2.0*z[r][c])*dy2inv;
		a[r][c] = (ax+ay)/2;
	    }
        for (r=1;r<ny-1;r++)  
    	    for (c=1;c<nx-1;c++)  {
               v[r][c] = v[r][c] + dt*a[r][c];
               z[r][c] = z[r][c] + dt*v[r][c];
            }

	if (it % 100 ==0)
	{
    	    double mx,mn;
    	    mx = -999999;
            mn = 999999;
            for(r=0;r<ny;r++)
                for(c=0;c<nx;c++){
           	    mx = max(mx, z[r][c]);
           	    mn = min(mn, z[r][c]);
        	}
    	    for(r=0;r<ny;r++)
                for(c=0;c<nx;c++)
                    output[r][c] = (char) round((z[r][c]-mn)/(mx-mn)*255);

    	    sprintf(filename, "./images/file%05d.png", frame);
            printf("Writing %s\n",filename);    
    	    write_png_file(filename,o_img,sz);
	    frame+=1;
        }

    }
    
    double mx,mn;
    mx = -999999;
    mn = 999999;
    for(r=0;r<ny;r++)
        for(c=0;c<nx;c++){
	   mx = max(mx, z[r][c]);
	   mn = min(mn, z[r][c]);
        }

    printf("%f, %f\n", mn,mx);

    for(r=0;r<ny;r++)
        for(c=0;c<nx;c++){  
	   output[r][c] = (char) round((z[r][c]-mn)/(mx-mn)*255);  
	}

    sprintf(filename, "./images/file%05d.png", it);
    printf("Writing %s\n",filename);    
    //Write out output image using 1D serial pointer
    write_png_file(filename,o_img,sz);
    return 0;
}

Overwriting 2d_wave.c

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Congratulations, we're done!

If you attend class in-person then have one of the instructors check your notebook and sign you out before leaving class. If you are attending asynchronously, turn in your assignment using D2L.

Course Resources:

• Website
• ZOOM
• JargonJar
• GIT

Written by Dr. Dirk Colbry, Michigan State University
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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