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FEM: How should it be taught?

I am designing a new course on FEM, to be offered privately in India. It will emphasize fundamentals, and try to supply (or bring out) the physical interpretations behind the mathematical formalisms.

More details: It probably will be directed to the working engineer who has already used existing commercial package(s). The initial idea is to split it up over about 6 week-ends, 4 hours per day of the week-end (say Saturday and Sunday each). However, minor details like that may change. I just wanted to give an idea of the length of the course, the time available for class-room interaction, that's all. Please see the attached brochure. (A typo in the test is now corrected in the version 0.7).

Important: Please tell me what I should teach. Depending on who you are, here are the things to consider:

(i) If you have not taken any course on FEM: Please jot down what you would like to learn from such a course.

(ii) If you have taken one (as an UG or a PG student): What is it that you would like to see done better. Please be specific. For instance, rather than saying "it should explain mathematics better," please say: "It would have been better if someone would have explained me...", e.g., "...in what way strain energy, as a concept, is different from the energy of the energy principles," "...what the idea of functional really is all about," "...a simpler or intutitive way to directly realize that the Galerkin technique is equivalent to a variational formulation," etc.

(iii) If you have taught a course on FEM: What topics in this course were the most difficult for your class to understand? Where did you have to repeat yourself just in order to clarify something which should have been obvious to the students but was not?

Finally, you may want to jot down something good that you found in a book or a course or an instructor or a tutorial... Something that is positive about the courses elsewhere. I would appreciate if you note down the specifics of such courses elsewhere too. Please note, I do not want advertisements here. Not even links. What I want are the *specific* aspects that you liked about some course---your take on it. The emphasis is on isolating the good points...

Thanks in advance for your replies.


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And yes, I do seriously mean to offer this course in near future. So, corporate training queries are most welcome, i.e. queries from the companies in India, preferably, from those who are in the Mumbai/Pune region.

However, as of today, I cannot entertain queries coming from isolated individuals. Instead, queries from groups of students (at least 5-6) are what I am looking for.

There are no plans to do a Webinar out of this any time soon.

Another important point: Engineering colleges in Mumbai and Pune (other than COEP and IIT Bombay, that is) may please excuse me from inviting to deliver this course at their institute at the rate of Rs. 75/- to Rs. 125/- per hour for the entire class in all, for typical class sizes of 60 students, and a student population that is overwhelmingly rich or well-to-do, but dumb, and worse: outright unmotivated to learn engineering. (Such colleges should also spare me having to explain to them why I am declining such a good money-making opportunity.)

To close, I would welcome serious queries from established corporates such as Tatas, Mahindras, Bajajs (run by COEP graduates), Firodiyas (at least one run by a COEP graduate), Thermax, Kirloskars, GM, GE, and so on. This list is purely indicative and does not indicate my personal preference of the companies to whom to deliver my course. But yes, inasmuch as these houses spend so much money on pure "corporate image" advertisements, absolutely worthless HR development seminars, women's empowerment, etc., it would seem worth it if at least some of the business houses named here spent at least some money on a superlative, world-class training program on a truly productive theme, and, as a by-product, in the process, helped me make money (read survive) too. I would appreciate if you brought this post to the notice of the appropriate decision makers. (Newspapers, media people, and the better people staffing the government "monitoring" agencies: thanks in advance for doing as much for me.)

Thanks in advance.

Update on April 23, 2008. Now, instead of attachment, there is a link to my personal Web site. So, download the brochure from here.

Comments

Hi Ajit,

Based on my experience, here's what I think what should and should not be included in an introductory FEM course:

1) I feel that the discussion of triangular and tetrahedron elements is not really essential, mainly because, as a user, I tend to avoid them as they add more nodes and elements in a particular problem.  So what I learned before about them was not really being put to use a lot.  In solid mechanics, standard triangular and tetrahedron elements tend to give stiffer solutions and will probably lock for nonlinear problems, so people who eventually end up being users may misuse these elements (very dangerous) due to the incomplete knowledge obtained from a first FEM course.  I would just focus on the quadrilateral element and perhaps add a brief discussion on how the standard quadrilateral would be modified (such as reduced integration with hourglass control) when it comes to nonlinear analysis. Similar comments apply to higher order elements.

2) Treatment of constraints using the penalty method and Lagrange multipliers - I feel that it is really important to understand how contraints are treated in programs. Single and multipoint constraints should be discussed.

