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<DIV><FONT face=Arial size=2>Hi,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>today I have a more theoretical question on
how</FONT></DIV>
<DIV><FONT face=Arial size=2>the FEM toolkit solves the displacement
problem.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>On a introductory paper about the Finite
Element Method</FONT></DIV>
<DIV><FONT face=Arial size=2>(dealing with mechanical problems), I read about
two different</FONT></DIV>
<DIV><FONT face=Arial size=2>methods (called Ritz and Galerkin) to solve
the problem of estimating </FONT></DIV>
<DIV><FONT face=Arial size=2>the displacements.</FONT></DIV>
<DIV><FONT face=Arial size=2>Both methods seem to work in a similar way on
minimizing the potential</FONT></DIV>
<DIV><FONT face=Arial size=2>energy formulation by using a function
representation for the displacement</FONT></DIV>
<DIV><FONT face=Arial size=2>components and stress and strain formulations.
</FONT></DIV>
<DIV><FONT face=Arial size=2>I know from the official itk registration -
tutorial ppt, that the ITK FEM toolkit also</FONT></DIV>
<DIV><FONT face=Arial size=2>uses this functional formulation for the
displacements.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I currently try to close the gap from the
mechanical problem to the registration</FONT></DIV>
<DIV><FONT face=Arial size=2>problem, and this causes still some problems in
understanding.</FONT></DIV>
<DIV><FONT face=Arial size=2>I mean, which of the described methods does the ITK
implementation use in general</FONT></DIV>
<DIV><FONT face=Arial size=2>and how are the forces, derived from the similarity
metric, related to general</FONT></DIV>
<DIV><FONT face=Arial size=2>stress and strain?</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>You will find the script at <A
href="http://www.ce.memphis.edu/7117/pdf_notes/chapter01.pdf">http://www.ce.memphis.edu/7117/pdf_notes/chapter01.pdf</A> .</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Also, I still don't understand how the variational
expression for the energy, you'll find it</FONT></DIV>
<DIV><FONT face=Arial size=2>also in the registration - ppt, fits to the
equation for minimum potential energy on page 12</FONT></DIV>
<DIV><FONT face=Arial size=2>(middle) of the mentioned script.</FONT></DIV>
<DIV><FONT face=Arial size=2>I hope somebody has the time and patience to help
me understanding these basic concepts.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Best regards,</FONT></DIV>
<DIV><FONT face=Arial size=2>Markus Weigert</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
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