Serguei Nazarov - The Big Fish

Prof. Nazarov was invited to Erlangen 2 weeks before. Within my project topology optimization is also done via topology gradients, mathematical hard core where pure mathematicians meet the applied ones. I'm an engineer, I do SIMP and it is hard for me to understand what the mathematicians do (I want to start another try for a functinal analysis book the next weeks).

Anyway I was asked to give a short talk and present the piezoelectric-mechanical-acoustic coupled PDE from an practical engineering point of view (application, meshing, boundary conditions, ...). The talk was to be given for Prof. Nazarov, I never heard of. So I googled and it was interesting what I found.

First the image from his website in Russia


He is an expert on asymtotical extensios. On His page are links to his 13 books!! and 366 papers!! There is really nothing to add beside that he is a nice and funny guy. :)

SIMP Introduction

From time to time I give a introductory talk about the SIMP method. I only cover linear elasticity as the results can be more easy understand as my piezoelectricity stuff. This is an update of the older version.

This time we made a movie of my talk (45 minutes).

Here are the slides (1.3 MB)

Here is the divx movie (460 MB !!)

Topology Optimization Using the SIMP Method

View SlideShare presentation or Upload your own.

This is the second time I record a talk of mine. The first time I used the internal mic of the cam and as such one could not hear me but the audience. This time I used a wireless mic. We did not adjust the sound but for a first try ... on can at least understand me. The next time we shall give more attention on zooming and light conditions.

P.S.: Do you know where I could put the video online? Youtube has a 10min limit.

The 'smartest' people in the world

One thing that is cool about doing a PhD (there are also uncool things - I just dont't have the money for the next (used) car, the current one is badly old :( ) is getting into contact to professors and such guys.

Albeit comming from a familiy where education has been well treasured, I am the first with a university degree. I remember when I was about 15 when I met the first students as my boy scout leaders. One of them, a guy doing his PhD in optics, explained me what a 'professor' is. His definition was "no one on earth knows more about a subject than him". Impressing! ... and it never matched reality when I did my diploma at an 'Fachhochschule' (university of applied science) - albeit I learned much!

Once my later PhD adviser told me "that you never know what a chair is when U don't do a PhD at a chair". I replayed "well I learn when doing my diploma thesis" and he replayed "no, you don't". He was right.

I believe, that a typical PhD (like me!) is just a normal person. Just as almost any other graduate student - having become a PhD student (more or less) just by random. But one truly meets some other guys, extraordinary intelligent people - what holds for probably most professors ...

I wouldn't want to miss coming into contact to such people and I'm happy to have such an opportunity. But the really interesting this is (and therefore I put that 'smart' in the headline into quotation marks) that these people are definetely highly
intelligent but beside that just normal people - having similar troubles and luck as all 'normal' people have.

Conference Season is over

Whew! That really was a tough time!

After preparing and giving three talks I had quite some pressure to produce results for the upcomming conference season. So no relaxing semester break but using this time where most students, bosses and colleagues are on holiday for concentrated working.

The good thing (in retrospect) was that I again had to write a paper. The first event was the OIPE, the 10th Workshop on Optimization and Inverse Problems in Electromagnetism from 14. to 17. September 2008 in Ilmenau. My submitted two page digest was my first peer reviewed work and it is published in the proceedings. I gave a poster presentation and it was a interesting event - that brought me also further in my subject. It's always good to see that also the others cook only with water:) The OIPE offered the possibility to submit a paper for review and publication in a journal. This gave the pressure but on the other hand was writing down the stuff essential to understand what my results actually mean (again).

The next step was the annual meeting of the research program where my project is a part of. We met in Kloster Banz, a huge former monastry known where politicians meet in conclave. It's one of the places I would not have visited otherwise and it was pretty cool to stroll around this place at night. A highlight was the guitar performance of two mathematicians with funny and ironic lyrics about beeing a mathematician. :)

And after that there was the Fourth International Workshop Direct and Inverse Problems in Piezoelectricity in a impressive castle (Pommersfelden). Here is the talk.



With the first PhD year beeing a starting year, scientific workshops where too early. Now I feel like becomming part of the "community" (also I still have no active contact to other groups doing SIMP optimization). With the good time one has at these conferences it's kind of sad that suddenly it's towards the end of the PhD time.

I have really cool results (with pretty cool 3D images with colors, transparency and all this stuff). I shall blog about this soon.

Fastest Topology Optimization on Mac ever?

This is the summer of work! After finishing the work on my paper, and a couple of presentations I gave (see the last two postings), I was looking forward to this summer.

Personally to spend time with my (almost two years old) doughter in the garden but also to actually code and test ideas before the writing time starts again. I four weeks I need a paper and a poster, then two presentations for the two following weekends. In November there are two important reports ... So concentrate on actually working now :)

The two chairs I'm working are almost deserted - a productive working atmosphere. Even the student working on his diploma thesis about topology optimization of an energy harvester (I "share" him with a colleague) is on holiday.

But now to the subject: One of my collaegues, Simon, is currently porting our finite element software to his MacBook. He's absolutely the right guy for this job - a really skilled hacker - and it took him just about two days. That's really respectably considering the complexity of our C++ monster with all the external libraries!

