Efficient and accurate algorithm for the full modal green's kernel of the scalar wave equation in helioseismology

HÉLÈNE BARUCQ, FLORIAN FAUCHER, DAMIEN FOURNIER, LAURENT GIZON, HA PHAM

Research output: Contribution to journalArticlepeer-review

Abstract

In this work, we provide an algorithm to compute efficiently and accurately the full outgoing modal Green's kernel for the scalar wave equation in local helioseismology under spherical symmetry. Due to the high computational cost of a full Green's function, current helioseismic studies rely on single-source computations. However, a more realistic modelization of the helioseismic products (cross-covariance and power spectrum) requires the full Green's kernel. In the classical approach, the Dirac source is discretized and one simulation gives the Green's function on a line. Here, we propose a two-step algorithm which, with two simulations, provides the full kernel on the domain. Moreover, our method is more accurate, as the singularity of the solution due to the Dirac source is described exactly. In addition, it is coupled with the exact Dirichlet-to-Neumann boundary condition, providing optimal accuracy in approximating the outgoing Green's kernel, which we demonstrate in our experiments. In addition, we show that high-frequency approximations of the nonlocal radiation boundary conditions can represent accurately the helioseismic products.

Original languageEnglish (US)
Pages (from-to)2657-2683
Number of pages27
JournalSIAM Journal on Applied Mathematics
Volume80
Issue number6
DOIs
StatePublished - Dec 17 2020

Keywords

  • Helioseismic observables
  • Helioseismology
  • Hybridizable discontinuous Galerkin
  • Modal Green's kernel
  • Radiation boundary conditions
  • Whittaker's functions

ASJC Scopus subject areas

  • Applied Mathematics

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