Backward
Posted: 7 months ago by: Niklas Rom | 2 Comments |
Did you know that it is easy to set up certain kinds of inverse problems in COMSOL real quick with the aid of the Global Equations feature? Imagine this: instead of asking "how hot will the house get if I fire the boiler with three logs per hour", you ask "I want the living room to be 72 °F, how many logs per hour should I feed the boiler with?".
If you set up a heat transfer PDE problem, you can add an additional equation and a degree of freedom that specifies the extra condition on the temperature. Let's call it a
For more advanced inverse modeling, like materials selection and regularization, you may need optimization algorithms. More of that will be covered further down the road in this blog.
Comments
Aug 21, 2009 at 8:46am UTC
I expect that your are talking about 72[degF] and not 72[degC], or was it the sauna you are referring to ;)
more seriously: why not also use COMSOL to calculate the torsional constant for your 3D Euler beam profiles (when these become complex, see the example in the Model Exchange),
or to optimise the aceleration profile of triangular scanning motion, with a smoothest possible velocity transition from the up and down motion (by adding the jerck(t) = dacc(t)/dt and applying boundary conditions on the position and the velocity).
Aug 27, 2009 at 7:20am UTC
No, I did not know that COMSOL is able to solve such inverse problem so easily, and it was interesting for me learn this.
I wonder what happens in the example shown in case that the temperature asked for is no longer a reachable aim for the forward model. Does the inverse modeling in this case yield the closest possible answer?
I have a keen interest in solving optimization problems using
COMSOL and there are several issues I am wondering about.
These include
* applying different regularization techniques;
* handling different sets of measurements in the least
objective (using a different fem structure for each
set?);
* solving shape optimization problems (as for
instance the acoustic horn) by doing the
differentiation of the state equations wrt
the design variables on a discrete level.
I wonder whether other readers of this blog share
some of these interest and whether we could use model
problems from literature to test one and other in COMSOL.
Best, Domenico Lahaye.
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