For this lab you will be writing a CUDA program to determine the steady state heat distribution in a thin metal plate using synchronous iteration on a GPU. You will be solving Laplace's             equation using the finite difference method which has wide application in science and                engineering.

Consider a thin plate is perfectly insulated on the top and bottom which has known                  temperatures along each of its edges. The objective is to find the steady state temperature    distribution inside the plate. The temperature of the interior will depend upon the                   temperatures around it. We can find the temperature distribution by dividing the area into a fine mesh of points, hi,j . The temperature at an inside point can be taken to be the average of the temperatures of the four neighboring points, as illustrated below.

For this calculation, it is convenient to describe the edges by points adjacent to the interior       points. The interior points of hi,j are where 0 < i < n, 0 < j < n [(n -1) x (n - 1) interior points]. The edge points are when i = 0, i = n, j = 0, or j = n, and have fixed values corresponding to the fixed temperatures of the edges. Hence, the full range of hi,j is 0 ≤  i ≤ n,  0 ≤ j ≤ n, and there are

(n + 1) x (n + 1) points. We can compute the temperature of each point by iterating the equation:

(0 ≤  i ≤ n,  0 ≤ j ≤ n) for a fixed number of iterations or until the difference between             iterations of a point is less than some very small prescribed amount. This iteration equation        occurs in several other similar problems; for example, with pressure and voltage. More complex versions appear for solving important problems in science and engineering. In fact, we are          solving a system of linear equations. The method is known as the finite difference method. It      can be extended into three dimensions by taking the average of six neighboring points, two in    each dimension. We are also solving Laplace’sequation.

Suppose the temperature of each point is held in an array h[i][j] and the boundary points       h[0][x], h[x][0], h[n][x], and h[x][n] (0 ≤ x ≤ n) have been initialized to the edge temperatures. The calculation as sequential code could be

using a fixed number of iterations. Notice that a second array g[][] is used to hold the newly     computed values of the points from the old values. The array h[][] is updated with the new       values held in g[][]. This is known as Jacobi iteration. Multiplying by 0.25 is done for computing the new value of the point rather than dividing by 4 because multiplication is usually more        efficient than division. Normal methods to improve efficiency in sequential code carry over to  GPU code and should be done where possible in all instances. (Of course, a good optimizing     compiler would make such changes.)

Setup:

A perfectly insulted thin plate with the sides held at 20 °C and a short segment on one side is held at 100 °C is shown below:

You need to write a C\C++ program using CUDA to solve the steady state temperature                  distribution in the thin plate shown above.  Your program needs to take the following command line arguments:

1.   -n 255 - the number of interior points.

2.   -I 10000 – the number of iterations

Both command line arguments need to be defined and make sure your code check for invalid command line arguments

Uses type double for your arrays.

Your code needs to output to the console the number of milliseconds it took to calculate the solution using CUDA events.

Example:

Thin plate calculation took 123.456 milliseconds.

Your code needs to write out to a text file the final temperature values using a comma to           separate the values in the file “finalTemperatures.csv” .  Each row of temperature values should be on a separate line.

Turn-In Instructions:

Place all the files (*.h, *.cpp, *.cu) used in your solution into a zip file called Lab4.zip and upload to the Canvas

assignment.

Notes:

You can write, debug and test your code locally on your personal computer.  However, the code you submit must compile and run correctly on the PACE-ICE server.

    Execution Time is important for this lab.

Grading Rubric

AUTOMATIC GRADING POINT DEDUCTIONS PER PROBLEM:

LATE POLICY

***You are free to post solution times on pizza so that other students can gauge their run times.

Appendix A: Coding Standards

Indentation:

When using if/for/while statements, make sure you indent 4 spaces for the content inside those.  Also make sure that you use spaces to make the code more readable.

For example:

for (int i; i < 10; i++)

{

j = j + i;

}

If you have nested statements, you should use multiple indentions. Each { should be on its own line (like the for loop) If you have else or else if statements after your if statement, they should be on their own   line.

for (int i; i < 10; i++)

{

if (i < 5)

{

counter++;

k -= i;

}

else

{

k +=1;

}

j += i;

}

Camel Case:

This naming convention has the first letter of the variable be lower case, and the first letter in each new word be capitalized (e.g. firstSecondThird). This applies for functions and member functions as well! The main exception to this is class names, where the first letter should also be capitalized.

Variable and Function Names:

Your variable and function names should be clear about what that variable or function is. Do not use one letter variables, but use abbreviations when it is appropriate (for example: “imag" instead of                       “imaginary”). The more descriptive your variable and function names are, the more readable your code   will be.  This is the idea behind self-documenting code.