![](https://secure.gravatar.com/avatar/27f6b03a726ccff3f7a5007b1df6bf8c.jpg?s=120&d=mm&r=g)
11 Jul
2013
11 Jul
'13
8:21 a.m.
Hi Ankit,
I have contacted a friend who suggested some algorithms to try out for solving the linear system:
algebraic brute force (does not address the nonlinearity, reported to work on moderately sized problems): gmres with ILU(0) preconditioning.
If ILU(0) does not work:
We are solving K*x = b where K has a block structure: K = | A B | | B^T -C | (C can be positive semi-definite or zero - our case)
Instead, an "augmented Lagrangian" technique would lead to Q*x = b with Q = | A + alpha*B*B^t B | | B^T -C | alpha>=0, small
Either the augmented system can be solved, or Q could be used in ILU(0) preconditioner.
- Ultimately you want to solve a time-dependent problem, so try also the Chorin-Temam projection method [1]. This could be used even for the stationary case by solving in time until a steady state is (hopefully) obtained.
r.
[1] http://en.wikipedia.org/wiki/Projection_method_%28fluid_dynamics%29
4056
Age (days ago)
4056
Last active (days ago)
0 comments
1 participants
participants (1)
-
Robert Cimrman