Thank you very much. I CC Bruno Turcksin and Damien Lebrun-Grandie in hope of receiving a reply from them.
Regards, Aslan On Thursday, November 17, 2016 at 5:22:00 PM UTC-7, Wolfgang Bangerth wrote: > > > Aslan, > > > I can see that there is an implementation of IRK method in deal.ii. If > you do > > not mind, may I ask what was the reason that that particular method was > chosen > > in your software? I am aware that IRK and BDF schemes have overall > similar > > efficiency, so that might have been just some personal preference of the > > developer(s). > > That would be a question for Bruno and Damien. I don't know. > > > > I am wondering how deal.ii solves the issue when the dimension > > of the problem is large and then it is impossible to store the matrix > > (I-tau*AxJ)^(-1) of the simplified Newton iteration in IRK (where x is > the > > Kronecker product; from Hairer & Wanner). I believe you use some > modification > > that leads to the use of simply (I-tau*J)^(-1) as it is seen from the > name > > /id_minus_tau_J_inverse/ of one of the variables in the code. Is it > recomputed > > for each Newton iteration? > > You never store this matrix. What you need to provide to the integrators > is a > function that multiplies a vector with this matrix. In practice, that > always > means that you solve a linear system with (I - tau J) and the given vector > as > the right hand side. > > Take a look at the tutorial program that demonstrates the use of these > time > integrators to see an example of how this is implemented in practice. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu > <javascript:> > www: http://www.math.colostate.edu/~bangerth/ > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
