Discussion Forum

Hi all,

Has anyone ever coded a BEM formulation for the eigen frequencies and eigen modes of a shoe box ?
I'm trying, but it doesn't seem to be that easy...

Basically, I want to solve _only on the boundary_ of a 3D domain, the following equation:
Int(dG/dn(M,M').p(M').dS) + p(M)/2 = Int(G(M,M').dp/dn(M').dS)
subject to the generalized boundary condition :
i.k.rho.c.p(M) + Z*dp/dn(M) = 0
Notations:
- M is any point of the boundary
- M' is another point that lies on an elementary patch dS of the boundary, and the integration is performed such that M' (and associated surface dS) sweeps the entire boundary.
- p(M) is the pressure in M
- dp/dn(M) is the gradient of p in M normal to the boundary in M
- G(M,M') is Green's function, that is exp(i.k.r)/(4.Pi.r), where r is ||vect(MM')||
- dG/dn(M,M') = is the derivative of G(M,M') along the normal to the boundary in M'. It is computed as the derivative of G along vect(MM'), multiplied by the projection of the unit vector of that direction on the normal axis to the boundary at M'
- Z is the specific acoustic impedance of the surface

For coding the integral equations, I was inspired by this post :
www.comsol.com/community/forums/general/thread/33357

except that I used the "boundary ode" physics node, stting the time derivative coefficients to 0.

My problem : at compilation, the model fails to evaluate some expressions (the error message is rather hard to decrypt...)

I attached my example.
Is anyone geek enough to look into this ?



NB : For deriving the eauqtions, I used the direct formulation given in Kirkup's book "The BEM in Acoustics" (2007 ed., available in PDF online, linked to the website www.boundary-element-method.com ). Relevant formulas are found pp. 9, 32-35, and 107-110 of the book.