Poisson-Equation-solved-with-DEAL.II

This Repository contains code for solving Poisson's Equations in three geometries of Square, Circle and a Ring.

Poisson's Equation

‍‍

$$-\Delta u = f \;\; in \;\; \Omega$$ $$u = 0 \;\; in \;\; \partial \Omega$$

Compiling

for compling the *.cc codes following commands must be executed:

sudo cmake -DDEAL_II_DIR="path\to\DEAL.II_directory" .

then:

make

the executable program will be compipled and after running it the solution.vtk, solution.gpl and grid.svg will be generated.

GnuPlot results

for visualizing the 3D surface the follwing commands must be executed in GnuPlot shell:

gnuplot
set style data line
splot "solution.gpl"

Results

Cube

Circle

Ring