steveschmidt
hw2

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***Running The 3D Heat Equation Solver***
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> make && ./ftcs

> make clean  //should be called after running, to rm the test files created

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*** OPTIONS ***
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Input a file (yes=1) or (no=0) use hard coded example

Choose your method (FTCS = 0 , CRANK-NICHOLSON = 1 , ADI = 2)

Choose your boundary conditions (Zeroes = 0 , Constant (the value 3) = 1, Periodic = 2)

OUTPUT <=> Timing

OUTPUT <=> This program CREATES FILES in the working directory (FTCS creates 4, Crank/ADI creates 3) called ftcs#.txt in the format:
x y val
x y val
x y val
.. .. ..


--These files were used in testing the code via gnuplot script:
$ gnuplot
> set cbrange [0:1.5];
> set palette defined (0 "blue", 1 "red");
> plot "xyz.dat"  w image;

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NOTES
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Due to space contrainsts, and timing analysis, the following 'strict' conditions are axiomatic to running the code:

FTCS is hard coded to run NT = 10000 times

CRANK-NICHOLSON is hard coded to run NT = 5 times - converges quickly

ADI is hard coded to run NT = 5 times

CRANK-NICHOLSON / ADI both max out at malloc size of 7x7x7 thusly the timings are analyzed for 3,4,5,6 



TIMING ANALYIS
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As expected, FTCS is with quadratic increase with N, and converges slowly, altho runs quickly

Crank-Nicholson scales exponentially as the problem becomse solving a 2D N^3 x N^3 system of equations with RREF, and is incredibly space intensive, as a malloc'd 2D array must be created and passed into the RREF function

ADI is 3x slower than Crank-Nicholson as each system described above is created and solved for each dimension (3), NT times, altho the space requirements remain the same as Crank-Nicholson


ATTACHMENTS
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matplots.m	// file to plot timings for analysis
analysis.fig	// figure showing plots of timings for various NxNxN
numfile.txt	// sample input file for the program to show formatting