3) I think C++ is too demanding for beginners - a language like Matlab is more suitable  and easier to use as the graphics and solvers are already included.  This will streamline the course a little.  I understand that Matlab is not free, but one can download and use the free GNU Octave software which is very similar to Matlab. I use both C++ and Fortran, but there are many times when I just want to focus on the problem at hand, and it is way faster to code something in Matlab or Octave. When I first started learning FEM, I spent too much time debugging code instead of understanding the physics and formulations.

4) Dynamic problems can be included within the context of the 1-d bar linear finite elements.  This simple problem will be sufficient to allow the discussion of standard time integration schemes such as the central difference and Newmark methods.  Such methods will provide the basis for the student to solve other dynamic problems, if they decide to do so.

Other topics can remain as they are. Hope the above points will help.

 

 

Hi Keng-Wit,

Thank you so much for your *thoughtful* reply.  The point numbers below correspond to those of yours, but add far more than just replying your points---in fact, my writing often just takes off in many directions unrelated to your points....

Before we begin, one point in general: The syllabus still is very much in a fluid state. So, I am very much open to revising it. (That's precisely why I put out this posting.)


1. The reason I wanted to work through both triangular (CST) and quadrilateral (4 node) elements in detail was so as to bring out the differences in the behavior of the interpolation functions over different domain geometries. These two provide the simplest example of such a difference. I will also treat this as the starting point for the many diverging angles that start from this point on, such as the higher-order elements, reversibility and nonlinearity as two different notions, etc.

But yes, Keng-Wit, you have a valid point in that when it comes to 3D, I think it would be OK to leave out tetrahedrons and cover only the brick element. This can save some time.

I am not emphasizing the detailed concepts denoting the specific aspects of nonlinearity in this course (be it differential, geometrical, or constitutional in nature). I only plan to introduce the various notions of nonlinearity as contrasts to the linear models. See further below.

I am not convinced about the superiority of p over h. (And, haven't I entered the h-p debate, too!!)

The locking and all are far too detailed and/or advanced ideas. If the student *has* been told, and *is* clear about, the simple fundamentals (like the basic nature, and, more important---though neither companies nor professors emphasize so---the limitations of FEM), he should not want to use only some of the elements/modeling abstractions.

But avoidance of any treatment of the simpler elements out of the fear of misuse would seem to be uncalled for. Talking of more advanced considerations, how about chaotic instability that might seep into a model? Are we going to therefore consider every advanced aspect right in the first course simply because its outcome is potentially dangerous?

I think what you say is a valid engineering concern, but in a fundamentals-based course one has to leave out the consequential things. I will certainly touch upon your point, but rather in the discussion of the limitations (near the end of the course).

Another sub-point: One of the goals I am keeping here is that my student, after he completes the course, won't feel like saying: "But, I am not yet clear as to which element is *really* better!"


2. Yes, you are absolutely right. Though the syllabus (as given in the brochure right now) doesn't say so, I was most certainly going to cover all the main methods dealing incorporating the specified boundary conditions into the algebraic FE model. In fact, I was planning to treat this topic fairly early on in the course. Both the exact and the inexact methods will be touched on.

Another point about BCs that I plan to emphasize is reinforcing the physics-wise important idea that in any BCIV problem (and this includes QM too), the whole game really gets set up only by what happens at the boundaries. The idea that the distant (and potentially vast) domain is just a slave---the real master is the BCs.

Also, thinking of varying the BCs, I am also going to establish some relation with the perturbation techniques, but purely only in the passing. (And, if I remember it when I actually come to teach the course!)

About Lagrange's Multipliers. Hmmm... I am sorry I do not know how to do adequate justice to this topic in my course.... If you have a ready-made set of slides, say less than 10 in number, that together can adequately convey the physics of Lagrange's Multipliers, I would love to use them in my course. Please note, I said *physics*. Otherwise, there is not enough time, and, frankly, is it really needed? From what angle?


3. No, Keng-wit, this course will not require C++. In fact, the course will not carry any programming exercise in any language, be it C++, FORTRAN, Matlab or any other. (Some people have even tried using VBScript and Excel! LOL!! (Sorry, but I just remembered my friends from the programing world here.) I won't.)

What the course will instead do is to *use* certain custom-written Windows .exe programs. I mean the binaries.

For instance, I plan to write and use a pedagogical piece of software that will help the student visualize the interpolations within the region of a finite element. The student will be able to take a 2D element (say a quad), and inspect the surface of the interpolated solution. He will be able to rotate this surface in 3D and look at it from various angles. The student will be able to select different kinds of interpolating functions (linear, quadratic, cubic, others, perhaps even sinusoidals!), and see what kind of field patterns thereby emerge and what values the method of FE ends up assigning to the various points within the element region. So on and so forth.

