Learned infinite elements for helioseismology -- Learning transparent boundary conditions for the solar atmosphere
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918090764189696 |
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| author | Fournier, Damien Preuss, Janosch Hohage, Thorsten Gizon, Laurent |
| author_facet | Fournier, Damien Preuss, Janosch Hohage, Thorsten Gizon, Laurent |
| contents | Context. Acoustic waves in the Sun are affected by the atmospheric layers, but this region is often ignored in forward models due to the increase in computational cost. Aims. The purpose of this work is to take into account the solar atmosphere without increasing significantly the computational cost. Methods. We solve a scalar wave equation that describes the propagation of acoustic modes inside the Sun using a finite element method. The boundary conditions used to truncate the computational domain are learned from the Dirichlet-to-Neumann operator, that is the relation between the solution and its normal derivative at the computational boundary. These boundary conditions may be applied at any height above which the background medium is assumed to be radially symmetric. Results. Taking into account the atmosphere is important even for wave frequencies below the acoustic cut-off. In particular, the mode frequencies computed for an isothermal atmosphere differ by up 10 μHz from those computed for the VAL-C atmospheric model. We show that learned infinite elements lead to a numerical accuracy similar to that obtained for a traditional radiation boundary condition. Its main advantage is to reproduce the solution for any radially symmetric atmosphere to a very good accuracy at a low computational cost. Conclusions. This work emphasizes the importance of including atmospheric layers in helioseismology and proposes a computationally efficient method to do so. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08059 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learned infinite elements for helioseismology -- Learning transparent boundary conditions for the solar atmosphere Fournier, Damien Preuss, Janosch Hohage, Thorsten Gizon, Laurent Solar and Stellar Astrophysics Instrumentation and Methods for Astrophysics Mathematical Physics Context. Acoustic waves in the Sun are affected by the atmospheric layers, but this region is often ignored in forward models due to the increase in computational cost. Aims. The purpose of this work is to take into account the solar atmosphere without increasing significantly the computational cost. Methods. We solve a scalar wave equation that describes the propagation of acoustic modes inside the Sun using a finite element method. The boundary conditions used to truncate the computational domain are learned from the Dirichlet-to-Neumann operator, that is the relation between the solution and its normal derivative at the computational boundary. These boundary conditions may be applied at any height above which the background medium is assumed to be radially symmetric. Results. Taking into account the atmosphere is important even for wave frequencies below the acoustic cut-off. In particular, the mode frequencies computed for an isothermal atmosphere differ by up 10 μHz from those computed for the VAL-C atmospheric model. We show that learned infinite elements lead to a numerical accuracy similar to that obtained for a traditional radiation boundary condition. Its main advantage is to reproduce the solution for any radially symmetric atmosphere to a very good accuracy at a low computational cost. Conclusions. This work emphasizes the importance of including atmospheric layers in helioseismology and proposes a computationally efficient method to do so. |
| title | Learned infinite elements for helioseismology -- Learning transparent boundary conditions for the solar atmosphere |
| topic | Solar and Stellar Astrophysics Instrumentation and Methods for Astrophysics Mathematical Physics |
| url | https://arxiv.org/abs/2402.08059 |