Well, as we all work on the same piece of code in the end (thanks a lot to the subversion team!), there is now a finite element code existing (unequals available!) on the Mac that shall be difficult to match (at least on OS-X). And this might be even more true for topology optimization (and all the other specialities my collegues are working on). :)

That doesn't really help anyone, is by no means an academic progress - but on the other hand this might be only possible in an academic environment. And the flying spaghetti monster alone might know which potentials this will have in the future. Simon's previous work to port our code to different plattforms released us from our Makefile hell and brought us a clean cmake based structure. As a result we can have debug-code and (ten times faster) release code concurrently and can now compile the whole code monster within 2 minutes (icecream cluster compilations thanks to Simon) instead of 20+ minutes.

While I'm often frustrated that I code my optimization algorithms not based on a clone of Ole Sigmuns's 99-line MATLAB code but in our FEM code where I sometimes need a week instead of an hour - then this are the things that make me prefer the C++ version, to code together with colleagues! (And I started recently to do more coding in Octave (a GNU MATLAB clone) anyway)

Two presentations I gave

In the last two weeks I gave 4 presentations. I'm happy it's over and I can concentrate on my work again. But I want to share them here.

From the first one (I gave in three variants) I cut my resent results. Such it is a more or less general introduction into the SIMP method. My piezoelectric stuff plays only a minor role. Actually it shall help people to understand about the ease and efficency of SIMP. The target audience are engineers with some FEM knowledge or mathematicians with no knowledge in optimization. For optimization experts it's too low level.

The presentation is not "self contained" but rather a keyword prompter for me. So don't expect to understand the issue only by the presentation.

SIMP presentation

The other talk was given for scholars. It was within the symposium Applied Mathematics in Science and Industry at "Students Day". So it is PDE within a page, FEM within a page, ... and almost no formula. It is in german and I should have added an animation.

Schuelervortrag

Meanwhile I'm really a fan of doing presentations with latex and the beamer stile. Maybe I write about my steps of generating nice pdf images from gnuplot another time.

First paper submitted

Finally my first paper is submitted! :)

I want to thank my co-authors (there are a lot of them) a lot for their help and patience (there are a lot of them). There is a preprint available:

Topology Optimization of Piezoelectric Layers Using the SIMP Method

To be honest, I'm not sure how to judge this paper. It contains no breathtaking new method but a detailed mathematical description of the model (thanks to both of the Kaltenbachers). I like the idea to follow the adjoint method approach in the weak formulation to answer the question of the boundary conditions for the adjoint equation. Clearly there might be other approaches but in the papers I read no word is spent about that issue.

From an engineering point of view, I think the result is quite interesting. It suggests practical designs for real world applications. And indeed, optimization helps to understand our models/ devices better. At least my colleagues who are really deep into the piezoelectric bussiness are interested. :)

This work took us about four month! Without it, I might be much further in the dynamic optimization - but on the other side writing your stuff down really helps. I found an important bug and it clarified some issues (e.g. excitation only via voltage =inhomogeneous Dirichlet boundary condition) instead of electric charges or other stuff.

And while most papers (especially the dutch ones) are really impressive - some others actually tell a lot of nonsense. Compared to them mine might really be worth to be published. :)

I cover only the static case in the paper. Since a couple of weeks I do harmonic optimization. In september I'll be at the OIPE 2008 in Ilmenau (the father of MP3 is a prof there). I have to write a paper and hopefully I have some interesting new (dynamic) results then.

Posters

Well, from the content of the blog I do nothing more than mechanical optimization as done with the 99-lines code of Sigumnd (with the minor extensions to the force inverter). In fact, I wait for the paper, I'm currently writing, to be submitted before posting about piezoelectric optimization stuff.

Well, there recently was kind of a publication I can blog: I participated at the poster exhibition at ASIM08. Concurrently I had to prepare a poster for one of my employing chairs: AM3. So I also present the draft here. In both cases the credits for the layout don't belong to me and the posters contain a contribution of my project partner Fabian Schury.



The first poster was created using CorelDraw - and as much as I hate pixel pushing and using texpoint to import tex-formulas, the much faster Latex version simply looks far less fancy.

Force Inverter

Well, I didn't blog for quite some time due to some reasons:

• lack of time


• I don't think one reads actually what I write :(


• I wanted to show pictures next :)

I did the force inverter, which is a optimization for selected
solution variables (e.g. max where l=(0 0 0 0 1 0 0)^T
(I call the objective "output") already in Denmark the last
summer in Matlab and shortly later in C++ in our own academic
FEM solver.

This requires the solution of the adjoint pde, technically
one only solves for another right hand side (l).

To optimize for the solution variable is a really interesting
objective, but the
optimization becomes quite challenging (in mechanics):

• IPOPT can't do it (at least the simple example I show)


• With SCPIP I had quite some problems but finally I found out
  with the help of SCPIP's author, Christian Zillober, that
  it was my fault. I compiled SCPIP with -O2 (g77) what was fine for
  compliance but led to wrong results here.


• As mentioned in the book by Bendsoe and Sigmund, one can adopt the optimality condition
  method. It is not that easy but works ok in an ugly way
  (implementation and performance) but doing it nicer cost me
  already too much time w/o good results. In the end I much prefer
  SCPIP

So finally: Here is the force inverter, the standard example we
did in Denmark within a very nice lecture by Ole Sigmund: We press
on the left and want the point on the right to move against the
input force direction. There is a small spring added the the output
node for regularization.




And the movie