## Computer Science 400 |

**Lab 5: Jacobi Iteration with OpenMP****Due: 11:59 PM, Monday, October 13, 2008**

Your task this week is to write a C or C++ program using OpenMP that solves Laplace's equation on a two-dimensional, uniform, square grid, using Jacobi iteration. Don't worry if none of those terms make any sense - this document tells you what little you need to know about the math and physics.

Laplace's equation is an elliptic partial differential equation that governs physical phenomena such as heat. In two dimensions, it can be written

Phi_xx + Phi_yy = 0.

Given a spatial region and values for points on the boundaries of the
region, the goal is to approximate the steady-state solution for
points in the interior. We do this by covering the region with an
evenly-spaced grid of points. A grid of *8 ×8* would look like
this:

* * * * * * * * * * * . . . . . . . . * * . . . . . . . . * * . . . . . . . . * * . . . . . . . . * * . . . . . . . . * * . . . . . . . . * * . . . . . . . . * * . . . . . . . . * * * * * * * * * * *

There are several iterative methods for solving Laplace's equation. Your program is to use Jacobi iteration, which is the simplest and easily parallelizable, though certainly not the most efficient in terms of convergence rate.

In Jacobi iteration, the new value for each grid point in the interior is set to the average of the old values of the four points left, right, above, and below it. This process is repeated until the program terminates. Note that some of the values used for the average will be boundary points.

When you are finished, submit using the turnin utility as
`lab5`. Your submission should include an appropriate
`Makefile`, your C or C++ source code (including the timer code
from class, if you choose to use it), a brief `README` file
expaining how to run your program and with your timings and analysis.
Please do *not* include object files or your executable.

determined by correctness, design, documentation, and style, as well as the presentation of your timing results.