For post-processing we can easily use the pfar operator for calculation of far-field acoustic pressure. However when defining an target using the optimisation module, pfar is not available.
In the model library there is a model for horn profile optimisation https://www.comsol.com/model/optimizing-the-shape-of-a-horn-4353
In this model they achieve this using the following expression across the boundary of the horn, which is also the z=0 plane
intop1(r*besselj(0,acpr.k*r*sin(theta))*pz)
intop1 is an integration coupling variable across that boundary. This expression used is some simplified version of the far-field calculation equation Eq(4) in the Multiphysics notes. This simplified version is available because the boundary is on the z=0 plane and there is an infinite baffle. In my case this is not available.
In my case I would like to use a general boundary, (e.g. the PML interface boundary) using the general equation Eq(3) in the Multiphysics notes.
My attempt is something like this but it seems there is a mistake or maybe several!
-0.5*intop2(r*exp(i*acpr.kzR/sqrt(Z^2+R^2))*(besselj(0,acpr.k*r*R/sqrt(Z^2+R^2))*ppr(acpr.nr*pr+acpr.nz*pz)-i*acpr.k*p/sqrt(Z^2+R^2)*(i*acpr.nr*R*besselj(1,acpr.k*r*R/sqrt(Z^2+R^2))+acpr.nz*Z*besselj(0,acpr.k*r*R/sqrt(Z^2+R^2)))))
R = sin(theta), Z = cos(theta), the evaluation point for the far-field with theta defined in the library model as the angle with the z-axis
I wonder if any other user has tried something similar and got it working. If you could share I would be very grateful