Hello Brian,<br><br>thank you for your help! Now my doubts are solved.<br><br>Greetings,<br><br>Cristina<br><br><div class="gmail_quote">On Wed, Feb 2, 2011 at 2:17 AM, brian avants <span dir="ltr"><<a href="mailto:stnava@gmail.com">stnava@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">hi jeremy , cristina<br>
<br>
here is a brief latex sketch of the method used in the<br>
FEMCrankNicolsonSolver --<br>
<br>
\text{matrix form parabolic PDE, heat equation type} \\<br>
M\frac{ \partial U}{\partial t} + K U = f \\<br>
\frac{ M U_t - M U_{t-1}}{\delta_t} + K U = f \\<br>
\frac{ M U_t - M U_{t-1} + \delta_t K U }{\delta_t} = f \\<br>
\text{ here i make the decision to represent $U$ and $f$ at $t$ rather<br>
than $t-1$ i believe this is backward Euler}\\<br>
( M + \delta_t K ) U_t = M U_{t-1} + \delta_t f_t \\<br>
\\<br>
\text{other choices are possible, e.g. } \\<br>
\text{ Crank-Nicolson discretization is based on averaging forward and<br>
backward Euler } \\<br>
( M + \alpha \delta_t K ) U_t = ( M - ( 1- \alpha ) \delta_t K )<br>
U_{t-1} + f \\<br>
f = \delta_t ( \alpha f_t + ( 1 - \alpha ) f_{t-1} ) \\<br>
\\<br>
\text{if}~ \alpha = 1 \text{ backward Euler }\\<br>
( M + \delta_t K ) U_t = M U_{t-1} + \delta_t f \\<br>
\\<br>
\text{if}~ \alpha = 0 \text{ forward Euler }\\<br>
M U_t =( M - \delta_t K ) U_{t-1} + \delta_t f_{t-1}<br>
<br>
hopefully this is helpful.<br>
<br>
brian<br>
<div><div></div><div class="h5"><br>
<br>
<br>
<br>
On Tue, Feb 1, 2011 at 4:01 PM, Jeremy Bournesel<br>
<<a href="mailto:jeremy.bournesel@gmail.com">jeremy.bournesel@gmail.com</a>> wrote:<br>
> Hi,<br>
> I have a decent background regarding FEM in the engineering domain and have<br>
> started looking at it for registering medical images as well.<br>
> I ran one of the ITK deformable registration demos, read the Software Guide<br>
> and the ITK Powerpoint Presentations, however there is still some magic<br>
> going on that I don't completely get.<br>
> From what I understand ITK is using a uniform grid/mesh (if a custom one<br>
> wasn't supplied) and then calculates the deformation for every element at<br>
> the nodal points (iteratively).<br>
> I couldn't find any information on how the exact process is working (besides<br>
> some high level slides of the type K U = F).<br>
> It'd be awesome if someone can point me to the right document or explain it<br>
> to me.<br>
> Thanks,<br>
> Jeremy<br>
><br>
><br>
><br>
><br>
><br>
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