A non-perturbative method for gravitational potential calculations within heterogeneous and aspherical planets
A non-perturbative method for gravitational potential calculations within heterogeneous and aspherical planets
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DOI：
10.1093/gji/ggz346
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发表时间：
2019-07
影响因子：
2.8
通讯作者：
Matthew Maitra;D. Al-Attar
中科院分区：
文献类型：
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作者：
Matthew Maitra;D. Al-Attar
我们提出了一种计算非球面和非均质行星内引力势和外引力势的数值精确方法。我们的方法是基于将泊松方程变换为在球面计算区域上提出的等价方程。这一新问题是基于伪谱/谱元混合离散化的高效迭代求解的。我们方法的主要优点是它的计算成本反映了行星的几何和结构的复杂性，在许多情况下只比边界微扰理论稍微贵一点。给出了几个数值算例，说明了该方法的有效性和潜在的应用范围。
We present a numerically exact method for calculating the internal and external gravitational potential of aspherical and heterogeneous planets. Our approach is based on the transformation of Poisson’s equation into an equivalent equation posed on a spherical computational domain. This new problem is solved in an efficient iterative manner based on a hybrid pseudospectral/spectral element discretization. The main advantage of our method is that its computational cost reflects the planet’s geometric and structural complexity, being in many situations only marginally more expensive than boundary perturbation theory. Several numerical examples are presented to illustrate the method’s efficacy and potential range of applications.