Computation of Eigenmodes in Three-Dimensional Structures

Abstract: In this thesis the eigenmodes and eigenvalues of three dimensional structures are analyzed using the Python environment FEniCS in combination with an implementation of the Arnoldi method in MATLAB for calculation of eigenpairs. This is done by considering separable solutions of the wave equation and subsequently expressing these as the solutions to an eigenvalue problem. The eigenvalue problem is then solved on two geometries inspired by two objects from Star Wars; the Death Star and a TIE fighter. To do this, the eigenvalue problem obtained from the wave equation is expressed in its weak form, also known as its variational form, and then discretized into a generalized eigenvalue problem. The eigenvalue problem is then solved approximately using the Arnoldi method, a method that can be used for finding approximate solutions to large and sparse eigenvalue problems. The main results are the plots of the eigenmodes of the two structures which are produced using the Python library vtkplotter.