Homework

Homework 5: Due Monday April 8

Solving Poisson's equation using MPI

This is a very basic domain decomposition problem. The program poisson_mpi.c uses 1-D domain decomposition with non-blocking communication.

Study the scaling behavior of this program. Modify the program so it saves the solution to a file. Make a 3-D plot of a typical solution.
Modify the program to another communication mode, e.g., choose any one of
- blocking communication using MPI_Send and MPI_Recv, or
- buffered communication using MPI_Bsend, or
- simulatneous send and receive MPI_Sendrecv,
and compare the scaling behavior. See the Intermediate MPI example programs on the MPI web site.
Modify any one of the above programs to use Gauss-Seidel with checkerboard updating, and compare with the Jacobi version.

Parallel multigrid solver for Poisson's equation

Modify any one of your programs above to use the multigrid algorithm and study its scaling behavior.

Homework 4: Due Wednesday March 13

Ising Monte Carlo: Serial Programs

Measure the heat capacity of the 2-D Ising model lattice as a function of number of spins N = LxL, and temperature T. Study the singular behavior of the heat capacity near the phase transition temperature T_c = 2.269. If c_max(N) is maximum value of the heat capacity per spin for given number of spins, the theoretical prediction is that c_max(N) ~ c₀ log(N). See if you can verify this prediction and estimate the constant c₀.

Perform these measurements using the Metropolis algorithm and at least one cluster algorithm, either Swendsen-Wang, or Wolff, and compare the algorithmic efficiencies, i.e., number of Monte Carlo steps required to obtain the same accuracy in the measured data.

Ising Monte Carlo: Parallel Speedup

Parallelize the Metropolis algorithm using

MPI,
OpenMP,

and measure the efficiency gains. See Parallel Metropolis Algorithms in Dr. Coddington's notes.

Homework 3: Due Friday March 1

MD: Spatial Decomposition and Systolic Algorithms

For this exercise you can write your own programs (straightforward by might need a lot of debugging time!) or use Dr. Nakano's Parallel MD program which uses spatial decomposition, and md_systolic.cpp.

Compare the spatial decomposition and systolic algorithms:

Get the programs to compile and run. Experiment with compiler flags like -O3 and -Ofast=IP27 on crosby. Do these optimizations significantly affect performance?
If you use pmd.c you need to modify it to include equilibration steps with velocity rescalings every 10 or 20 steps to obtain the desired temperature. You also need to modify eval_props() to measure the pressure. Make sure both programs are giving the same answers for physical quantities like temperature and pressure!
Compare the run times and the scaling behavior of the two algorithms for nprocs = 1, 2, 4 and maybe 8.

Homework 2: Due Wednesday February 13

Molecular Dynamics of Lennard Jones System

For this homework you can write your own programs or modify the ones given in the Topic2 directory.

Serial Program

Consider a system of argon atoms. Find values of N, V, and T appropriate to the

solid phase,
liquid phase,
gas phase.

Run the simulation for each of these three choices, measure the pressure P and compare with the experimental data.

Graphics

Learn how to run the OpenGL graphics version and make pictures of typical solid, liquid and gas configurations.

OpenMP Paralleization

Locate the most time-consuming loops in the serial program. Parallelize them and measure the performance gain.

Homework 1: Due Friday February 1

Monte Carlo program to compute pi

This homework exercise represents the minimal programming skills you need to be able to complete this course. Download the simple Monte Carlo program from the MPI Web Site Using MPI in Simple Programs.

Learn how to run the program and study how it scales with number of processes (say 1,2,4,8). Also compare its accuracy with the rectangle formula program to compute pi which was discussed in lecture.

You can use the Fortran 90 or Fortran 77 versions if you prefer.

Write an OpenMP version of this program and compare it with the MPI version.

Questions or comments: phygons@buffalo.edu
Last updated: Monday, 01 April 2002, 12:37:06