dolfin team mailing list archive

[Victor Prosolin <flyaway1212@xxxxxxxxx>]

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.

> 
> 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. ;-)
> 
> 
> 
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