Assignment #4

Particle Mesh Code -Part II

Problem Description:

1. Read in x, y, vx, vy, and mass from a datafile
2. Initialize your Green's function and its FFT
3. Map your particles on the grid using the NGP scheme
4. convolve with the Green's function assignment #3 results
5. use a centered finite different routine to calculate a force matrix (see below)
6. map these forces back to the particles using NGP
7. calculate the potential and kinetic energies of the particles
8. move the particles using a simple Euler's method routine (assignment #2)
9. save particle positions to a data file at selected intervals (Make sure to multiple the complex numbers correctly!!!!)
10. save the energy data to a file every timestep
11. profile the code
12. describe the results in a 3-5 page short report with plots of the run and energy conservation
13. include a short 1 page summary of where you should optimize your code

Problem Parameters

1. Use your assignment 3 code for this project! This means:
   • Solve the problem on a 64 by 64 grid. All the mass should be in a one 32 by 32 corner of this grid.
     
   • The Green's function should be of the form 1/sqrt(r*r + eps*eps) where eps is a softening length for the POTENTIAL. This is slightly different from a softening length for FORCE, but behaves in much the same way.
     
   • You may beg, borrow, or share the FFT routines from "Numerical Recipes" or other platform independent libraries.
     
   • You can work in a group of two, if you like.
     
   
   
2. The file format for the input and output data files should be the same. One record per line ascii format, with
   x, y, vx, vy, mass
   delimited by spaces.
   
3. Energy output should be
   time, Total energy, kinetic energy , potential energy
   again, one record per line, space delimited, ascii format.
   
4. Assume that the particles will be located with positions between 0 and 32 initially. For our test case, generate a file with 256 particles with zero initial velocities and random positions. Assume they all have masses of 1.
   
5. Make sure to keep the particles inside the grid (32x32 active region). If they move outside the grid, you may map them to the other grid wall. (Ie. if a particle's position is less than 0, move it to 32 + current position.)
   
6. To calculate the forces, it is usually easer to apply finite different technques on the ENTIRE grid at one time. You will produce a Force-X grid and a Force-Y grid. This is slightly inefficient with both memory, and may be inefficent with computation. However, to interpolate the forces, you need only find the force associated with a particular particles cell.
   
7. Remember the tricks about calculating the potential. Multiple the mass and potential matrix elements together, sum them, subtract self-force, then divide by two.
   
8. You should provide output of the evolution of the system over a few hundred timesteps. What step size? YOU have to figure that out yourself. The system should at least go through a full collapse and re-expansion. It should also probably go through a second collapse to really test the code.
   
9. Create some images of the initial and final states, as well as the evolution. Also, a plot of the energy - total, ke, pe, is essential for the run.
   
10. Profiling the code is pretty easy. Take a look at the profil, gprof, and prof commands. The idea is to track preformance. YOU DO NOT HAVE TO OPTIMIZE YOUR CODE IN THIS PROJECT! ANALYSIS OF THE CODE IS SUFFICIENT! You should discuss what should be done and suggest what things you would do to speed things up.
11. Don't for get to write a report about the project and the tests you use to make it work.

Graphics Output:

Assignment requirements:

2. You can create an on-line version of the project which is accessable through the Web. This is the easiest way for me to grade your projects.

3. You should include instructions on how to compile this code. A "Makefile" would be nice, especially if you have multiple files and subprograms.

4. Graphics output may be created on any machine using any graphics package, and turned into a postscript file. You can also create Web pages and give me the URL.

5. You should write a short 3-5 page report documenting the code and your results. This doesn't have to be fancy, but it should summarize your work.
6. When you have completed the project, use the Unix tar command to create a single file which contains:

	documentation file (postscript, html, or text)
	C, C++, or fortran program
	Makefile and/or compilation instructions
	graphics output file (postscript)
	A short README file explaining what each file contains.

tar -cvf username.tar directory
The file username.tar is the name of the newly created tar file.
The tar file names should be your email account with a number
indicating the assignment number.  To extract the file,
type 
tar -xvf username.tar

6. Use anonymous ftp to leave the file in the pub/nbody directory of galileo.gmu.edu