# #012: BEM and Optimization in COMSOL Multiphysics 5.3a

With COMSOL introducing the Boundary Element Method (BEM) in their Acoustics interface in v5.3a, we all get some new possibilities, especially when dealing with exterior problems. Here is a little teaser of how you can combine BEM and optimization.

First, I investigate a simple parameter optimization, but I as will be show later you can also do true shape optimization, if you should so desire. I have two geometries; a cylinder with height and radius of 1 m, and a small sphere down the x-axis. Both are meshed with their own surface mesh:

A plane wave propagates down the x-axis. The scattered sound pressure level field looks like the following:

Next, an optimization node is included, where a single parameter can move the cylinder upwards via the parameter zoff, with the objective to minimize the sound pressure level on the small sphere. A simple gradient-free optimization is carried out, and within minutes, it is found that for this particular frequency, the cylinder should be moved almost 1 meter upwards, in order to have the sphere be in acoustic "shadow":

The sound pressure level is reduced by approximately 6 dB.

This exterior problem is very simple, but it very nicely highlights how 1) when using BEM, meshing and radiation conditions are very easy to handle, compared to FEM, and 2) how COMSOL Multiphysics has the option of letting the user decide which physics the optimization should work on.

Next, I will show that you can also combine BEM and shape optimization. It is partly based on a COMSOL blog post, but of course the physics and objective function are changed. Initally, a 2D rectangle is being hit by an incoming wave propagation from bottom to top. A certain sound pressure level distribution is found for this this particular frequency. Below the rectangle resides a sphere, and the SPL on that sphere is sought minimized. The rectangle shape is now allowed to change, and the result for a minimum SPL at the sphere is shown below.

The shape is now more smooth, and a lower pressure zone has been moved downwards to conincide with the fixed sphere. Again, this is a fairly simple example, but it shows how BEM and shape optimization can now be combined in COMSOL Multiphysics 5.3a.

Also, check out my full investigation of BEM in COMSOL Multiphysics. The addition of BEM, and the fact, that you can combine it with e.g. optimization, creates some very cool and unique opportunities. I hope this new module will be very well received in the community.

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