Iterative Method to solve FEM problems (not iterative system solver)

had this idea to solve an FEM problem: While fixing all nodes of the
elements that connect to one node one could calculate the balanced state of
this specific node. Doing this for all nodes one can get in a few
pass-troughs's a global minimum of the energy for the complete system. Since
this seams a quite simple approach to the problem I did some Internet
research on this and found quite nothing about such a method.
Only the Program "Sinter-FEM"
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only in German) of Dr. Jörg Möller seams to use this method
but he don't knows if any other programs are using this approach or if there
has been any research according to this.
Using this approach would spare the Memory Problems that one gets in Big
Systems since no system Matrix has to be generated (the necessary memory
would increase linear and not quadratic with the amount of elements). The
same should be true for the amount of calculations witch are needed to get
the results.
Furthermore it seems a lot easier to be programmed, especially if it gets to
nonlinear or dynamic Problems. And if a System is instable the Program wound
crash but the System would start drifting in our virtual Space and that
could be useful for crack propagation Problems.
Now I was wondering if there has been any research to this approach or if
there are more Programs using it, if there are any books, papers or anything
where it has been mentioned and what are the problems? Why hasn't it been
used in More Programs?
Sincerely
Marko Thiele
Reply to
Marko Thiele
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I think this is called the relaxation technique. Maybe that will help you to find references to it.
I agree that it is a good way of minimising the wavefront... but the processing cost in requiring an iterative approach counterbalances this.
In the olden days we used to solve substructures before solving the whole structure - partitioning your FE model was an important skill. Perhaps you've reinvented that?
Cheers
Greg Locock
Reply to
Greg Locock
as ralaxation technique i've found only references to the so called "dynamic relaxation techniques". For this method it is not neccesary to solve the linear system but you will still need a complete stifness Matrix. If I understand it corect it has been shown that the dynamic relaxation methods can be equaly fast as the CG methods when solving a the linear system of a FE problem iteratively. Nevertheless, the method i proposed was a different (might be I just didnt found out about the rigth references to "relaxation techniques" jet). Partitioning an FE model could undoubtly be used to speed up the convergence of this methode but I thing there might be even more effective methods to get fast convergence. Anyway... I thing that further investigation of this method would be interesting.
so long... Marko Thiele
Reply to
Marko Thiele

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