dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

The new PDE class is now in place and takes care of some of the
standard stuff you need to do to solve a static linear PDE: define
vectors and matrices, assemble bilinear and linear forms, solve linear
system and create a Function from the degrees of freedom.

Here's the new version of the Poisson demo:
  
  // Set up problem
  UnitSquare mesh(16, 16);
  Poisson::BilinearForm a;
  Poisson::LinearForm L(f);
  PDE pde(a, L, mesh, bc);

  // Solve
  Function u = pde.solve();

  // Save function to file
  File file("poisson.pvd");
  file << u;

This works for all linear static PDEs. I imagine that we can use the
PDE class to automate the solution of static nonlinear PDEs,
time-dependent etc. Depending on the arguments to the constructor
(among other things), the PDE class would know what to do to solve the
system. A first step would be to integrate Garth's Newton-solver with
the PDE class. Perhaps we need to partition it in the same way as the
Function class (GenericPDE, StaticLinearPDE etc) so it's easy to
plugin a new solver.

Note that as an alternative to

  Function u = pde.solve();

one can do

  Function u;
  pde.solve(u);

which is slightly more efficient (avoids one copy of the vector of
degrees of freedom).

The PDE class i parametrized and has one parameter "solver", so you
can do either

  pde.set("solver", "direct"); // default option

or

  pde.set("solver", "iterative");

/Anders