[petsc-users] Dear Sir or Madam

[Guoyi Ke]

Dear Sir or Madam,


Recently, our research group try to use the PCfieldsplit  method in Petsc to construct the preconditioner for the linear equation system. For example, if we have following system,

K11, K12, K13      u1      f1

 K21, K22, K23      u2  =  f2                                     (1)

 K31, K32, K33      u3      f3



we construct the preconditioner as follows:

 K11, K12, K13

 0,     K22, K23

 0,       0,    K33.


We also can reorder the system (1):

 K22, K21, K23      u2      f2
 K12, K11, K13      u1  =   f1                                  (2)
 K32, K31, K33      u3       f3


with the preconditioner

K22, K21, K23
 0,    K11, K13
 0,    0,     K33


We use the same solver for Eq.(1) and Eq. (2) with corresponding preconditioner. The question is: is solving the Eq. (1) equivalent to solving Eq. (2) in Petsc? From our results, it seems not. Thank you so much.


Best,

Guoyi



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