Modelling magnetohydrodynamic waves in waveguides of irregular cross-sectional shape with the implicitly restarted Arnoldi method

The aim of the research is to adapt the methodology of the implicitly restarted Arnoldi method to model linear magnetohydrodynamic waves observed in solar sunspots and pores with high resolution data. The advantage of this method is that by an iterative algorithm, if convergence conditions are satisfied, it will, to high accuracy, calculate the natural oscillatary modes (i.e. the eigenvalues and eigenfunctions) of irregularly shaped magnetic waveguides with no obvious symmetries which can be exploited to simplify the problem. This is a most promising approach to model the oscillations observed in sunspots and pores, which often have highly irregular cross-sections, and this research will be most timely due to the recent construction of the 4m Daniel K. Inouye Solar Telescope, the most powerful solar telescope ever built.