Now, it is these special-purpose pedagogical programs which are being written in C++ and OpenGL. This is what I meant when I mentioned C++. So, the student himself won't have to know C++ (or any other programming langauage), though it would help. He will only use these programs.

Basically, it all will also depend on what kind of audience there is. Perhaps, the audience could be a highly paid team of very young software engineers who have been given a project of writing solvers, but don't know how to make the head or tail of it.

Here, if I may add (and it is this which is going to be very looooong)....

Though Pune/Bangalore/Indian CAE software development companies (and their masters sitting in the USA) do not wish to hire me (citing any number of weird reasons, the most prominent being my age, the other being non-experience in the CAE field) they do occasionally want to have someone readily available to talk to their handsomely paid young employees, about writing FEM and CAE solvers.

You see, these Indian IT folks are extremely good in using their "political" connections abroad to *get* the software development contracts from those American/British/other companies into India. Often times, such foreign companies themselves are headed by BAs, not engineers. (For example, see the board of PTC---the owners of the "Pro/Engineer" brand.) Ever since a weird set of self-congratulating notions about "management" got generated at Harvard and Stanford and Sloan and Chicago and so on during the period after the WW II, engineers and inventors have all but become untouchables in the higher echelons of business houses. The recent "techie" boom--and bust--in silicon valley was only an exception.) One way or the other, even though these Indian IT companies or the Indian offices of MNCs don't always have very competent engineers on their teams, they have no difficulty in getting projects outsourced to India. (May be bribing is involved, who knows? I, for one, certainly, *don't*---but I do have intelligence, and can certainly take a guess.)

Once the project lands in India, these Indian companies find, all of a sudden, that their young (certainly) and "talented" (doubtfully) engineers don't know how to talk with all of their project colleagues abroad (some of who *are* competent), on the domain technology involved in that particular s/w dev. project.

Now, as per the currently fashionable paradigm of management (in India and more importantly, in the USA), the way these "smart" (actually myopic) Indian managers (and their American masters) figure the situation out is the following: "Why, we went from IT to ITES (IT-enabled-services), from software development to BPO (i.e. call centers), and all that transition was a tremendous business success. [Raise a toast now, will you?] Why, some of us made such a successful transition from jewellery exports to software exports too. [Claps, claps, claps, the Harvard Business School style.] Now, from our success of BPO, we might just as easily go over to engineering software services too. So, if our talented engineers don't get it right, it must be just a language training issue---how to speak the customer's language right, to serve him, to delight him. That's what Steve [Ballmer, of Microsoft] was saying too."

And, I might add, this is what any BA/BCom type would---whether he had engineering degree beforehand or not.

In other words, these guys (starting from the captains of the Indian IT industry) do not want knowledgeable people. What they want is the people who can *talk* as if they were knowledgeable.

But, since these Indian guys do not hire anyone unless the project has already been approved and funds released by their American masters, they have no local "talent-pool" readily available with them when the project does arrive. (If they don't hire people like me, how can they? But none raises such a question because it is presumed that a person like me would feel shame in raising such a question. And, in a sense, they are right, too. I also took a cumulative 7 years of unemployment and 4 years of trying honestly for a job in the CAE software field before I finally lost my sense of shame, or the care for future consequences in my career, and began talking against these Indian managers and their American masters. The fault, I believe is shared by both Indian IT Managers and their American masters---after all, it is the American masters who do exercise control down to the level of selecting every individual on every project team. And, Americans are notoriously short-sighted about their operations abroad.)

Anyway, to continue the story, once these Indian managers get the project, it is then that they want someone to be available locally in India, to introduce topics like FEM or writing CAE solvers, to their decidedly young employees.

Now who are these young employees anyways? Often times, they are incompetent in any *serious* sense (be it engineering or any other domain), but they are rather smart, glib talkers. Often, they have been selected by the politically correct bunch of MBAs (who get paid in crores of annual salary right out of their MBA school). That means, these engineers are politically correct and convenient. For example, women engineers, with computer science or electronics or IT specializations in their degrees.

The idea then is that the FEM course should be such that these handsomely earning and definitely *young* Indian engineers from Pune/Bangalore/etc. should get, say, an "Idiot's guide" worth of FEM in their heads fast. Rather, more importantly, they should get FEM terminology fast on their lips---remeber, it's a language and speech-accent issue.

