Secuential implementation of Finite Diferences for heat equation solution in 1D and 2D.

for now we just code explicit solution for heat equation in 1D and 2.

###Table of contents Finite Diferences for heat equation in 1D

Finite Diferences for heat equation in 2D

##Finite Diferences for heat equation in 1D.

Explicit solution in 1D directory

Dependencies

• Armadillo
• octave

Compile and run

mkdir build
cd build
cmake ../
make
./fdtd_1D < ../in

keep in mind that fdtd_1D executable receives the following parameters that you can put in file in:

• xa: init position in X
• xb: last position in X
• ta: init value in time
• tb: last value in time
• N: number of point to calculate heat value
• T: number of steps in time.
• gamma: heat difusion value in equation.

Runing example

remove build directory and exec in terminal

./run.sh

the output example image is "image.jpg"

example Docs

this program had been tested with these papers:

heat Equation example 1

heat Equation example 2

##Finite Diferences for heat equation in 2D (rectangular objects)

Explicit solution in 2D directory

Dependecies

• Armadillo
• Gnuplot

###Compile and Run in 2D directory type:

./run.sh

executable file is ./build/fdtd_2d and its input file is in2d and have de following parameters:

• xa: init position in X
• xb: last postition in X
• ya: init position in y
• yb: last position in y
• ta: init time
• tb: last time
• Nx: discretization points in X
• Ny: discretization points in Y
• T: discretization points in time
• k: heat difusion value in equation

###Output output values are init state and last state of heat in object.

###Runing and ploting example

in 2D directory delete build dir (if you have it ) and run:

./run.sh
./plot_Example

this is a little example of rectangular object with a center heat source and plot in files time0.png and timeT.png the init and end heat state of object

###References two dimensional heat equation with FD