On May 22, 2012, at 4:46 AM, <[email protected]>
<[email protected]> wrote:
> I'm trying to solve the following system of PDE and Non-Liner Algebraic
> Equations (NLAE):
>
> the PDEs read:
> \frac{\partial{\phi}}{\partial t} = \nabla ( D(y) \nabla y)
> where both phi and y are arrays of cellVariable and the number of PDE equals
> the length of the \phi array
>
> and the set of NLAE
>
> F(\phi, y)= 0 at every node in the domain
> where y is the local root of F, i.e. \frac{\partial F}{\partial y} is a
> square full matrix.
> This local problem is non-linear and I use SciPy.optimize.fsolve as solver.
>
>
> My problem:
>
> I don't know an explict way of writing y = G{\phi} (and its derivatives) as
> suggested for example
> here:http://www.ctcms.nist.gov/fipy/examples/phase/generated/examples.phase.simple.html?highlight=expansion%20source
>
The equations you have posed are fully explicit, so I'm not sure any of that is
germane.
> Do you have any suggestion for improving the performance of this resolution?
> and avoiding the use of setValue getValue for this kind of coupled problem?
It's hard to say, as I'm not sure I accurately understand what you are trying
to do. If I assume that
D(y) = y^2
F(\phi, y) = \phi + y
is this a fair representation of your code?
import scipy.optimize
from fipy import *
mesh = Grid1D(nx=10, dx=1.)
x, = mesh.getCellCenters()
phi = CellVariable(mesh=mesh, name=r"$\phi$", value=x, hasOld=True)
y = CellVariable(mesh=mesh, name="y", value=1., hasOld=True)
D = y.getFaceValue()**2
eq = TransientTerm() == (D * y.getFaceGrad()).getDivergence()
viewer = Viewer(vars=(phi, y))
def F(x, *args):
return phi.getValue() + x
for step in range(100):
phi.updateOld()
y.updateOld()
res = 1e100
while res > 1e-3:
res = eq.sweep(var=phi, dt=1e-4)
y.setValue(scipy.optimize.fsolve(func=F, x0=y.getValue()))
viewer.plot()
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