Hello Florian,
I usually apply following steps before going to preconditioners;
- Construct a smaller matrix and examine the nonzeros, try to use permutations 
to get a smaller bandwidth (minimum degree or symrcm).
- Use symmetric diagonal scaling, which usually helps a lot but mostly not 
enough by itself.
- I have found out that (as a part of my master thesis), ParaSails is a good 
general purpose preconditioner and you can have symmetric ParaSails 
preconditioners easily.
I hope this helps. 
Regards,Abdullah Ali Sivas

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