On Tue, Feb 19, 2008 at 10:23:32AM -0500, Hatef Monajemi wrote: > > > > Anders Logg wrote: > > > >On Tue, Feb 19, 2008 at 08:03:04AM -0500, Hatef Monajemi wrote: > >> > >> > >> On Tue, 2008-02-19 at 09:55 +0100, Anders Logg wrote: > >> > On Sun, Feb 17, 2008 at 12:13:50AM -0500, Hatef Monajemi wrote: > >> > > Dear Dolfin Users: > >> > > I am interested to find out the most efficient way to > >> > > implement solution of coupled differential equations in Dolfin: > >> > > > >> > > Class I: a partial differential equation (PDE) coupled with > >> > > an ordinary differential equation. > >> > > > >> > > Class II: A PDE coupled with one or more PDEs > >> > > > >> > > > >> > > For instance, a wave equation when cast in the state space form, > may > >> > > belong to Class I. I understand that wave equation has already > been > >> > > solved using Dolfin. But I am unable to find any documentation in > this > >> > > regards. > >> > > Typically, what will be the "*.form" file associated with the wave > >> > > equation? > >> > > Can anyone point me to the right place to find such docs? > >> > > Thanks in advance. > >> > > Hatef > >> > > >> > For a demo solving a time-dependent problem, look at > >> > > >> > src/demo/pde/convection-diffusion/ > >> > >> Convection-Diffusion is a first Order pde with respect to time. what I > >> am interested in is equations such as Wave which are second order with > >> respect to time and when we cast them in the state space form become a > >> set of coupled Differential equations. I understand that Wave Equation > >> has been solved by you and reported as an Example. However, I did not > >> find any document regarding the *.form File and setting the Variational > >> form of this Kind of coupled equations. > > > >Please resend to dolfin-dev.
DOLFIN does not care (or help you) regarding which method you use to solve an equation, so you need to construct the method/scheme yourself. But basically there are two ways to do this: either do "manual" time-stepping and write a form for a variational problem to be solved in each time step (like in the convection-diffusion demo) or you may throw everything in the right-hand side and call the ODE solvers. In the latter case, look in src/bench/ode/wave/. In both cases, you may choose to either rewrite it as a first order system or keep it as a second-order system (and do some kind of central differencing). -- Anders _______________________________________________ DOLFIN-dev mailing list [email protected] http://www.fenics.org/mailman/listinfo/dolfin-dev
