COMSOL Forums: A simple question...

Re: A simple question...

Tue, 27 Apr 2010 10:03:12 +0000

Hi
then catch Duncan, and Niklas if he is there, and discuss it thoroughfully
Ivar

Re: A simple question...

Tue, 27 Apr 2010 05:47:30 +0000

...
I can only say: pls take it up with the local Comsol people when they passes by, (and I see that is for tomorrow and thursday for the real north of the US ;)
...

Yes, the regional (Palo Alto for Alaska) Comsol rep is conducting a workshop here on campus tomorrow. There are quite a large number of people (>25) who have signed up for it, not bad for such an out of the way place, eh? VERY excited about this!

Re: A simple question...

Mon, 26 Apr 2010 16:15:45 +0000

Dear all

I can only say: pls take it up with the local Comsol people when they passes by, (and I see that is for tomorrow and thursday for the real north of the US ;)
I have noticed that Comsol is still a "small" company with reactive people, so long we explain to them what we need and that we are clearly understood. On the other side they must balance the number of request versus their total user group, so the more we are with constructive suggestions if possible similar, the more we will get back ;

So pls play the game ...

Have fun Comsoling
Ivar

Re: A simple question...

Mon, 26 Apr 2010 14:05:26 +0000

Dear Antti,

Many thanks for the tip! If fact, I do have an earlier set of FEMLAB 2.x manuals. One of the complaints I, too, have had is that the new version of Comsol does not ship with a hard copy of the Reference Manual. Also, their Help function needs to be updated with something better than just a set of pdf or html files. Something along the lines of the Matlab Help function would be great.

Beyond these, there is also a need for a set of structured tutorials that focus on elementary concepts. They don't necessarily have to correspond to any particular "real world" example, but instead focus on a single concept at a time. The Model files included with the software are great and work spectacularly as advertised, but many of them are too complicated to be of much use when trying to learn how things work. There are too many things going on at once - change a parameter setting and nothing works any more, and we're left without a clue as to why. It's a matter of pedagogy. Start simple, and then work up from there.

Another thing that is desirable is better error reporting, with error messages that give some indication about where the source of the error might be in the model, and reporting something more widely understandable than the somewhat cryptic traceback strings.

Thanks,
Dave

Re: A simple question...

Mon, 26 Apr 2010 07:38:24 +0000

Hi all,

Just a short note (I'm really sorry, I didn't read through the whole thread)...

Thanks Ivar for your comment. What I haven't been able to find anywhere
is a good tutorial discussion with diagrams that show PRECISELY the relationship
between such things as, but not limited to, normal vectors and the underlying cells,
and diagrams to supplement the words on the definitions of "up" and "down", etc.

...but I from time to time return back to the documents (Reference Manual) of early FEMLAB versions, even 2.x, which, in my opinion, have nice and detailed documents, even examples, of how the "matrices fly" inside the COMS... I mean... the old computation engine. Of course, these are officially obsolete, but at least they've helped me get some picture of a few rather detailed problems I've sometimes wondered about COMSOL. Naturally all specifics aren't covered as features have expanded and naturally caution must be taken... but it helps you get a picture, is what I'm saying.

If you can get your hands on some, I recommend you to have a look. Imo, it's a shame the newer versions of COMSOL don't have such "Reference Manuals".

Thanks,
Antti

Re: A simple question...

Mon, 29 Mar 2010 10:47:42 +0000

Hi Ivar,

Thanks for the tip. I haven't used the private message, but will keep
your advice in mind.

I've been busy with the simple question, and have learned a lot by
just setting up small examples. A couple things of possible interest
to others.

1. The free space solution to the 2-D Poisson's equation using
coupling variables seems to hold up (I had to iron out some sign
questions, but otherwise it works.) I assume this technique, which
uses the Green's function, is commonly known.

