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
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
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