<html><body><div style="color:#000; background-color:#fff; font-family:arial, helvetica, sans-serif;font-size:12pt">FYI: an example of the implementation of deflated GMRES <br>in PETSc can be found at: <br><br>http://onlinelibrary.wiley.com/doi/10.1002/nla.1882/full<br><div><br><span></span></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: arial,helvetica,sans-serif; background-color: transparent; font-style: normal;"><span>Possibly this helps. Kind wishes, Domenico Lahaye. <br></span></div><div><br></div> <div style="font-family: arial, helvetica, sans-serif; font-size: 12pt;"> <div style="font-family: times new roman, new york, times, serif; font-size: 12pt;"> <div dir="ltr"> <hr size="1"> <font face="Arial" size="2"> <b><span style="font-weight:bold;">From:</span></b> Jed Brown <jedbrown@mcs.anl.gov><br> <b><span style="font-weight: bold;">To:</span></b> Matteo Parsani <parsani.matteo@gmail.com> <br><b><span
style="font-weight: bold;">Cc:</span></b> Mark H. Carpenter <mark.h.carpenter@nasa.gov>; petsc-users <petsc-users@mcs.anl.gov> <br> <b><span style="font-weight: bold;">Sent:</span></b> Monday, June 17, 2013 10:31 AM<br> <b><span style="font-weight: bold;">Subject:</span></b> Re: [petsc-users] Deflated GMRES in PETSc<br> </font> </div> <div class="y_msg_container"><br>[Cc'ing petsc-users since people may be interested.]<br><br>Matteo Parsani <<a ymailto="mailto:parsani.matteo@gmail.com" href="mailto:parsani.matteo@gmail.com">parsani.matteo@gmail.com</a>> writes:<br><br>> Hi Jed,<br>> do you know if in PETSc we can start a Krylov iteration with problematic<br>> eigenmodes in the Krylov subspace at the beginning of the iteration?<br><br>Deflation is identical to a Galerkin coarse grid correction. I would<br>use PCMG to create a two-level method. Write your deflation space into<br>the prolongation operator and use
Galerkin. You can compose a PCMG with<br>other preconditioners. I would leave DGMRES to only deal with adaptive<br>identification of those problematic modes. Note that the DGMRES basis<br>vectors will be global, but when you provide vectors a priori, you are<br>free to localize them.<br><br>> Machinery should be there already because we see that this is used when<br>> GMRES stagnates.<br>><br>> Thanks,<br>><br>> -- <br>> Matteo<br><br><br></div> </div> </div> </div></body></html>