On Tue, Aug 19, 2008 at 03:40:13PM +0200, Jed Brown wrote: > On Tue 2008-08-19 14:06, Anders Logg wrote: > > On Tue, Aug 19, 2008 at 01:49:22PM +0200, Jed Brown wrote: > > > On Tue 2008-08-19 13:40, Anders Logg wrote: > > > > On Tue, Aug 19, 2008 at 12:12:50PM +0200, Jed Brown wrote: > > > > > On Tue 2008-08-19 11:59, Anders Logg wrote: > > > > > > On Thu, Aug 14, 2008 at 10:10:03PM +0000, Jed Brown wrote: > > > > > > > One way to implement this is to allocate a vector for Dirichlet > > > > > > > values, > > > > > > > a vector for Homogeneous values, and a Combined vector. The > > > > > > > Homogeneous > > > > > > > vector is the only one that is externally visible. > > > > > > > > > > > > Isn't this problematic? I want the entire vector visible externally > > > > > > (and not the homogeneous part). It would make it difficult to plot > > > > > > solutions, saving to file etc. > > > > > > > > > > > > Maybe the Function class could handle the wrapping but it would > > > > > > involve a > > > > > > complication. > > > > > > > > > > Right, by `externally visible' I mean to the solution process, that is > > > > > time-stepping, nonlinear solver, linear solvers, preconditioners. The > > > > > vector you are concerned about is the post-processed state which you > > > > > can > > > > > get with zero communication. It is inherently tied to the mesh and > > > > > anything you do with it likely needs to know mesh connectivity. I > > > > > don't > > > > > think it is advantageous to lump this in with the global state vector. > > > > > > > > > > Jed > > > > > > > > I don't understand. What is the global state vector? > > > > > > The global state vector is the vector that the solution process sees. > > > Every entry in this vector is a real degree of freedom (Dirichlet > > > conditions have been removed). This is the vector used for computing > > > norms, applying matrices, etc. When writing a state to a file, this > > > global vector is scattered to a local vector and boundary conditions are > > > also scattered into the local vector. The local vector is serialized > > > according to ownership of the mesh (you have to do this anyway). > > > > > > Jed > > > > I'm only worried about how to create a simple interface. Now, one may > > do > > > > u = Function(...); > > A = assemble(a, mesh) > > b = assemble(L, mesh) > > bc.apply(A, b) > > solve(A, u.x(), b) > > plot(u) > > > > How would this look if we were to separate out Dirichlet dofs? > > How about a FunctionSpace object which manages this distinction. > Something like the following should work. > > V = FunctionSpace(mesh, bcs); // Is this name clearer?
We've discussed introducing a FunctionSpace concept earlier (on ufl-dev) to handle boundary conditions, and to enable sharing of function space data like meshes and dof maps. This might be a good idea, but it has to be something like V = FunctionSpace(element, mesh, bcs) > u = V.function(); I think this should be u = Function(V) > A = V.matrix(a); > P = V.matrix(p); // preconditioning matrix, optional [1] What do these accomplish? Return a matrix of appropriate size? I don't think that's necessary since the assembler can set the size. > solver = LinearSolver(A, P); > u0 = u.copy(); // if nonlinear, set initial guess > > V.assemble(A, a, u0); // builds Jacobian matrix [2] > V.assemble(P, p, u0); // preconditioning form, optional > V.assemble(b, L, u0); // the ``linear form'' (aka nonlinear residual) > solver.solve(u, b); The problem here is that the solver needs to be aware of Functions. Now, a solver only knows about linear algebra, which is nice. > Note that u0 disappears if the problem is linear and P disappears if you > use the real Jacobian as the preconditioning matrix. The key point is > that boundary conditions are built into the function space. It is no > more work, it just happens in a different place. > > [1] It is essential that the test/trial spaces for the preconditioning > matrix are the same as for the Jacobian. > > [2] I don't like the implicit wiring of the state vector into > assemble(). It is really hard to track dependencies and the current > state is not a property of the Bilinear/Linear forms. Maybe one could do (A, b) = assemble(a, L, mesh, bc) solve(A, u.dofs(), b) This would be in addition to the current (A, b) = assemble(a, L, mesh) bc.apply(A, b) solve(A. u.vector(), b) In the first version, the assembler knows about the boundary conditions and in the second it doesn't. This would require having two members in the Function class that return a Vector: u.vector() // Returns entire vector u.dofs() // Returns non-Dirichlet dofs -- Anders
signature.asc
Description: Digital signature
_______________________________________________ DOLFIN-dev mailing list [email protected] http://www.fenics.org/mailman/listinfo/dolfin-dev
