[petsc-users] Questions about TS

[Blaise Bourdin]

On Oct 19, 2011, at 4:16 PM, Jed Brown wrote:

> On Wed, Oct 19, 2011 at 16:08, Blaise Bourdin <bourdin at lsu.edu> wrote:
> I get it now... My confusion was due to being used to derived all scheme on the pde, then discretizing, whereas the documentation assumes that the equation is already discretized. I should have figured it out. 
> 
> For software purposes and sometimes also for analysis, the "method of lines" approach is often useful. That's how the TS interfaces are set up.
That make sense. I work mostly on problems where whose time-continuous formulation is obtained by writing a time discrete problem, then letting the time discretization interval go to 0. I have too much of a tendency to think this way.

>  
> 
> Is it right to think of the division between ODE, DAE and IMEX in the documentation as Fully Explicit vs. Fully implicit vs. Semi-implicit?
> 
> Sure, but it's a matter of the interface more than the method. You can write
> 
> Xdot = F(X)
> 
> and use -ts_type beuler to solve it fully implicitly. I would consider
> 
> G(X,Xdot) = F(X)
> 
> to be the most general interface. When an IMEX method is used, this has the clear semantics that G is implicit and F is explicit. Explicit methods usually assume G(X,Xdot) = Xdot which is the default if you never call TSSetIFunction. I think we will eventually have support for using standard explicit methods where you just put the mass matrix into G, but that isn't done yet.

OK, this is clear. It will be really nice indeed when everything is reorganized this way. 

Thanks again,

Blaise


-- 
Department of Mathematics and Center for Computation & Technology
Louisiana State University, Baton Rouge, LA 70803, USA
Tel. +1 (225) 578 1612, Fax  +1 (225) 578 4276 http://www.math.lsu.edu/~bourdin







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