Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1912.00114

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

Jia Shi·Ruipeng Li·Yuanzhe Xi·Yousef Saad·Maarten V. de Hoop
View original source ↗Read source document ↗Export metadata ↓

Abstract

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 extended Lanczos vectors forming a subspace computed from a non-rotating planet -- with the shape of boundaries of a rotating planet and accounting for the centrifugal potential -- to reduce the dimension of the original problem significantly. The subspace is guaranteed to be contained in the space of functions to which the seismic normal modes belong. The reduced system can further be solved with a standard eigensolver. The computational accuracy is illustrated using all the modes with relative small meshes and also tested against standard perturbation calculations relative to a standard Earth model. The algorithm and code are used to compute the point spectra of eigenfrequencies in several Mars models studying the effects of heterogeneity on a large range of scales.

Explore related subjects

physics.comp-phastro-ph.EP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jia Shi, Ruipeng Li, Yuanzhe Xi, Yousef Saad, Maarten V. de Hoop. 2021-09-26. The computation of seismic normal modes with rotation as a quadratic eigenvalue problem. https://arxiv.org/abs/1912.00114

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bi-Hamiltonian in Semiflexible Polymers built upon Overdamping Process

Quantifying the interaction between a system of interest and its ambient conditions, the memory effect links the states of two distinct Hamiltonians: one for the target system and one for the environment. In this paper, we propose the diffusion process derived from the Smoluchowski equation that can derive the evolution process described by the memory effect integration in a non Markovian regime. The Smoluchowski picture, within the framework of stochastic thermodynamics, justifies a diffusion process incorporated into the equations of motion, and the result of the derivation enables a coarse-grained molecular dynamics simulation with the modified equation of motion to reproduce attenuation from collisions between single walled carbon nanotubes (SWCNTs) under far from equilibrium conditions. The results of the numerical experiments on the collision confirm that heat diffusion compensates for the correlated momentum arising from the memory effect between the two Hamiltonians in both equilibrium and far from equilibrium states.

physics.comp-ph↗
arXiv2026

Learning continuous reaction paths for transition-state prediction

Transition states are defined by reaction pathways, yet most machine-learning methods predict them as isolated geometries. We introduce MARC-TS, a two-stage framework that learns a continuous, endpoint-conditioned path, queries it at any resolution and uses local path context to refine a transition-state candidate. We construct T1x-IRC-8K, a dataset of 8,209 reactions and 1,088,725 path-resolved geometries. On held-out reactions, the path model reduced complete-path error by 48.4% relative to endpoint interpolation, and the localizer achieved a mean aligned structural error of 0.127 Å. Quantum-chemical optimization and vibrational analysis yielded 405 frequency-confirmed first-order saddle-point candidates from 410 predictions. In a 100-reaction nudged elastic band comparison, learned-path initialization reached a joint geometry-and-force target for 66% of reactions, compared with 12% for geometric interpolation after 100 optimizer steps. By treating the path as a reusable representation rather than an auxiliary output, MARC-TS connects transition-state prediction, mechanistic interpretation and quantum-chemical refinement.

physics.comp-ph↗
arXiv2026

A subcell-refined entropy-residual-driven limiting strategy for high-order discontinuous Galerkin methods

Fine-grained, subcell-level dissipation control is essential for achieving robust high-order discontinuous Galerkin (DG) simulations of nonlinear hyperbolic systems in under-resolved regimes while preserving accuracy. This paper proposes a subcell-refined entropy-residual-driven limiting strategy for DG on Legendre-Gauss-Lobatto nodes. The limiter introduces only nearest-neighbor pairwise dissipation within each element, with closed-form coefficients that supply the minimal dissipation required to restore the element entropy inequality. The strategy is a diagonal, locally stable approximation of classical entropy-stable methods, and a generalized subcell framework reveals split-form DG and residual-distribution-based entropy correction schemes as particular choices of the limiting coefficients. For the Euler equations, a physically consistent jump operator separately models thermal and shear entropy production while preserving velocity and pressure equilibrium; a subcell refinement of the Zhang-Shu positivity limiter ensures pointwise positivity. Extensive numerical tests confirm that the scheme maintains optimal high-order accuracy, strictly enforces entropy dissipation, and significantly reduces the difficulty of a posteriori positivity-preserving procedures.

physics.comp-ph↗