Project #2 2D and 3D Heat Diffusion Solution

In this exercise you will be simulating the diffusion of heat in two or three dimensions using CUDA. As in SE2, we will be using simpli ed heat diffusion equations. For 2 dimensions assume that there is a rectangular room that is divided into a grid. Inside the grid will be "heaters" with various xed temperatures.










Figure 1 { 2 dimensional room with xed "heaters"




Given the rectangular room and con guration of heaters, you need to simulate what happens to the temperature in every grid cell as time progresses. Cells with heaters in them always remain constant for simplicity. At each timestemp we assume heat ows between a cell and its neighbors. If a cell's neighbor is warmer that it is, it will tend to heat up. Conversely, if a cell's neighbor is colder than it is, it will tend to cool down. We will use the following simpli ed equation to model this behavior




X

Tnew = Told +
k(Tneighbor Told)
(0.1)


neighbors





In the previous equation, k represents the rate at which heat will ow through the system. A large value of k will drive the system to a constant temperature quickly. For the 2 dimensional case, we will consider only four neighbors (top, left, bottom, right) so we can simplify the equation to




Tnew = Told + k (Ttop + Tbottom + Tlef t + Tright 4 Told)
(0.2)
Similarly the equation we will be using for 3D will be


Tnew = Told + k (Tf ront + Tback + Ttop + Tbottom + Tlef t + Tright 6 Told)
(0.3)
k will remain constant during execution but will be a parameter provided to your program. For boundary conditions, use the current value of Told. For example for the grid point x = 0, y = 1, there is not a Ttop, since it is o the grid, therefore use Told for the current cell as Ttop.




WHAT YOU NEED TO DO You need to implement a CUDA program that will output the temperature at each grid point after running the equation for a speci ed number of timesteps. Example execution




./heat2D3D sample.conf






sample.conf is a con guration le which will specify the parameters for your simulation. Below are example con - guration les for 2 and 3 dimensions.




##### 2D
CONFIGURATION EXAMPLE
#####


#your code should ignore lines
starting with
’#’
#you can
assume arguments will
always follow
this ordering however whitespace may vary



#2D or 3D




2D




#the value for k




4




#number of timestep to run




200




#width (x-axis) and height (y-axis) of grid 800,800







#default starting temperature for nodes




5



#list of fixed temperature blocks (squares for 2D)




#can be 0, 1 or more




#assume blocks won’t overlap




#location_x, location_y, width, height, fixed temperature 5, 5, 20, 20, 200







500, 500, 10, 10, 300




##### 3D CONFIGURATION EXAMPLE #####




#your code should ignore lines starting with ’#’




#you can assume arguments will always follow this ordering however whitespace may vary




#2D or 3D




3D




#the value for k




4




#number of timestep to run




200




#width (x-axis) height (y-axis), depth (z-axis) of grid 800,800,800







#default starting temperature for nodes




5




#list of fixed temperature blocks (cubes for 3D)




#can be 0, 1 or more




#assume cubes won’t overlap




#location_x, location_y, location_z, width, height, depth, fixed temperature 5, 5, 5, 20, 20, 20, 200







500, 500, 500, 10, 10, 10, 300




You may design your program however you wish as long as it is reasonably e cient. We will discuss possible implementations in class. At the end of execution, your program should write an output le named heatOutput.csv listing the temperatures at each grid point in comma separated format. Use oats for all values.




You MUST use CMake for con guring your project. I must be able to build your project using cmake .. from a build folder within your submission. You will need to use online resources to determine how to correctly refer to needed header les. Do NOT write your own Make le directly. For submission, compress your solution into p2.zip (NOT .TAR.GZ, or .RAR or anything else). zip is installed on the login node. Submit via canvas.




Example Output 2D grid with width = 3, height = 2




334.2, 342.2, 300.2




342.1, 343.1, 32.0




Note the newlines and commas for each row.




Example Output 3D grid with width = 3, height = 2, depth = 4




334.2, 342.2, 300.2




342.1, 343.1, 32.0




*blank line*




323.2, 302.2, 230.2




142.1, 323.1, 332.0




*blank line*




323.2, 302.2, 230.2




142.1, 323.1, 332.0




*blank line*




323.2, 302.2, 230.2




142.1, 323.1, 332.0




Insert a blank line between each x,y slice