dolfin team mailing list archive

["Johan Hoffman" <jhoffman@xxxxxxxxxxx>]

>> >> Heat equation discretized by Crank-Nicolson:
>> >>
>> >> a = v*u*dx + k*0.5*dot(grad(v), grad(u))*dx
>> >> L = v*u0*dx - k*0.5*dot(grad(v), grad(u))*dx + v*0.5*(f+f0)*dx
>> >>
>> >> compared to
>> >>
>> >> a = v*u.dt()*dx + k*dot(grad(v), grad(u))*dx
>> >> L = v*f*dx
>> >
>> > What is wrong with the second alternative? Isn't that what we want?
>>
>> The second alternative is great, that is what I try to say. I would like
>> to automatically generate DOLFIN code corresponding to the first alt.
>> from
>> the second alt. by just specifying "Crank-Nicolson".
>
> Then I would suggest that a better option is to do the second
> alternative and just ask the ODE solver to use cG(1).
>
> Using the ODE solver with cG(1) + Newton is very similar to
> Crank-Nicolson with very little overhead.

Is cG(1) + Newton based on any left-hand side (u_t + A(u) = f(u)), or just
the mass matrix corresponding to u_t=f(u) ?


>> > I must be missing something. We already support (1) today and we will
>> > soon support (2).
>> >
>> > /Anders
>>
>> Do you mean that today I can write a FFC form-file with
>>
>> a = v*u.dt()*dx + k*dot(grad(v), grad(u))*dx
>> L = v*f*dx
>>
>> where I just specify what time-discretization I want to use, and that
>> FFC
>> generates code to DOLFIN with that time discretization? Then I must be
>> missing something... or? Isn't it necessary to write out the
>> semi-discretized form according to the first alt. above?
>
> No, .dt() is not supported yet. My suggestion would be that either a
> user specifies a time derivative and trusts the ODE solver to do the
> time integration (using cG(1), dG(0), dG(15) or whatever), or
> alternatively writes out the time discretization by hand if she
> doesn't want to use the ODE solver.

Ok, so the functionality of writing out the time discretization would
rather be in the ODE solver then.

> The ODE solvers are starting to come in pretty good shape, at least
> the standard mono-adaptive solvers.
>
> Johan Jansson has done some benchmarking for elasticity and the
> overhead was very small compared to explictly forming the system by
> hand and solving. I don't remember the exact numbers, maybe Johan can
> give us the details?
>
> /Anders

That's great! Interesting to see the results.

/Johan