Discussion Forum

Hi, i suppose you're talking about a fredholm equation so see the attached file that carries out a BEM for the maxwell equation. i take a bet on the fact that it gives some hint on how to cope with convolution integral within comsol

i precise the integral boundary function :

-1/(2*pi)*u*(nx*(x-dest(x))+ny*(y-dest(y))+nz*(z-dest(z)))/nonzero(((x-dest(x))^2+(y-dest(y))^2+(z-dest(z))^2)^(3/2))

so if you have a formulation of the green's function you can solve the Fredholm equation
in the same idea see at the library models "An Integro-Partial Differential Equation"
last point i believe that some model have already been implemented with plasma equation (see papers and user's presentation cds.comsol.com/access/dl/papers/6480/Meneghini.pdf )

integro differential eqauation seem to be the key of future simulation especially with BEM (infinite radiation condition) for acoustic mechanic stoke flow ,plasma ,Boltzmann

this is why i call anybody who has worked with BEM implementation to share his experience
PS:
see the very interesting paper of Weijun dong
"A combined finite and infinite element approach for modeling spherically symmetric transient subsurface flow"

Seems to me that projection coupling variable does exactly what you need here
look at the projection coupling variable section in the documentation
jf

A projection coupling variable evaluates a series of line integrals on the source domain, where the line positions depend on the positions of the evaluation points in the destination domain. In this way you can calculate the integral of an expression over one space variable for a range of different points along the other space axis, giving a result that varies over the latter space variable. For example, you can obtain the average along the y direction of a variable u defined on some 2-dimensional domain in the xy-plane by calculating the integral

u(x) = int u(x,y)dy




COMSOL Multiphysics uses a method whereby it first applies a one-to-one transformation to the mesh of the source domain. The last space dimension in the transformed mesh is the one integrated over, so the lines used to integrate are vertical in the transformed source mesh. The software takes the placement of the vertical lines in the transformed source mesh from the positions of the transformed destination evaluation points. It then carries out the integrals in the source domain over curves that correspond to the vertical lines in the transformed source mesh.
Then it applies a second transformation to the evaluation points in the destination domain, and it uses the resulting points or the interpolation of an expression at points in the transformed source mesh.
You can define the transformation between source and destination in two ways: as a linear transformation or as a general transformation.

it seems that jean François is right

Hi

the way I understand the integrations in COMSOL is:

1) sub-domain = triple integral over dx dy dz
2) domain/boundary = double ds1 ds2 which means typically dx dy
3) edge = simple ds which corresponds to dx if line is along x, dy if line along y

Hope this helps

ivar

Hi all,

I have additional question regarding projection variables. Is there a way to get u(x) = integral(u(x,y)dy) as a global variable (data set ...)?

Basically, I do need precisely what the projection variables are, but without coupling. I just need u(x) as a way for evaluation of solution.

Any help would be appreciated.

Regards,
Nenad

Dear Marc,

I'm trying to implement Maxwell equations as a boundary integral following your post and attachment. I'm having a difficulty in defining nonzero function. I tried using If condition as,

if(abs(x-dest(x))+abs (y-dest(y))+abs (z-dest(z))==0,1) in function expression and set arguments to x, y,z. But I get an error message saying "Wrong number of function arguments".

I'm much thankful if you can help me get this corrected. Also please be kind enough to share any tutorials or examples that would be useful in solving this surface charge integral equation.

Please find my model attached here with.

Thanks in advance.

Best regards,
Ind Atan