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

[Mark F. Adams]

CG is a better method than GMRES for symmetric positive definite problems.  

You want to use a better preconditioner.  Try '-pc_type gamg -pc_gamg_agg_nsmooths 1'


On Feb 19, 2013, at 11:36 AM, Marcelo Xavier Guterres <m.guterres at gmail.com> wrote:

> 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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