A Rayleigh-Ritz method based approach to computing seismic normal modes in the presence of an essential spectrum. (arXiv:1906.11082v1 [physics.comp-ph])
<a href="http://arxiv.org/find/physics/1/au:+Shi_J/0/1/0/all/0/1">Jia Shi</a>, <a href="http://arxiv.org/find/physics/1/au:+Li_R/0/1/0/all/0/1">Ruipeng Li</a>, <a href="http://arxiv.org/find/physics/1/au:+Xi_Y/0/1/0/all/0/1">Yuanzhe Xi</a>, <a href="http://arxiv.org/find/physics/1/au:+Saad_Y/0/1/0/all/0/1">Yousef Saad</a>, <a href="http://arxiv.org/find/physics/1/au:+Hoop_M/0/1/0/all/0/1">Maarten V. de Hoop</a>

A Rayleigh-Ritz with Continuous Galerkin method based approach is presented
to compute the normal modes of a planet in the presence of an essential
spectrum. The essential spectrum is associated with a liquid outer core. The
presence of a liquid outer core requires the introduction of a mixed Continuous
Galerkin finite-element approach. Our discretization utilizes fully
unstructured tetrahedral meshes for both solid and fluid domains. The relevant
generalized eigenvalue problem is solved by a combination of several highly
parallel, computationally efficient methods. Self-gravitation is treated as an
N-body problem and the relevant gravitational potential is evaluated directly
and efficiently utilizing the fast multipole method. The computational
experiments are performed on constant elastic balls and the isotropic version
of the preliminary reference earth model (PREM) for validation. Our proposed
algorithm is illustrated in fully heterogeneous models including one combined
with crust 1.0.

A Rayleigh-Ritz with Continuous Galerkin method based approach is presented
to compute the normal modes of a planet in the presence of an essential
spectrum. The essential spectrum is associated with a liquid outer core. The
presence of a liquid outer core requires the introduction of a mixed Continuous
Galerkin finite-element approach. Our discretization utilizes fully
unstructured tetrahedral meshes for both solid and fluid domains. The relevant
generalized eigenvalue problem is solved by a combination of several highly
parallel, computationally efficient methods. Self-gravitation is treated as an
N-body problem and the relevant gravitational potential is evaluated directly
and efficiently utilizing the fast multipole method. The computational
experiments are performed on constant elastic balls and the isotropic version
of the preliminary reference earth model (PREM) for validation. Our proposed
algorithm is illustrated in fully heterogeneous models including one combined
with crust 1.0.

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