[Getdp] ... Formulation question ...
Olivier Castany
castany at quatramaran.ens.fr
Thu Mar 1 22:43:42 CET 2007
Hello,
your formulation probably contains a term like :
Galerkin { [ Dof{d Phi} , {d Phi} ] ; ... } (1)
which makes it possible to build a matrix equation.
You can then add a term :
Galerkin{ [ Spd[] * Norm[{d Phi}] , {Phi} ] ; ... } (2)
and solve the problem recursively with a non-linear scheme
(InitSolution, IterativeLoop, GenerateJac, SolveJac).
> However, if I leave out the Dof{} term, won't that mean that Phi is no
> longer treated as a variable to be solved for, but rather as something
> given already? In other words, I won't be solving the right problem?
This is the point of the recursive scheme (InitSolution, IterativeLoop,
GenerateJac, SolveJac)
* First iteration :
Phi has been initialized. The default initial value is : Phi = 0
everywhere (but another initial value can be given in the "Constraint"
section with "Type Init")
The value of the field "Spd[] * Norm[{d Phi}]" in eq. (2) is 0.
The matrix equation is then solved and you get a field Phi.
* Second iteration :
The value of the field "Spd[] * Norm[{d Phi}]" in eq. (2) is calculated
based on the result of the first iteration.
The matrix equation is then solved and you get another field Phi.
* Third iteration ... ...
If you're lucky, the process converges to a fixed point which is your
solution.
Regards,
O.C.