University of Twente Student Theses
Finding eigenmodes of linear systems using a universal preconditioner with applications to dielectric cavities
Hanskamp, Gernt (2023) Finding eigenmodes of linear systems using a universal preconditioner with applications to dielectric cavities.
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| Abstract: | A method is introduced that finds eigenmodes of linear systems. These eigenmodes may possibly be quasi-normal modes, where the frequency is complex to model the damping of energy in an open cavity. The method locates eigenfrequencies using the fact that the operator A(ω) is singular at an eigenfrequency ω0 and therefore the norm ∥A^(−1)(ω)ψ∥ is large for ω close to ω0, where ψ is a random vector. Thus, the function f(ω) = 1 ∥A^(−1)(ω)ψ∥ has a minimum at ω0. A^(−1)ψ is found by solving the linear system Aϕ = ψ using a universal preconditioner and the BiCGSTAB algorithm. The method is validated and illustrated using the Helmholtz equation, applied on a onedimensional Fabry-Perot resonator and a dielectric circular cavity in two dimensions and compared with analytical solutions. It is found that it locates eigenfrequencies accurately and approximates the eigenfunction well in most cases, except for lowfrequency asymmetric modes. Furthermore, the method is illustrated for a distorted circular cavity. |
| Item Type: | Essay (Bachelor) |
| Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |
| Subject: | 31 mathematics, 33 physics |
| Programme: | Applied Mathematics BSc (56965) |
| Link to this item: | https://purl.utwente.nl/essays/95838 |
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