2. Getting the definition of the unit normal vector on boundaries
required just experimenting. The rule is, the unit normal vector is outward
away from a domain on the boundaries, as you indicated previously.
But it's different for an internal boundary INSIDE a domain. Here,
it depends on the direction of the arc or line segment. Basically,
each line segment, whether it is of a simple line or as part of a
2-D shape such as a square or circle, is drawn from, say, A to B.
"Up" is defined to be toward the left side of this segment, and
"down" toward the other side. This means that a circle, say,
has half of its unit vectors along its boundaries pointing outward
and half inward. You can see all this in action by turning on the
boundary vector display in post processing mode. It is apparently
this behavior that necessitates some of the complexities in coding
weak terms involving boundaries, especially the domain ultra weak
(bd.weak) terms. Understanding these has helped resolve some
of the mysteries of the coding of the upwinding scheme.

Let me pose another question. Instead of using the integration
coupling variables to solve the free space Poisson's problem,
is it possible to solve it by requiring the gradient along the boundary
be the same as in the next immediate inward group of cells, which
would be accesses using he up() or down() functions?

Re: A simple question...

Sun, 28 Mar 2010 06:43:19 +0000

Hi Dave

A note for everyone here: pls do not abuse with "private messages" as us others cannot follow.

And have you noticed, that your "simple question" has rapidly become the longest thread on the forum !

As I have always been told, there is no simple question, and the simpler the more replies ;)

Have a nice day
Ivar

Re: A simple question...

Fri, 26 Mar 2010 08:34:34 +0000

{Note to self: pause before posting...)

It SHOULD read "...behavior for |grad(u)|..."

My apologies for the confusion.

(Addendum - now testing the edit function...Thanks Sven.)

Re: A simple question...

Fri, 26 Mar 2010 08:25:11 +0000

Correction to the above post:

"..the asymptotic solution should have behavior for |abs(u)|
(the electric field magnitude) that goes as 1/r..."

should read

"...the asymptotic solution should have behavior for |ux|
(the electric field magnitude) that goes as 1/r as measured
radially away from the point source..."

Re: A simple question...

Fri, 26 Mar 2010 07:58:16 +0000

The above model for the free space solution to the 2-D Poisson
equation needs to be checked. Although the solution has the
correct azimuthal symmetry about the point source, the actual
boundary values don't match the adjacent domain values. Also,
the asymptotic solution should have behavior for |abs(u)|
(the electric field magnitude) that goes as 1/r, which it does
not appear to have. Any help from anyone to explain this
would be greatly appreciated.

Thanks,
Dave

Re: A simple question...

Fri, 26 Mar 2010 04:24:04 +0000

About the free space solution of Poisson's equation in 2-D:

I found an elegant solution that uses integration coupling variables
and does not require auxiliary surfaces.

The basic idea is to use coupling variables to map the solution to
the boundaries, using the Green's function kernel and the dest()
operator, and then use these to specify the Dirichlet
BC. The specific form of the integration coupling expression is:
rho*log(sqrt((x-dest(x))^2 + (y-dest(y))^2))/2/pi, which
is the kernal of the Green's function. The 2Pi factor is very
important. These are mapped to each of the surfaces in the
geometry.

Attached is a model created in 3.5a showing the solution for
a point source inside a square, with a number of holes inside
the domain and a notch out of the corner. The equipotential
contours are circular about the source, as they should be.

The "point" source here is actually a very small square, so the
integration is domain-to-boundary, and this is how it would be
used in an actual application with distributed charge. But an
illustrative example could also be set up using an actual point,
for which the coupling would be point-to-boundary integration,
instead of a domain-to-boundary as has been done here.

The basic idea should be extendable to 3-D, with appropriate
modification of the Green's function kernel.

Re: A simple question...

Tue, 23 Mar 2010 06:54:42 +0000

I agree 100% with you Ivar.
As for the weak term I have recently spent a significant amount of [ unbilled :-)] hours testing various example in 1d so if you have something written and want a fresh eye feel free to throw it at me. I have the same mindset as you in finding valuable for myself to look at other people problems..

and I now I will come back soon with question of my own :-)

JF

Re: A simple question...

Tue, 23 Mar 2010 05:54:55 +0000

Hi Davis

I would say again thanks for the question, there are no "simple/trivial" questions, I learned also a lot with this one.

