[Dune] Parallel CG Solver

Andreas Dedner andreas.dedner at mathematik.uni-freiburg.de
Tue Nov 18 15:45:59 CET 2008

here are a few remarks - I hope they help.
You stated the advantages and disadvantages quite
accurately - at lot depends on the question if memory
or computational time is your limiting resource.

One other thing to keep in mind is the question, 
how often you will iterate in your cg method and how
often you can use the same matrix.
If (for example in a time dependent problem) your
initial guess for the solution is very accurate and you
are solving a non-linear problem or are adapting your
grid, then very few iterations may be required for one
fixed matrix. In this case 
setting up the matrix A can be more time consuming then
evaluating the product Ax on the fly a few times.
On the other hand if you have to use many cg iterations
and might want to use some preconditioner then setting
up the matrix is probably the better choice.
Greetings Andreas

On Tue, 18 Nov 2008 15:35:36 +0100
 Arne Rekdal <arne at stud.ntnu.no> wrote:
> Thanks for the feedback. I will try out the suggestions.
> Is it more more common to construct the global matrix (in
> sparse  
> format) than have a linear operator that iterates over
> all the  
> elements for each operator evaluation? I can see that
> storing the  
> global matrix reduces the time per iteration, but that
> way also  
> increases the memory usage.
> Greetings
> Arne Rekdal
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