Atmospheric radiation boundary conditions for the Helmholtz equation

Hélène Barucq, Juliette Chabassier, Marc Duruflé, Laurent Gizon, Michael Leguèbe

Research output: Contribution to journalArticlepeer-review


This work offers some contributions to the numerical study of acoustic waves propagating in the Sun and its atmosphere. The main goal is to provide boundary conditions for outgoing waves in the solar atmosphere where it is assumed that the sound speed is constant and the density decays exponentially with radius. Outgoing waves are governed by a Dirichlet-to-Neumann map which is obtained from the factorization of the Helmholtz equation expressed in spherical coordinates. For the purpose of extending the outgoing wave equation to axisymmetric or 3D cases, different approximations are implemented by using the frequency and/or the angle of incidence as parameters of interest. This results in boundary conditions called atmospheric radiation boundary conditions (ARBC) which are tested in ideal and realistic configurations. These ARBCs deliver accurate results and reduce the computational burden by a factor of two in helioseismology applications.

Original languageEnglish (US)
Pages (from-to)945-964
Number of pages20
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number3
StatePublished - May 1 2018
Externally publishedYes


  • Atmosphere.
  • Helmholtz equation
  • Radiation boundary condition

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics


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