I am interested in the adjoint method for shape optimization problems. However, I couldn't find a helpful introduction. So I come here and look forward to some enlightening advices.

Could you direct me to any textbooks, published papers or free online source course materials.

And to clearify several things: I am familiar with FEM, matrix computation, calculus of variation, etc.; I only want to learn the adjoint method for shape optimization in solid mechanics, specifically on continuous level.

Though the question does not perfectly fit this website, but it seems to be the best choice for a shot amongst stack-websites.



There is a nice chapter on adjoint based optimization in the book "The finite element method for engineers" by Kenneth Huebner. Unlike many other (mostly unhelpful) references that focus purely on theory, it shows the implementation (examples with all math worked out) but only for static solid mechanics problems.

For quasi-static problems I have no idea (maybe others here can provide pointers).

For dynamic (wave propagation) problems try the paper here.

  • $\begingroup$ Hi stali, I just came back from library. The book has been checked. Unfortunately the adjoint method is on discrete level, what I am looking for is the explanation on continuous level. Still, thanks for your reply. Do you have any suggestions in the mentioned direction? $\endgroup$ – newbie Mar 15 '12 at 16:23
  • $\begingroup$ No unfortunately not. $\endgroup$ – stali Mar 17 '12 at 14:28

A short explanation of the underlying principle is given in slides 12 and 13 of my lecture http://www.mat.univie.ac.at/~neum/ms/slopeslides.pdf (It is in terms of an ODE and slopes, but the PDE case is easy to derive once the principle is understood, and the usual derivative case is obtained by specializing the slope to two equal arguments.)


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