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A Continuous Galerkin method-based approach is presented to compute theseismic normal modes of rotating planets. Special care is taken to separate outthe essential spectrum in the presence of a fluid outer core using a polynomialfiltering eigensolver. 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. Ourdiscretization utilizes fully unstructured tetrahedral meshes for both solidand fluid regions. The relevant eigenvalue problem is solved by a combinationof several highly parallel and computationally efficient methods. We validateour three-dimensional results in the non-rotating case using analytical resultsfor constant elastic balls, as well as numerical results for an isotropic Earthmodel from standard ``radial" algorithms. We also validate the computations inthe rotating case, but only in the slowly-rotating regime where perturbationtheory applies, because no other independent algorithms are available in thegeneral case. The algorithm and code are used to compute the point spectra ofeigenfrequencies in several Earth and Mars models studying the effects ofheterogeneity on a large range of scales.

A non-perturbative approach to computing seismic normal modes in rotating planets