On 14 June 2011 23:02, Martin Sandve Alnæs <[email protected]> wrote: > I think one of the main problems with VariationalProblem > is the mix of problem and solver in one abstraction. > > A problem is usually formulated: > > Find u in V such that > a = L in Omega // pde > u = g on Gamma // bcs > > Find u in V such that > F = 0 in Omega // pde > u = g on Gamma // bcs > > Here's my suggested variation of VariationalProblem: > > # Generic form: > problem = VariationalProblem(unknown, lhsform, rhsform, bcs) > solve(problem) > > # Examples and variations follow, all consistent with the above: > > # Typical linear system > p = VariationalProblem(u, a, L, bcs) > # Note that ordering and sign is consistent with a linear system > p = VariationalProblem(u, J, -F, bcs) > # Possibly(!) nonlinear system F(u) = 0 > p = VariationalProblem(u, F, 0, bcs) > > # Note the 0 which maybe makes this less ambiguous(?) > > # The fully automated variant of solve: > solve(p) # Autodetect linear or nonlinear and differentiate if necessary > > # With optional behaviour changes: > solve(p, nonlinear=True) # Force nonlinear solver > solve(p, nonlinear=False) # Force linear solver > solve(p, u=u2) # place solution in u2 instead of p.u, useful for linear > solvers > solve(p, solver=mysolver) # Use nondefault solver (need solver API) > > # Pseudocode for solve, showing it's feasible: > def solve(p, nonlinear=None, solver="auto"): > # Allow alternative solvers in some way > if solver != "auto": > check properties of solver and adjust what is necessary below > > # Differentiate if necessary (skip if we use a solver that doesn't need > it): > if isinstance(p.rhs, int) and p.rhs == 0: > lhs, rhs = derivative(p.lhs, p.u), -p.lhs > else: > lhs, rhs = p.lhs, p.rhs > > # Detect nonlinear or linear equation unless forced > if nonlinear is None: # Set to True or False to force this > # I have this function in my private sandbox > nonlinear = ufl.algorithms.depends_on(lhs, p.u) > > # Solve with linear or nonlinear default solver > if solver == "auto": > if nonlinear: > return solve_nonlinear(p.u, lhs, rhs, p.bcs) > else: > return solve_linear(p.u, lhs, rhs, p.bcs) > else: > return solver.solve(...) > > > Good properties of this solution: > - Makes the VariationalProblem independent of the solver method > - Allows explicit or automatic choice of nonlinear/linear solver > - Consistent ordering of forms given to VariationalProblem > - Binds u to the problem, which is in accordance with (*) and allows > differentiation > There may be something I've forgotten of course, so speak up. > > The binding of u to the problem is not really necessary in > the case of a linear problem, but makes things consistent. > With solve(p, u=u2) we still allow reuse of the VariationalProblem. > > Martin
Plus this is a fairly small iteration from the current design, with the book and all... Martin _______________________________________________ Mailing list: https://launchpad.net/~dolfin Post to : [email protected] Unsubscribe : https://launchpad.net/~dolfin More help : https://help.launchpad.net/ListHelp
