This work studies the solution of Helmholtz problems arising from coupled wave--polarization systems. Such systems appear when a wave field interacts with local material responses, leading to frequency-dependent behavior in the corresponding time-harmonic problem. This frequency dependence makes the resulting Helmholtz equation dispersive and motivates the use of time-domain methods for solving frequency-domain problems.
We extend the WaveHoltz method to this coupled dispersive setting. The method solves the Helmholtz problem by evolving the associated forced time-dependent system and applying a temporal filter to extract the desired time-periodic component. We formulate the WaveHoltz iteration for the coupled system, and analyze the method at both the continuous and fully discrete levels.
About the Speaker: 
I am Fansu Meng, I am currently a 3rd year PhD student focusing on numerical computation.
