have trouble to understand cahn-hilliard demo code

Asked by cutejeff on 2010-03-23

There is a demo code under src/demo/pde/cahn-hilliard/ to solve the Cahn-Hilliard equation, which is a fourth-order nonlinear time-dependent problem. Since my problem is also nonlinear initial value problem, I want to follow this code as an example.
I have gone through the nonlinear and time-dependent prob parts in the tutorial. But I still have trouble to understand the approach the author did. He seems to split the original eqn into 2 eqns. Does anybody know the original eqn and the derivations?

I also have trouble to understand the following code:
dk, dc = split(du)

class CahnHilliardEquation(NonlinearProblem):
    def __init__(self, a, L):
        NonlinearProblem.__init__(self)
        self.L = L
        self.a = a
        self.reset_sparsity = True
    def F(self, b, x):
        assemble(self.L, tensor=b)
    def J(self, A, x):
        assemble(self.a, tensor=A, reset_sparsity=self.reset_sparsity)
        self.reset_sparsity = False

They haven't been covered in the tutorial. Are there any other documents to learn these?
Any help will be appreciated.

Question information

Language:
English Edit question
Status:
Solved
For:
DOLFIN Edit question
Assignee:
No assignee Edit question
Solved by:
Andy R Terrel
Solved:
2010-03-30
Last query:
2010-03-30
Last reply:
2010-03-26
Best Andy R Terrel (andy-terrel) said : #1

I believe this is the paper describing the methods used in the demo.

http://dx.doi.org/10.1016/j.jcp.2006.03.010

The split is done to separate the equations based on the Mixed Space.
This comes from the UFL specification so the manual there could give
you more information. It is written this way so that a and L can be
automatically linearized for the Newton-Raphson method.

The CahnHillardEquation class is a NonlinearProblem. This is the
simple way to use Newton-Raphson method that is coded in dolfin. In
this style you need to specify the application of F and its jacobian
J. The easiest way to do that is to define a form and have UFL/FFC
generate the derivatives for you. The newon solver will reconstruct F
and J as it needs to for the Newton-Raphson method.

I hope that helps.

-- Andy

On Tue, Mar 23, 2010 at 10:53 AM, cutejeff
<email address hidden> wrote:
> New question #105304 on DOLFIN:
> https://answers.launchpad.net/dolfin/+question/105304
>
> There is a demo code under src/demo/pde/cahn-hilliard/ to solve the Cahn-Hilliard equation, which is a fourth-order nonlinear time-dependent problem. Since my problem is also nonlinear initial value problem, I want to follow this code as an example.
> I have gone through the nonlinear and time-dependent prob parts in the tutorial.  But I still have trouble to understand the approach the author did. He seems to split the original eqn into 2 eqns. Does anybody know the original eqn and the derivations?
>
> I also have trouble to understand the following code:
> dk, dc = split(du)
>
> class CahnHilliardEquation(NonlinearProblem):
>    def __init__(self, a, L):
>        NonlinearProblem.__init__(self)
>        self.L = L
>        self.a = a
>        self.reset_sparsity = True
>    def F(self, b, x):
>        assemble(self.L, tensor=b)
>    def J(self, A, x):
>        assemble(self.a, tensor=A, reset_sparsity=self.reset_sparsity)
>        self.reset_sparsity = False
>
> They haven't been covered in the tutorial. Are there any other documents to learn these?
> Any help will be appreciated.
>
> --
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cutejeff (illw84u) said : #2

Thanks Andy R Terrel, that solved my question.