If you think the above is a caricature, unfortunately, you are dead wrong. I speak from experience. In the last one year, I have been asked twice (without my trying in any sense anywhere) if I could impart *this* kind of a training in FEM, to a large software development company operating in the field of CAD/CAD/CAE, a company headed by a Harvard MBA. (Both of them---the company and the man---I cannot respect, and none could while also staying within reason.) Apart from these queries received by me first-hand, I also know of two other M Tech CAE consultants who *have* actually provided that kind of a training in Pune over the last couple of years. Teaching FEM to CS graduates, within 2 weeks (!!)

Now, if the audience is of this kind, they would know C++ fairly well, wouldn't they?

Well, the words "fairly well" are qualified too. I mean if you are young and if you have been paid handsomely to do nothing but keep compiling some or the programs for 4 years after your graduation, you are bound to pick up at least some things about programming. No surprises there. After all, it is hard to find the "perfect" dumb too. ... So, that's the level of "goodness" they often operate at. Not always, but quite often. I mean, if they are good in C++, you cannot therefore presume that they would be good in multi-threading too. (That's right. I reached this conclusion after I ran into a relatively young and highy assuming engineer guy with some 8 years' experience. His reputation about his talent had rested on the solid grounds of his ability to very confidently pronounce the words: "I am good in multi-threading." He was very well paid at an American MNC, and was supposed to be a very typical case of what "talent" really means, I was firmly told by our V/P back then.)

But yes, sometimes, they do know C++ enough to want to have some programming too included in an FEM course.

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I do know sometimes I do sound bitter or impolite, but I can't help it. I am honest. Honest enough that I reacted to those hypocritical (i.e. Indian) companies asking me to conduct the required kind of FEM course in such a way that they did not pursue the "training FEM in 2 weeks" matter with me again.

I hope that I can stay honest and still make money. Some money, preferably, large amounts of money. Hope doesn't leave one until one is dead. That's why I pushed myself to create this course.

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Coming back once again more to this course itself (and less to the socio-economic context and the specific circumstances despite which it is being created):

In this course, there indeed is one session on writing a toy solver C++, but it is purely optional.

It does not form the main emphasis of this course. Leaving aside all considerations, even if the audience were to be competent and knowledgeable of C++, I still would want the emphasis of this course to remain on physics and not on programming. Just the way, the emphasis is not on mathematics.

Incidentally, this emphasis and attention to physical principles is what, in my eyes, would make the course superlative, compared to any other course anywhere in the world.


4. About dynamic problems. I will try to see if I can do something on this count. But frankly, there are far too many considerations, even the basic ones like implicit and explicit formulations, errors, energy leakages (if the time variable comes in only through the finite differencing even if the space part is through FEM), stability, etc. Giving a physically based explanation of all such factors will take far too much of time. Therefore, it seems better to keep them all aside for a later, more advanced course.... I don't know. I am just loud thinking... I might change the course content dynamically if there is enough audience interest.

But at least, for an 18 session course (2 hour/session), there seems to be no room left for giving even an introduction to dynamic FEM.

Ditto, for many other issues like: eigenvalue problems in detail, FEM of electromagnetic fields, FEM of coupled differential equations, nonlinear FEM, large deformation FEM, FEM treatment of shocks and their propagation, meshless FEM, particles-based FEM, etc.

Now, all of these are likely candidates for special purpose course(s), probably costlier course(s).

But I don't think there is market for this all in Pune/Mumbai/India, as of today. At least, not for someone like me. It may exist for a *BTech* graduate of an IIT (or for an IIT professor)---i.e. to an Indian government-certified "genius". But I don't think that such a "market" exists in India for someone like me---a non-BTech-IITian. Not at least as of today. The Indian concept of casteism ("eliticism" being just a euphemism) percolates to every realm, and do not permit me to even think of creating such a market here unless an IIT is already doing something in it and its BTech graduates can be already snooty about it. And neither does the American companies' "not invented here" attitude (who are practically the only ones outside the influence of the BTech IITians).


But then, come to think of it, why should I always be the first to supply the physics to the mathematical messes created by others? Why shouldn't people who have been doing all that advanced mathematics in/for FEM also pick up the tab of supplying the physics of whatever they have been doing, when they come down to writing their books, or designing their courses, or when they pick up their assorted technical society medals and honors? Really speaking, at least half of them stand to really get exposed, and the fear of this might be the actual reason why they don't make that kind of an attempt. Medals and honors are far more comfortable---aren't they? And mathematics, so much the safer heaven to keep protecting them---isn't that the usual feeling?


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Anyway, Keng-Wit, all in all, I really appreciated your thoughts.... Easy to see that they were written with a serious, genuine concern. Actually, on second thoughts, I might just as well include an introduction to the FEM of dynamic problems, as you say.

