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

Barucq, H., Faucher, F., Fournier, D., Gizon, L., & Pham, a. H. (2020). Efficient and accurate algorithm for the full modal green's kernel of the scalar wave equation in helioseismology. SIAM Journal on Applied Mathematics, 80(6), 2657-2683. doi:10.1137/20M1336709.

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 Creators:
Barucq, Hélène, Author
Faucher, Florian, Author
Fournier, Damien1, Author              
Gizon, Laurent1, Author              
Pham, and Ha, Author
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1Department Solar and Stellar Interiors, Max Planck Institute for Solar System Research, Max Planck Society, ou_1832287              

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 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.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Published in print
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 Rev. Type: Peer
 Identifiers: DOI: 10.1137/20M1336709
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Title: SIAM Journal on Applied Mathematics
Source Genre: Journal
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Pages: - Volume / Issue: 80 (6) Sequence Number: - Start / End Page: 2657 - 2683 Identifier: -