SIAM Journal on Applied Mathematics, Volume 80, Issue 6, Page 2657-2683, January 2020.
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.

中文翻译：

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高斯地震学中标量波动方程全模格林核的高效精确算法

SIAM应用数学杂志，第80卷，第6期，第2657-2683页，2020年1月。
在这项工作中，我们提供了一种算法，可以在球形对称性下有效，准确地计算局部弹性地震学中标量波动方程的完整输出模态格林核。由于完整格林函数的计算成本高，当前的地震分析研究依赖于单源计算。但是，对日震产物（互协方差和功率谱）进行更实际的建模需要完整的格林核。在经典方法中，狄拉克源是离散的，一个模拟可以在线上给出格林函数。在这里，我们提出了一个两步算法，通过两次仿真，可以提供域上的完整内核。而且，我们的方法更加精确，因为精确描述了Dirac源引起的解的奇异性。此外，它与精确的Dirichlet-to-Neumann边界条件结合在一起，在逼近即将离去的格林核方面提供了最佳精度，这在我们的实验中得到了证明。此外，我们表明，非局部辐射边界条件的高频近似可以准确表示日震产物。