Biconjugate gradient stabilized solver for non-symmetric matrices

[ateshian]

I would like to initiate a discussion and a possible implementation of a quasi-Newton method for solving non-symmetric systems. We already know that poroelastic materials produce a non-symmetric matrix, though we have been lucky enough to find a workable symmetric version of that matrix that works really well for most problems (less well for the contact algorithm). Now that I am extending FEBio to include solute transport, I am discovering that there is no simple way to formulate a symmetric version for the corresponding stiffness matrix. (So far, all my attempts fail to produce convergence with a symmetric solver and I must use the non-symmetric solver.)

Therefore, it would seem to me that it is important to implement a quasi-Newton solver in FEBio, that works with non-symmetric matrices. I did a google search and I found this Wikipedia link on "Biconjugate gradient stabilized method" (http://en.wikipedia.org/wiki/Biconju...bilized_method), which would seem to satisfy our needs. Does anyone have experience with this? Any other suggestions?

Thanks,

Gerard

[maas]

Hi Gerard,

I'm not very familiar with different solution methods for non-linear systems, but I think the full-Newton method should always work, regardless of symmetry. Off course, it would be nice to have a method that does not require the reformation of the stiffness matrix in every iteration, so I will look into it.

Cheers,

Steve.