From: Manav Bhatia <bhatiamanav@gm...>  20130424 16:59:43

Hi, Has anyone attempted space varying dt for time stepping problems using libMesh? I am looking along the lines of creating a solver using domain decomposition where each domain works with quasiindependent dt. A first look at it seems like a lot of development effort, but I am curious if some effort has alredy been added in the direction. Thanks, Manav 
From: Roy Stogner <roystgnr@ic...>  20130424 17:13:37

On Wed, 24 Apr 2013, Manav Bhatia wrote: > Has anyone attempted space varying dt for time stepping problems using > libMesh? No, but we've got an application where it might be a decent idea. Halfignorant rant: I'm skeptical, though. Space varying dt is ideal if you're doing a timeaccurate solve of a hyperbolic problem, or if you can do operatorsplitting and limit the space varying dt to the explicit operator(s) in a parabolic problem, but I've never seen how you can do implicit spacevarying dt in a timeaccurate way on parabolic problems without adding more DoFs to each spacetime slab and so canceling out most of your benefits. What other implicit hypersonics people do with spacevarying dt seems to be limiting it to nontimeaccurate solves, where you're just pseudo time stepping to get to a quasi steady state. Which is fine, we do pseudo time stepping too... except that I think the right thing in this case may be to go coarser in time *and* space; if you're basically using the nontimeaccurate parts of your solve just to get the shock moved into place so you can use larger dt, you might as well do most of that movement on a coarse grid.  Roy 
From: Manav Bhatia <bhatiamanav@gm...>  20130424 17:40:41

I might have to respond with a halfignorant rant from my end too, since I am just getting started with the literature. I am using two domain decomposition books as reference: one by Quarternoni and Valli and the other by Toselli and Wildund. My motivation is the second point in your message: I am pseudotime stepping towards a steady solution. My application is inviscid transonic flow simulation on a swept wing using GLS method. This goes back to my message about the linear solver convergence last week: hrefinement leads to a point where the linear solver refuses to converge. I have tried a lot of options (modifying the GMRES restart iteration to 1000, ASM preconditioners that Jed had suggested, reducing the dt post refinement to as low as 1% of original value, etc.) but none have worked for me so far. I have not tried modifying my "tau" matrix, though. On one side, I am a little perplexed as to why others have not faced this issue: perhaps there is a bug in my code, perhaps the nature of transonic flow makes it a difficult problem, perhaps it is a weakness in GLS, or other reasons. I doubt there is a bug though, since there hasn't been an error in solution so far in all other simulations that I have done. On the other side, I feel like chopping up the matrix for linear solve might lead to a set of separate and better conditioned linear solves. Hence, I am looking at walking down this path. I do not yet know of the challenges you pointed out, but from what I have read in the books so far, it seems possible to setup appropriate Dirichlet and Neumann BCs at the interfaces to enable consistent solution for different kinds of physics. Ofcourse, now one needs to iterate between domains till convergence. On a related note, I have a feeling that the latest addition of separate parallel communicators in 0.9.1 might come in handy. Manav On Wed, Apr 24, 2013 at 1:13 PM, Roy Stogner <roystgnr@...>wrote: > > On Wed, 24 Apr 2013, Manav Bhatia wrote: > > Has anyone attempted space varying dt for time stepping problems using >> libMesh? >> > > No, but we've got an application where it might be a decent idea. > > Halfignorant rant: > > I'm skeptical, though. Space varying dt is ideal if you're doing a > timeaccurate solve of a hyperbolic problem, or if you can do > operatorsplitting and limit the space varying dt to the explicit > operator(s) in a parabolic problem, but I've never seen how you can do > implicit spacevarying dt in a timeaccurate way on parabolic problems > without adding more DoFs to each spacetime slab and so canceling out > most of your benefits. > > What other implicit hypersonics people do with spacevarying dt seems > to be limiting it to nontimeaccurate solves, where you're just > pseudo time stepping to get to a quasi steady state. Which is fine, > we do pseudo time stepping too... except that I think the right thing > in this case may be to go coarser in time *and* space; if you're > basically using the nontimeaccurate parts of your solve just to get > the shock moved into place so you can use larger dt, you might as well > do most of that movement on a coarse grid. >  > Roy > 
From: Kirk, Benjamin (JSCEG311) <benjamin.kirk1@na...>  20130424 18:45:36

