Hi again,
When using the getMatrix() routine as Daniel suggested, I'm not sure exactly
what difference matrix fipy is pulling. As a simplified 1D example of a
particle in an infinite well:
nx = 5
dx = 1
mesh = Grid1D(nx = nx, dx = dx)
psi = CellVariable(name='solution variable', mesh = mesh, value = 0.)
valueLeft = 0
valueRight = 0
BCs = (FixedValue(faces=mesh.getFacesRight(), value=valueRight),\
FixedValue(faces=mesh.getFacesLeft(), value=valueLeft))
eqn = -ImplicitDiffusionTerm(coeff=mass)==0
eqn.cacheMatrix()
eqn.solve(var = psi, boundaryConditions=BCs)
pymat = eqn.getMatrix().matrix
gives the correct sparse differencing matrix:
3.000000 -1.000000 -------- -------- --------
-1.000000 2.000000 -1.000000 -------- --------
-------- -1.000000 2.000000 -1.000000 --------
-------- -------- -1.000000 2.000000 -1.000000
-------- -------- -------- -1.000000 3.000000
However, if I turn the step size to dx=0.1, I get:
30.00000 -10.00000 -------- -------- --------
-10.00000 20.00000 -10.00000 -------- --------
-------- -10.00000 20.00000 -10.00000 --------
-------- -------- -10.00000 20.00000 -10.00000
-------- -------- -------- -10.00000 30.00000
The actual difference matrix should have a factor of (1/dx^2), not (1/dx) in
front of it, which results in eigenvalues that have to be rescaled. Of course,
the problem is easy to fix, but I would love to know where the factor of 1/dx
is going.
Many thanks,
John
On May 3, 2010, at 2:59 PM, John Gamble wrote:
>
> Thanks, Daniel. I'll give that a try!
>
> On Mon, 2010-05-03 at 11:03 -0400, Daniel Wheeler wrote:
>> Hi John, You'll need to interface with pysparse directly. Using
>>
>> <http://pysparse.sourceforge.net/jdsym.html#eigenvalue-solver>
>>
>> You can get the pysparse matrix for you problem by doing
>>
>> eqn.cacheMatrix()
>> eqn.solve(...)
>> pysparseMatrix = eqn.getMatrix().matrix
>>
>> You'll have to figure how to pass it to the jdsym module. I am not
>> sure how to do that. Hope this helps. Cheers.
>>
>> On Sun, May 2, 2010 at 11:31 PM, John Gamble <[email protected]> wrote:
>>>
>>> Dear all,
>>>
>>> I am attempting to use fipy to solve a coupled system consisting of the
>>> Poisson and Schroedinger equations. To solve the Schroedinger equation,
>>> I need to solve an eigenvalue problem to find allowed energies. Is there
>>> a way to tell fipy to search for the required eigenvalues?
>>>
>>> Many thanks,
>>> John Gamble
>>>
>>>
>>>
>>
>>
>>
>
>
>
