At first: BOOT LINUX  ;-) !!!
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https://personalpages.manchester.ac.uk/staff/david.silvester/ifiss/

--> Download

Install ifiss
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tar xvzf Downloads/ifiss3.5.tar.gz

cd ifiss3.5/

Edit gohome.h

--> set home directory correct, something like:

cd('/HOME1/users/students/xxxx/ifiss3.5')


Start Matlab
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setpath


helpme
--> 1 for square_diff

... understand the problem to solve


Run the test example
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square_diff

spy(Agal)

See diffusion/specific_bc.m for understandig the boundary conditions


x2=Agal\fgal
norm(x_gal -x2) 
 

Now use Agal, fgal for own solver implementation
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1. Write a function that does the Jacobi scheme for this!
   (Implement a parameter for number of iteration steps)

2. Implement the PCG method!

Now solve the problem Agal * x = fgal with on ways:

4. Use your Jacobi iteration to solve the problem

5. Use your pcg method with P=I as preconditioner ( i.e. no preconditioning)

6. Use your pcg method with P=diag(diag(Agal)) as a preconditioner!

7. Use your pcg method with 3 steps of your Jacobi scheme as a preconditioner

8. Think about your results, make a graphical evaluation