In general the convergence will be different; though one hopes the resulting answer is the same. The reason is that the upper diagonal pattern determines the order the solution entries are solved for. In the first case it solves for x3, then x2, then x1, in the second case it solves for x3, x1, x2 in that order. When solving for x2 in the second case it has a different right hand size and hence, of course, a different solution. There is, I think, some trial and error in determining what ordering is best for one particular problem.
> On Jun 5, 2019, at 9:56 PM, Guoyi Ke via petsc-users > <[email protected]> wrote: > > 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 > > > Note: This e-mail may contain PRIVILEGED and CONFIDENTIAL information > intended only for the use of the specific individual or entity named above. > If you or your employer is not the intended recipient of this e-mail or an > employee or agent responsible for delivering it to the intended recipient, > you are hereby notified that any unauthorized dissemination or copying of > this e-mail is strictly prohibited. If you have received this transmission in > error, please immediately delete the message.
