EE221 Assignment 3

Program 1 Alternative 1 (30pts.)

Complete the provided partially developed program that calculates the steady state temperature distribution for the printed circuit board (PCB) with up to ten heat sources. The calculations are performed based on the following assumptions and simplifications:

The PCB divided into a number of regions (a grid) that are simulated using a two dimensional array of double. Each array entry stores the temperature of the corresponding PCB region.
At each time interval (time step) some amount of power is dissipated from the heat sources to the grid. That is modeled by adding certain values to the corresponding array elements. For the sake of simplicity we will skip the physical model and just operate on rough numbers. However, those numbers can be calculated from the average power dissipated, thermal capacity and resistance, and the time step duration.
At each time interval the heat propagates to the surrounding areas. The heat is transferred from the warmer places to the cooler places. This is modeled by weighted averaging the values of neighboring cells and calculating the new value that is to be used during the next time step of the simulation.
For this year problem please use the following formula: NEW[r][c] = (OLD[r-1][c] + OLD[r+1][c] + OLD[r][c-1] + OLD[r][c+1] ) /4.0 Please note, that ordinarily you cannot apply that formula to the border rows and columns. For border rows, columns and corners please modify the formula accordingly and substitute the nonexistent array elements with ambient temperature.
Although for the sake of simplicity, we just use rough numbers and weights of 1.0, the actual weights could have been calculated from the thermal resistance and thermal capacitance of the PCB and the time step duration.
The calculations are repeated until the steady state is reached. We determine that the steady state is reached if there is no significant change in the temperature distribution between the two consecutive time steps. We define the change as a so-called mean square error. In order to calculate that error we add up squared differences between the corresponding cells of the old (before adding heat and averaging) and the new array. After adding up the squared differences, we divide the sum by the number of cells in the array so that the value of the error does not depend on the size of the array. (We average it per cell.)
When the temperature distribution converges to a steady state solution and calculations are finished the final distribution is svaed to a file called tempplate.csv. You should be able to open that file in a spreadsheet and plot a surface graph of the distribution.
Please follow the more detailed instructions included in the partially developed program. Please run your program at least two times for different data and provide both the screen printout and the contents of the file with the final values of the temperature array.

Run your program for a grid of 20x20, 2 heat sources: (5,5,10) and (10,15,5), ambient temperature of 70F, and MSE error of 1E-6. After the program completes (approximately 350 iterations) import file tempplate.csv into Excel spreadsheet and print the result table using surface plot. Change the z-axis from autorange to the range of values observed in the output numbers. Attach that to the program source code and output printout. The surface plot should look like this.

The idea of the program is loosely based on the problem 10 from Chapter 3, page 140 and on past course assignments. However, solving the original textbook problem instead of this one will not receive any credit. Please refer to the instructor's comments that were (will be) made during lectures if the rough description included on this page combined with comments provided in the source code and the textbook problem description are not detailed enough.

Program 1 Alternative 2 (30pts.)

Complete the provided outline of the Game of Life simulation program. The program has been written except that contents of most functions has been removed and left for you to do as an exercise. The functionality of functions is briefly described in the form of comments. The functionality of the whole program is also somewhat commented.

From wikipedia: The original universe of the Game of Life is an infinite two- dimensional orthogonal grid of square cells, each of which is in one of two possible states, live or dead. Every cell interacts with its eight neighbours, which are the cells that are directly horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur:

Any live cell with fewer than two live neighbours dies, as if by loneliness
Any live cell with more than three live neighbours dies, as if by overcrowding
Any live cell with two or three live neighbours lives, unchanged, to the next generation
Any dead cell with exactly three live neighbours comes to life

The initial pattern constitutes the 'seed' of the system. The first generation is created by applying the above rules simultaneously to every cell in the seed—births and deaths happen simultaneously, and the discrete moment at which this happens is sometimes called a tick. (In other words, each generation is a pure function of the one before.) The rules continue to be applied repeatedly to create further generations.

Your job is to analyze the provided program in order to find out how it implements the algorithm described above. Complete the missing implementation for functions. Also note the commented swapping of array pointer that is actually a preferred alternative to copying contents of the arrays.

Run your program a few times and capture a few most recent screens prior to program termination for a run that produced some interesting results such as persistent constant or oscillating patterns. This program will stop automatically when it detects a constant or two phase oscilating pattern but will fail to notice three or more phase patterns. Use the world of 10 by 20 for your experiments.

This homework is based on the textbook problem Chapter 3, Problem 11, Page 140. You may also want to look at Conway's Game of Life and its GUI implementation.

Game of Life Extra Credit (10pts.)

Improve the game of life program so that it can detect also three- and four-phase patters as stop condition, and also make it more efficient by utilizing pointer swapping instead of array copying that is now commented for one- and two-phase patter detection. You may turn in the improved version instead of the original assignment but to expedite grading please write "includes extra credit" at the top of the program. Please note that it may be too difficult to fully test if your improvement works as there is very little chance that you would encounter higher phase patterns from random initial condition.

Boring Extra Credit 2 (10pts.)

Redo the array-based city zone population assignment from Homework 2 using pointer-based dynamic arrays created according to the user specified number of zones at the time of executing the program. Also create and use a function that prints the populations for current year instead of printing directly from the main program. You may also develop and use more functions if you have time to exercise. (Pass all necessary data to the function, no global variables allowed.) Remember to prevent memory leaks. Mostly only the modified portions of code will be graded but the program must be functional to qualify for the extra credit.

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