An all-frequency stable integral system for Maxwell's equations in 3-D penetrable media: continuous and discrete model analysis
<|reference_start|>An all-frequency stable integral system for Maxwell's equations in 3-D penetrable media: continuous and discrete model analysis: We introduce a new system of surface integral equations for Maxwell's transmission problem in three dimensions. This system has two remarkable features, both of which we prove. First, it is well-posed at all frequencies. Second, the underlying linear operator has a uniformly bounded inverse as the frequency approaches zero, ensuring that there is no low-frequency breakdown. The system is derived from a formulation we introduced in our previous work, which required additional integral constraints to ensure well -posedness across all frequencies. In this study, we eliminate those constraints and demonstrate that our new self adjoint, constraints-free linear system expressed in the desirable form of an identity plus a compact weakly-singular operator is stable for all frequencies. Furthermore, we propose and analyze a fully discrete numerical method for these systems and provide a proof of spectrally accurate convergence for the computational method. We also computationally demonstrate the high-order accuracy of the algorithm using benchmark scatterers with curved surfaces.<|reference_end|>
@article{ganesh2024an,
    title={An all-frequency stable integral system for Maxwell's equations in 3-D
  penetrable media: continuous and discrete model analysis},
    author={Mahadevan Ganesh, Stuart C. Hawkins, Darko Volkov},
    journal={arXiv preprint arXiv:2402.17713},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.17713},
    primaryClass={math.NA cs.NA math.AP}
}