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We compare two high order finite-difference methods that solve the elastic wave equation in two dimensional domains with curved boundaries and material discontinuities. Two numerical experiments are designed with focus on wave boundary…

Numerical Analysis · Mathematics 2015-11-25 Kristoffer Virta , Christopher Juhlin , Gunilla Kreiss

In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…

Analysis of PDEs · Mathematics 2023-07-28 Shijie Zhou , Hongyinping Feng , Zhiqiang Wang

We present a novel space-time isogeometric discretization of the acoustic wave equation in second-order formulation that is intrinsically unconditionally stable. The method relies on a variational framework inspired by [Walkington 2014],…

Numerical Analysis · Mathematics 2025-06-19 Matteo Ferrari , Ilaria Perugia

We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Othmar Brodbeck , Simonetta Frittelli , Peter Huebner , Oscar A. Reula

We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…

Numerical Analysis · Mathematics 2018-05-15 Lise-Marie Imbert-Gerard , Felipe Vico , Leslie Greengard , Miguel Ferrando

Wave propagation in time-varying media enables unique control of energy transport by breaking energy conservation through temporal modulation. Among the resulting phenomena, temporal disorder-random fluctuations in material parameters-can…

Optics · Physics 2025-10-17 Seulong Kim , Kihong Kim

We devise a Hybrid High-Order (HHO) method for the coupling between the acoustic and elastic wave equations in the time domain. A first-order formulation in time is considered. The HHO method can use equal-order and mixed-order settings…

Numerical Analysis · Mathematics 2025-06-23 Romain Mottier , Alexandre Ern , Rekha Khot , Laurent Guillot

This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of…

Mathematical Physics · Physics 2011-01-25 V. N. Pilipchuk

An incremental wave superimposed on a pre-deformed hyper-elastic material perceives an elastic media with the instantaneous modulus of the current material. This offers a new route with a broadband feature to control elastic waves by…

Classical Physics · Physics 2017-09-12 Dengke Guo , Yi Chen , Zheng Chang , Gengkai Hu

The matrix-vector wave equation is a compact first-order differential equation. It was originally used for the analysis of elastodynamic plane waves in laterally invariant media. It has been extended by various authors for laterally varying…

Applied Physics · Physics 2020-06-11 Kees Wapenaar

In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…

Fluid Dynamics · Physics 2023-05-02 Etienne Mémin , Long Li , Noé Lahaye , Gilles Tissot , Bertrand Chapron

We obtain stochastic stability of C2 non-uniformly expanding one-dimensional endomorphisms, requiring only that the first hyperbolic time map be L^{p}-integrable for p>3. We show that, under this condition (which depends only on the…

Dynamical Systems · Mathematics 2014-11-04 Vitor Araujo , Maria Jose Pacifico , Mariana Pinheiro

Elastic wave speeds are fundamental in geomechanics and have historically been described by an analytic formula that assumes linearly elastic solid medium. Empirical relations stemming from this assumption were used to determine nonlinearly…

Classical Physics · Physics 2023-12-05 David M. Riley , Itai Einav , François Guillard

We are concerned with the reconstruction of inclusions in elastic bodies based on measurements from a laboratory experiment. In doing so, we solve the inverse problem of the time-harmonic elastic wave equation, in contrast to the stationary…

Analysis of PDEs · Mathematics 2026-05-21 Sarah Eberle-Blick , Jochen Moll

Nonlinear hydroelastic waves along a compressed ice sheet lying on top of a two-dimensional fluid of infinite depth are investigated. Based on a Hamiltonian formulation of this problem and by applying techniques from Hamiltonian…

Analysis of PDEs · Mathematics 2025-01-15 Philippe Guyenne , Adilbek Kairzhan , Catherine Sulem

Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour…

Soft Condensed Matter · Physics 2025-02-18 S. O. Sperling , T. Guo , R. H. J. Peerlings , V. G. Kouznetsova , M. G. D. Geers , O. Rokoš

We consider time-harmonic elastodynamic problems in heterogeneous media.cWe focus on scattering problems in the high-frequency regime and incnearly incompressible media, where the the angular frequency $\omega$ and ratio of the Lam\'e…

Analysis of PDEs · Mathematics 2024-03-13 T. Chaumont-Frelet , S. Nicaise

In geophysics, wave propagation in elastic media is a crucial subject. In this context, seismology has made significant progress as a result of numerous advances, among these stands out the advancement of numerical methods such as the…

Physics Education · Physics 2021-08-02 Gabriela Landinez , Santiago Rueda , Fabio D. Lora-Clavijo

Elastic wave propagation is studied in a heterogeneous 2-D medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident…

Classical Physics · Physics 2016-06-29 Mathieu Chekroun , Loïc Le Marrec , Bruno Lombard , Joël Piraux

We generalize the invariant imbedding theory of the wave propagation and derive new invariant imbedding equations for the propagation of arbitrary number of coupled waves of any kind in arbitrarily-inhomogeneous stratified media, where the…

Optics · Physics 2009-11-10 Kihong Kim , Dong-Hun Lee , H. Lim