I'm now still fighting how to present simply the LM's and different weak terms contributions on a simple 1D second order diff-equation (thermal Fourier law is a good starting point to have the physicsal link), one should alws start simple, but who hase time ?
I notice that we use so many implicit assumptions on functi, mostly we forget them too, and different ones if we are thinking math or physics.

By the way I have seen that COMSOL is changing the way to access the Langrange multipliers in V4, I understand they are not removing any functionality, just trying to improve the logic. I was very sceptical going to the conference last fall, but once haing been explained the new approach/methodology, I ended up finding it much clearer, even if it demanded me to turn somewhat up sidedown what I had learned myself so far.

Have nice day
Ivar

Re: A simple question...

Tue, 23 Mar 2010 03:38:40 +0000

Thanks very much Sven. You and Ivar and Jean have given me enough to keep me busy for a while. I appreciate very much your patiently responding to questions that must no doubt seem trivial to you, but they were very helpful to getting me pointed in the right direction. Thanks again. Dave

Re: A simple question...

Tue, 23 Mar 2010 03:36:37 +0000

Hi

As a quick reply, I would say that working on the interiour boundaries is exactly what the "assembly" mode is for, the only thing is that by default COMSOL puts no assumptions on the continuity between the adjacent faces so its up to you to set the correct physics and equations.
This is OK so long there are a few of them, getting tedious if you have dozens or far more, but by using cleaverly the combine geometry you can draw complex geometries, and have only a few common "assembly" boundaries, while you remain with many "continuous" by default interiour boundaries in your construction, where this is OK.

Thaks for coming with this example, it has allowed me to learn a couple of things, that really is only showing up when you start really simple (that is why I like the forum, by decomposing the issues of the other to very simple cases you learn quite a lot yourself, that is also why I'm "hooked" on the forum). I notice for my own problems, at work, I have no time and (want to) go directly to the results, sometimes cutting too quickly through the bushes ;)

Have fun with COMSOL, I'm really enjoying doing physics again

Ivar

Thanks Ivar. I'm learning a lot, but can now see that I need to spend some more time with the documentation. I hadn't considered the assembly modes. Thanks again.

Re: A simple question...

Mon, 22 Mar 2010 12:38:49 +0000

Hi,

Free space problems are very common to COMSOL users (especially in electromagnetics, heat transfer hydrology, to name just a few). We have implemented powerful tools to cope witch such situtations efficiently:

1) Infinite elements: If you have for instant a 2D Poisson eq. on a circle of radius R you would add an ring outside of R. The inifinte elements map the region between [R, R+dR] to [R, infinity]. The resulting solutions are highly accurate as you can check with samples.
http://www.comsol.com/showroom/documentation/model/1412/

2) Reduced potential formulation: The fundamental solution of a poissons equation is well known, i.e. we know the analytical solution V(k) in a homogeneous space say of conductivity k. Now, if we want to know the solution for an inhomogeneous space with conductivity k+dk only the inhomogeneities will contribute. The equation can be solved for the disturbance only. For the distrubed potential we can conventionally assume that it is zero at infinity (Dirichlet conditions) but can also set more exotic ones.
http://www.comsol.com/shared/downloads/products/new_feature_highlights.pdf

Both concepts are provided (including tutorials) in the COMSOL ACDC Module and 1) is provided also in the Heat Transfer Module and the Earth Science Module. Although you might try to re-implement such tools starting from the equation base modes, most people interested in efficiently solvoing their problem will propbably not do so.

To answer the general question:

"Is it possible to programatically create and destroy boundaries that may be embedded at arbitrary locations in the computational domain, and which could then be pressed into service to solve problems."

Yes - you have reading and e.g. integrating access on internal boundaries. Furthermore you can also acrivate internal boundaries to have different settings than the typical continuity. Moreover - as Ivar has pointed out - you can also use the assembly concept to set non-classical discontinuous boundary conditions.
However - to solve the above problem of infinite domains, all this is not necessary. I highly recommend 1) and 2).

Sven

Re: A simple question...

Mon, 22 Mar 2010 07:48:55 +0000

Re: A simple question...

