dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Thu, Nov 13, 2008 at 11:24:55AM -0700, Victor Prosolin wrote:
> Anders Logg wrote:
> > 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.
> 
> In the docs it says:
>   /// It is also possible to solve implicit systems of the form
>   ///
>   ///     M(u(t), t) u'(t) = f(u(t),t) on (0,T],
>   ///
>   ///     u(0)  = u0,
>   ///
>   /// by setting the option "implicit" to true and defining the
>   /// function M().
> 
> Is this what you meant? Can M be used with an explicit method?
> 
> Victor Prosolin.

All the methods we have implemented are implicit: cG(q) and dG(q) for
general degree q.

-- 
Anders

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