[Insight-users] FEM: PDE of Crank-Nicolson solver

[brian avants]

Hi Cristina

The specific PDE depends upon the specific elements you choose.  For
instance, if you set up a triangular mesh via the
2DC0LinearTriangularMembrane  element, then you will use a membrane
energy penalty term.

The Crank-Nicolson solver uses the Crank-Nicolson approach to
accumulate the solution to the registration problem over time.

Wikipedia provides a reasonable general explanation of the C-N
approach and gives an example for the heat equation;

http://en.wikipedia.org/wiki/Crank%E2%80%93Nicolson_method

B.


On Fri, Dec 10, 2010 at 10:07 AM, Cristina Oyarzun
<coyarzunlaura at googlemail.com> wrote:
> Hello,
>
> I am using itk FEM registration filter. This filter makes use of
> itkFEMSolverCrankNicolson. In the header file of the solver one finds the
> equation that the solver tries to solve. However, one can only find there
> its Crank-Nicolson formulation but not the original PDE that leads to that
> equation.
>
> I tried to get the discretized equation by using the equation of motion that
> is described in a book and Crank-Nicolson scheme but did not arrive to the
> same solution. Could someone tell me which on is the original PDE that is
> solved in itkFEMSolverCrankNicolson?
>
> Thank you!!
>
> Greetings,
>
> Cristina
>
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