In order to make computations more efficient and possibly allow the set of boundary conditions based on Liu and Thorne's suggestion of a gravitational force preventing bulk motion of the mirror (described in http://nodus.ligo.caltech.edu:8080/COMSOL/3) we want to be able to more optimally mesh our structures. In particular, we would like to have a finer mesh on the face of the mirror and especially near the center of the mirror. Doing so will allow us to significantly reduce the total number of elements contained in the mesh while keeping a large number in the regions which require them.
The best way to improve the meshing that I have found so far is to introduce a new geometry and mesh around it. In order to test this method, I constructed an additional cylinder in my model centered at the same location as the mirror. I gave the cylinder the same height as the mirror so that they can be changed by modifying a single variable and set the cylinder's radius equal to the Gaussian beam size of the laser. I then constructed a user-defined mesh composed of two free tetrahedral operations. The first of these I restricted to the smaller cylinder. By selecting a distribution using a fixed number of elements, this region can be meshed fairly uniformly and densely. The second meshing region can be specified again using the inner cylinder's top face as well as the edges running along its side. For this region, it seems optimal to use a predefined distribution type and select a geometric sequence. Using this method provides a much finer mesh in the areas where we want one, without wasting computational power performing more calculations in uninteresting regions. A screenshot demonstrating the results of this method is shown below.
I ran the previous analysis using the simplest boundary condition of a fixed back using this new mesh. The newly constructed mesh contained 7038 elements instead of the previous 7243 and obtained a Umax=1.57985*10^-10 J instead of 1.52887*10^-10 J. This is about a 3% difference in results. In the next few days, I will run the simulation again on a computer with more RAM using a finer version of the original mesh in order to confirm that the results of the new mesh agree better with it than with the current mesh with a similar number of elements. As a more immediate test, I constructed a mesh of 1940 elements using the new method and obtained a result of Umax=1.56085*10^-10 J which is closer to the value obtained using the original meshing technique, though far enough away to indicate that they may not agree, which encourages me to run the original mesh design with more elements.
The next thing to consider is further improving the mesh by increasing the element density near the mirror's front face. From what I have seen it may be more difficult to implement both of these improvements together, in which case we can perform testing to determine which of the two methods provides better computational efficiency.