I have done supg in the past with local time stepping. I assign a different dt for each node and use that dt when evaluating all element residual/jacobian information for that node. It's trivially easy. Just beware of errors I've made along the way: elementwise timestep is a horrible idea for continuos FE approximations, and make sure you get a consistent dt for nodes on processor boundaries. Scheme works well in practice for steady problems. I guess if time accuracy is important you'd be looking to imbed this in a dualtime scheme because of Roy's concerns? As for your concern about a bug  lets get together offline and maybe I can run your mesh with some various options and report my experience... Ben On Apr 24, 2013, at 10:40 AM, "Manav Bhatia" <bhatiamanav@...> wrote: > I might have to respond with a halfignorant rant from my end too, since I > am just getting started with the literature. I am using two domain > decomposition books as reference: one by Quarternoni and Valli and the > other by Toselli and Wildund. > > > My motivation is the second point in your message: I am pseudotime > stepping towards a steady solution. My application is inviscid transonic > flow simulation on a swept wing using GLS method. > > This goes back to my message about the linear solver convergence last week: > hrefinement leads to a point where the linear solver refuses to converge. > I have tried a lot of options (modifying the GMRES restart iteration to > 1000, ASM preconditioners that Jed had suggested, reducing the dt post > refinement to as low as 1% of original value, etc.) but none have worked > for me so far. I have not tried modifying my "tau" matrix, though. > > On one side, I am a little perplexed as to why others have not faced this > issue: perhaps there is a bug in my code, perhaps the nature of transonic > flow makes it a difficult problem, perhaps it is a weakness in GLS, or > other reasons. I doubt there is a bug though, since there hasn't been an > error in solution so far in all other simulations that I have done. > > On the other side, I feel like chopping up the matrix for linear solve > might lead to a set of separate and better conditioned linear solves. > Hence, I am looking at walking down this path. > > I do not yet know of the challenges you pointed out, but from what I have > read in the books so far, it seems possible to setup appropriate Dirichlet > and Neumann BCs at the interfaces to enable consistent solution for > different kinds of physics. Ofcourse, now one needs to iterate between > domains till convergence. > > On a related note, I have a feeling that the latest addition of separate > parallel communicators in 0.9.1 might come in handy. > > > Manav > > > > On Wed, Apr 24, 2013 at 1:13 PM, Roy Stogner <roystgnr@...>wrote: > >> >> On Wed, 24 Apr 2013, Manav Bhatia wrote: >> >> Has anyone attempted space varying dt for time stepping problems using >>> libMesh? >> >> No, but we've got an application where it might be a decent idea. >> >> Halfignorant rant: >> >> I'm skeptical, though. Space varying dt is ideal if you're doing a >> timeaccurate solve of a hyperbolic problem, or if you can do >> operatorsplitting and limit the space varying dt to the explicit >> operator(s) in a parabolic problem, but I've never seen how you can do >> implicit spacevarying dt in a timeaccurate way on parabolic problems >> without adding more DoFs to each spacetime slab and so canceling out >> most of your benefits. >> >> What other implicit hypersonics people do with spacevarying dt seems >> to be limiting it to nontimeaccurate solves, where you're just >> pseudo time stepping to get to a quasi steady state. Which is fine, >> we do pseudo time stepping too... except that I think the right thing >> in this case may be to go coarser in time *and* space; if you're >> basically using the nontimeaccurate parts of your solve just to get >> the shock moved into place so you can use larger dt, you might as well >> do most of that movement on a coarse grid. >>  >> Roy >  > Try New Relic Now & We'll Send You this Cool Shirt > New Relic is the only SaaSbased application performance monitoring service > that delivers powerful full stack analytics. Optimize and monitor your > browser, app, & servers with just a few lines of code. Try New Relic > and get this awesome Nerd Life shirt! http://p.sf.net/sfu/newrelic_d2d_apr > _______________________________________________ > Libmeshusers mailing list > Libmeshusers@... > https://lists.sourceforge.net/lists/listinfo/libmeshusers 