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: element-wise 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 dual-time 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...
On Apr 24, 2013, at 10:40 AM, "Manav Bhatia" <bhatiamanav@...> wrote:
> I might have to respond with a half-ignorant 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 pseudo-time
> 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:
> h-refinement 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.
> On Wed, Apr 24, 2013 at 1:13 PM, Roy Stogner <roystgnr@...:
>> On Wed, 24 Apr 2013, Manav Bhatia wrote:
>> Has anyone attempted space varying dt for time stepping problems using
>> No, but we've got an application where it might be a decent idea.
>> Half-ignorant rant:
>> I'm skeptical, though. Space varying dt is ideal if you're doing a
>> time-accurate solve of a hyperbolic problem, or if you can do
>> operator-splitting 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 space-varying dt in a time-accurate way on parabolic problems
>> without adding more DoFs to each space-time slab and so canceling out
>> most of your benefits.
>> What other implicit hypersonics people do with space-varying dt seems
>> to be limiting it to non-time-accurate 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 non-time-accurate 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.
> Try New Relic Now & We'll Send You this Cool Shirt
> New Relic is the only SaaS-based 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
> Libmesh-users mailing list