[petsc-users] "error of the solution" of GMRES

[Marcelo Xavier Guterres]

Esteemed colleagues,



My problem is:

Div ( Grad ( phi ) ) = 0

mesh:

0 < x < 1;
0 < y < 1;

with boundary conditions:

phi ( x , 0 ) =  x;
phi ( 0 ,y )  =  x;
phi ( x , 1 ) =  x;
phi ( 1 ,y )  =  x;

with serial processing.


solved with ( KSPCG x PCJACOBI ) and  (KSPGMRS x PCJACOBI). I have a
question, why the "*norm error** **of the solution*" of GMRES is high, when
the mesh is large. It is a problem in methods or truncation error?


the results were:


  *m* *n* *m x n* *error ( KSPCG x PCJACOBI )* *error ( KSPGMRS x PCJACOBI )
*  3 3 9 1,92E-16 4,42E-16

 4 4 16 2,08E-16 6,46E-16

 5 5 25 4,41E-16 9,63E-16

 6 6 36 8,77E-16 8,26E-16

 7 7 49 2,37E-06 2,52E-06

 8 8 64 1,17E-05 1,33E-05

 9 9 81 9,32E-06 1,26E-05

 10 10 100 7,33E-06 9,93E-06

 20 20 400 4,22E-05 3,16E-04

 30 30 900 1,06E-04 2,37E-02

 40 40 1600 2,14E-04 3,77E-02

 50 50 2500 3,37E-04 9,36E-03

 100 100 10000 1,27E-03 6,53E-02

 200 200 40000 4,32E-03 3,67E-01

 300 300 90000 9,53E-02 1,02E+00

 400 400 160000 1,68E-02 2,10E+00

 500 500 250000 2,61E-02 3,66E+00


how can I improve the performance of GMRES?


a good week for all.


-- 
Ph.d student Marcelo Xavier Guterres
Rio de Janeiro , Brazil.
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