Skip to content
  • Publications
  • Jobs
  • enzuazua
  • Seminars
  • Events Calendar
cmc.deusto.eus
  • Home
  • About us
    • About the Chair
    • Head of the Chair
    • Team
    • Past Members
  • Research
    • Projects
    • ERC – DyCon
    • DyCon Blog
    • DyCon Toolbox
    • Industrial & Social TransferenceContents related to the industrial and social transference aspects of the work in the Chair of Computational Mathematics.
  • Publications
    • Publications (All)
    • Publications Relased
      • Publications 2022
      • Publications 2021
      • Publications 2020
      • Publications 2019
      • Publications 2018
      • Publications 2017
      • Publications 2016
    • AcceptedAccepted to be released
    • SubmittedSubmitted publications
  • Activities
    • Events calendar
    • Past Events
    • News
    • Seminars
    • Courses
    • enzuazua
    • Gallery
  • Jobs
  • Contact

Gaussian Beam ansatz for finite difference wave equations

Biccari U, Zuazua E. Gaussian Beam ansatz for finite difference wave equations (2023)

Abstract. This work is concerned with the construction of Gaussian Beam (GB) solutions for the numerical approximation of wave equations, semi-discretized in space by finite difference schemes. GB are high-frequency solutions whose propagation can be described, both at the continuous and at the semi-discrete levels, by microlocal tools along the bi-characteristics of the corresponding Hamiltonian. Their dynamics differ in the continuous and the semi-discrete setting, because of the high-frequency gap between the Hamiltonians. In particular, numerical high-frequency solutions can exhibit spurious pathological behaviors, such as lack of propagation in space, contrary to the classical space-time propagation properties of continuous waves. This gap between the behavior of continuous and numerical waves introduces also significant analytical difficulties, since classical GB constructions cannot be immediately extrapolated to the finite difference setting, and need to be properly tailored to accurately detect the propagation properties in discrete media. Our main objective in this paper is to present a general and rigorous construction of the GB ansatz for finite difference wave equations, and corroborate this construction through accurate numerical simulations.

Read Full Paper

arxiv: 2209.13976

Last updated on July 21, 2023

Post navigation

Previous Post
Optimal design of sensors via geometric criteria
Next Post
A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation

Last Publications

Control of neural transport for normalizing flows

A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation

Gaussian Beam ansatz for finite difference wave equations

Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave

Optimal design of sensors via geometric criteria

  • Control of neural transport for normalizing flows
  • A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation
  • Gaussian Beam ansatz for finite difference wave equations
  • Optimal design of sensors via geometric criteria
  • Eigenvalue bounds for the Gramian operator of the heat equation
  • Control of neural transport for normalizing flows
  • A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation
  • Gaussian Beam ansatz for finite difference wave equations
  • Optimal design of sensors via geometric criteria
  • Eigenvalue bounds for the Gramian operator of the heat equation
Copyright 2016 - 2023 — cmc.deusto.eus. All rights reserved. Chair of Computational Mathematics, Deusto Foundation - University of Deusto
Scroll to Top
  • Aviso Legal
  • Política de Privacidad
  • Política de Cookies
  • Configuración de Cookies
WE USE COOKIES ON THIS SITE TO ENHANCE USER EXPERIENCE. We also use analytics. By navigating any page you are giving your consent for us to set cookies.    more information
Privacidad