I could actually make the course 24 sessions long (rather than today's 18), and, if so, I could include some material on dynamic problems too... To give them a taste of the time dimension is a *fundamentally* good idea... Let's see if I can think of a nice way to simplify its discussion in my proposed teaching.

Please feel free to add other suggestions too---and even correct me if I am going wrong. FEM is one field where it is easy to grow overconfident... And, one likes to be kept honest (read corrected) too.


----- A general note

These days, it is difficult for me to find money to even use a cybercafe, and neither of my dial-up services in India---Tata Indicom or Nokia---gives me bandwidth above 2 to 5 kbps. (That's right. Two to Five kilo-bits per second, in place of the advertised 57 and 43 kbps, respectively. That's the bandwidth I get.)

Also, I have to do an inordinate amount of jumping around of topics depending on where the next job opportunity might come from. This, among other things, takes time off me.

So, all fellow mechanicians here, excuse me if I do not always respond on time. And, thanks for reading some of the things I vented out in this thread. It is true.

 

Dear Moderators/Managers of iMechanica, 

What I can see in the immediately above posting (my own, dated 16th March, 2008) is a version of my post that does not show a certain change made to it by me.

In particular, the passage containing the accusation that I have heard most frequently in the Pune city (and it must be coming out of keeping the Brahministical standards of judgment is what I believe) have disappeared completely from the post here. For instance, I do remember having written a paragraph containing the quote "I have heard that you get too angry," and the entire paragraph has disappeared.

Today, I wanted to clarify that the phrase "Brahministical standards" that I used in that passage was a correct description of the standards of judgment employed in the professional matters in the Pune city, and overwhelmingly often in the other Indian cities too. But I also wanted to further add that such a standard was nothing but a mystical standard.

Thus, I did wish to keep highlighting that the irrational standard often employed in judging my characters in the Pune city (or by many IITians) is one of Brahministic variety among the all possible mystical standards. Yet, today, I also wanted to add that the Brahministic is not the only variant of mystic standard possible. (BTW, I had also noted to the effect that the standard could be practised by anyone.)

I wrote about the Brahministical standard because it is this using which I have been made to suffer most---that's all. And, frankly, I was not too far off the mark, inasmuch as "Boston Brahmins" is a well-known phrase too. (My writing also had this word.) Once we have more Buddhists in more positions of power in India, people will begin suffering more at the hands of the Buddist mystical standards of judgment too.

Yet, the issue is the specifics---so far, Brahministical mystics are in an overwhelming majority as compared to Buddhist, Islamic, and others, in IT industry and engineering and CAE industry, in Pune, India, as per my personal experience.  

Of course, I did hint at the idea that I mean everything in a broad sense.

Of course, the whole passage seems to have been annihilated by someone.

Two items of action, now:

(i) If the moderators/managers *have* a copy of all the intermediate changes I made here, could they please let me know about so, immediately. It's OK if they wish to discuss this in private (though I also wish to have it highlighted here that they have not always responded to my private emails.) What I would presently like is to have that intermediate version sent to me by email.

(ii) If the moderators/managers do not have it (the intermediate version), could one of them please clarify (publicly or privately) if this has been a deliberate change made by one of them, and if so, why. Or, was it an accident---at their hands, or out of some "fault" of the updating process, or, as a slim chance, a change made by me, on my own, while hurried revising the last post. (I don't think so, but when changes are made that fast, none can be too sure.) Or, as an even slimmer chance, was it a change made by a hacker?

The nature of their reply will help me decide whether I should continue writing here or not. If the likes of "Amit.Ranade" (who I had mentioned in the subversion that has now disapparead) is what these iMechanica founders, moderators, and managers like better to protect, then I cannot also be in it.

If I go out, I would like to reciprocate in kind: I would want *every* posting of mine to be deleted to a "tabula rasa" state, without exception---i.e. including the one about stress and strain. Please remember, despite what I write in my resume (or the "about" descriptions in my blogs elswhere), in my mind, my reputation does not fundamentally rest on the iMechanica or Harvard brand-names. It does so, on my work---i.e. my specific achievements.

Let me have the thoughts. The aspect of unwarranted changes (whether by "fault" of the software or otherwise) is non-negotiable, in principle. And, I mean it.

Sincerely,

Ajit R. Jadhav
Pune, India
19th March, 2008
PS: If anyone considering any of my job application(s) wishes to take this as a proof of my unsuitability for "team-work", he is advised to please take it and run amock with it as fast as possible---I couldn't care less about such evaluators. 

 

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