update. btw for the inhomogeneous acoustic case I normalize by taking u_homo[0], but that doesn't work for dirichlet because then you divide by 0. Change this tomorrow

Put notebooks in seperate files, cleaned up, wrote derivations, analysed homgeneous acoustic case quite carefully

added a weird version with deleting the first mode if it is close to zero, but using this as a checkpoint

Tried using the generalized eigenvalue method for the first time. For the acoustic equations it gave a nice result. For the coupled piezoelectric equations however, it did not. Here I made a vector X = (u, phi)^T and used block matrices

Okay it gives the same results for the homogeneous case, but when it is applied to a space dependent version it gives really weird results..

worked on the FD normal mode simulation. The space dependent problem does not give the expected results for homogeneous case. Slope is too high. For the inhomogeneous case the results are just super weird