dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Thu, Nov 13, 2008 at 11:16:33AM +0000, Garth N. Wells wrote:
> 
> 
> Victor wrote:
> > Dear developers and users of DOLFIN.
> > I am considering using DOLFIN to solve the equations of
> > magnetohydrodynamics (MHD).
> > The equation looks like this:
> > 
> > dU/dt + grad(F)=0
> > 
> > where U is a vector of physical quantities, dU/dt is a partial
> > derivative and F is flux, which is a non-linear function of U. It is a
> > non-linear hyperbolic system of equations similar to Euler equations.
> > 
> > The method I am trying to implement is an explicit Runge-Kutta
> > Discontinuous Galerkin (RKDG) method by Cockburn et al. So the
> > discretized equation should look like this:
> > 
> > M dU/dt = R(U)
> > 
> > where U is the solution vector, M is a mass matrix, dU/dt is a full time
> > derivative and R(U) is a function of U.
> >
> 
> If you want to use a Runge-Kutta scheme, you should be able to do this 
> without the DOLFIN ODE solvers. Just build the time stepping scheme into 
> your forms. Examples of this can be found in 
> demo/pde/convection-diffusion and /demo/nls/cahn-hilliard.

It is possible to use the ODE solvers directly and they allow you to
specify that the time derivative is multiplied by a mass matrix.

Unfortunately there is no demo, so you'll have to figure out how to
use it yourself. If you get it working, consider submitting a demo
that we can add. ;-)

-- 
Anders


> 
> > So my question is as follows: Is it possible to use the DOLFIN ODE
> > solver to solve this kind of system or am I saying complete nonsense?
> > Has anybody done any work with similar equations or methods using DOLFIN?
> > 
> > 
> > Also, most of the ODE demos in DOLFIN 0.8.1 won't compile on my machine.
> > Is there interest in bug reports?
> >
> 
> Yes. Send a summary of the problems to this list (error messages, OS, 
> compiler version, etc).
> 
> Garth
> 
> 
> > Any advise or pointers would be greatly appreciated.
> > 
> > Sincerely,
> > Victor Prosolin.
> > Graduate student,
> > University of Calgary.
> > _______________________________________________
> > DOLFIN-dev mailing list
> > DOLFIN-dev@xxxxxxxxxx
> > http://www.fenics.org/mailman/listinfo/dolfin-dev
> 
> 
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