# The computation of seismic normal modes with rotation as a quadratic eigenvalue problem

@article{Shi2019TheCO, title={The computation of seismic normal modes with rotation as a quadratic eigenvalue problem}, author={Jia Shi and Ruipeng Li and Yuanzhe Xi and Yousef Saad and Maarten V. de Hoop}, journal={arXiv: Computational Physics}, year={2019} }

A new approach is presented to compute the seismic normal modes of a fully heterogeneous, rotating planet. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core. The relevant elastic-gravitational system of equations, including the Coriolis force, is subjected to a mixed finite-element method, while self-gravitation is accounted for with the fast multipole method (FMM). To solve the resulting quadratic eigenvalue problem (QEP), the approach utilizes…

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