用于日震学的学习型无限元——学习太阳大气的透明边界条件
Learned infinite elements for helioseismology -- Learning transparent boundary conditions for the solar atmosphere
AI总结：
针对太阳大气计算成本高的问题，提出基于 Dirichlet-to-Neumann 算子的学习型无限元方法，以低计算成本高精度求解波动方程并实现透明边界条件。
摘要：
背景。太阳中的声波受大气层影响，但由于计算成本增加，正向模型中常忽略该区域。目标。本工作旨在在不显著增加计算成本的情况下考虑太阳大气。方法。我们使用有限元方法求解描述太阳内部声学模式传播的标量波动方程。用于截断计算域的边界条件是从 Dirichlet-to-Neumann 算子学习得到的，即解及其在计算边界处法向导数之间的关系。这些边界条件可应用于假设背景介质在径向对称的任意高度之上。结果。考虑大气层很重要，即使对于低于声学截止频率的波频率也是如此。特别是，等温大气计算出的模式频率与 VAL-C 大气模型计算出的模式频率相差达 10 μHz。我们表明，学习型无限元达到了与传统辐射边界条件相似的数值精度。其主要优势在于以低计算成本高精度地重现任意径向对称大气的解。结论。本工作强调了在日震学中包含大气层的重要性，并提出了一种计算高效的方法来实现这一点。
英文摘要：
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.
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