Sun, 21 Mar 2010 10:23:04 +0000

Hi again

I had a discussion here with our local COMSOL specialist Sven (and head of the local COMSOL office), he pointed out that if we read carefully the modelling.pdf page 247 and on (v3.5a) the BVP the way it is defined in COMSOL, which is a widely accepted way, require that the external boudaries = dOmega to be define.

It is mathematiacally proved that in this way we have then an unique solution inside, while if we take and only define the internal boundaries, in all generality (and not restricting us to 1D), the solution might not be unique.

In 2D the issue is perhaps more evident, as the flux is defined only projected on the perpendicular vector "n" that means that one dimension is still free and we are not defining enough DoF's.

Now, what I have discovered with this is that by default when I define fluxes on interiour boundaries they have no direct effect (they only scale the Langrange multiplers, if we look at them), due to the condition of continuity of flux on interiour boundaries.

This clearly limits the mathematical extend to solve for all cases in full generality, but by reexpressing the equations as above as two first order we can still get the desired result out.

I have already read through, numerous times, the modelling.pdf doc, but I still learn new things ;)

Remains to find how to correctly find the third path: "float" the fluxes at the boundaries, via I expect a weak formulation, and force a flux on the interiour, and solve this 1D issue, as example, something for next week-end ;)

Have a nice day
Ivar

Hi Ivar,

I'll post my thanks here to all your posts concerning this "simple question." Thank you for pursing this and bringing it Sven's attention. I've responded to him separately on another post.

As I indicated to him, I'm really interested in free space problems, specifically, modeling a lighting discharge, for which there are no outer boundaries. The specific problem that has to be solved is the free space 3-D Poisson's equation, for which there are no outer boundaries. Of course, one has to establish a computational domain, but one would like the solution within that domain to be the free space solution. One of the standard ways of doing this using FD modeling is in two steps: (1) First, solve Poisson's equation using the integral form for the potential on the boundaries, and then (2) with the BVs so derived, solve the Dirichlet BV problem, typically with SOR methods. Presumably this same procedure could be carried out in Comsol, although I haven't yet tried it. (I'm still on training wheels, as you probably noticed.)

The more general question is, though, how to solve PDEs with BCs that are specified elsewhere than on the actual outer boundaries. One question I had is whether it is possible to programatically create and destroy boundaries that may be embedded at arbitrary locations in the computational domain, and which could then be pressed into service to solve problems.

Re: A simple question...

Sun, 21 Mar 2010 09:55:55 +0000

...
First we need to understand that the problem constitutes not a classical boundary value problem as typically solved with COMSOL. Nevertheless it can easily be solved with very simple means - you dont need any dest() operator or splitting into two equations and the way is just as straightworward as writing it down with pencil an paper.

I attach a brief description and two models for COMSOL 3.5a.

Thank you very much Sven. Very helpful. I think I see the way forward now for this simple problem.

There are useful applications for which the BV cannot a priori be defined. For example, consider the 1-D Poisson's equation for a delta function source at some location in the interior, but for which you would like to determine the free space solution. In this case, one could certainly calculate the Green's function form of the potential and then evaluate them at the boundaries and manually insert them as Dirichlet conditions. But it would seem that a cleaner way, and in the spirit of the example you provided, would be to calculate them, not on the actual boundaries, but rather at, say, two points close to the source and then integrate out to the boundaries. If then one had a continuous distribution of sources one could then solve the general problem by simple summation.

One would think this could then be extended to 2-D, where one now constructs a small circle of fixed radius around each point source, for which the potential would be known, and then march on out to the boundaries the same as with the 1-D solution. The same would hold for 3-D.

Of course, this would require being able to programatically construct the interior boundaries in these cases. Is there a way to do this? The ability to do this would be very useful for solving free space geometries, which is my primary interest, and for which there are no outer boundaries (except at infinity).

Re: A simple question...

Sun, 21 Mar 2010 08:46:36 +0000

Hmmm...I was away for a few days and just discovered the great responses above. It'll take a while to digest them all, but thanks to everyone for jumping into the fray. BTW, I also have Zimmerman's book and it's really pretty good, typos and all (and even despite the fact that he gets "contours" and "streamlines" confused, and the index could be more detailed).