The finite volume method (FVM) as a numerical method can be straightforwardly applied for global as well as local gravity field modelling. However, to obtain precise numerical solutions it requires very refined discretization which leads to large-scale parallel computations. To optimize such computations, we present a special class of numerical techniques that are based on a physical decomposition of the computational domain. The domain decomposition (DD) methods like the Additive Schwarz Method are very efficient methods for solving partial differential equations. We briefly present their mathematical formulations, and we test their efficiency in numerical experiments dealing with gravity field modelling. Since there is no need to solve special interface problems between neighbouring subdomains, in our applications we use the overlapping DD methods. Finally, we present the numerical experiment using the FVM approach with 93 312 000 000 unknowns that would not be possible to perform using available computing facilities without aforementioned methods that can efficiently reduce a numerical complexity of the problem.

中文翻译：

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解决大地边界值问题的计算优化

有限体积法（FVM）作为一种数值方法可以直接应用于整体以及局部重力场建模。但是，要获得精确的数值解，需要非常精细的离散化，这会导致大规模并行计算。为了优化这种计算，我们提出了一种特殊的数值技术，它基于计算域的物理分解。像加性Schwarz方法这样的域分解（DD）方法是求解偏微分方程的非常有效的方法。我们简要介绍了它们的数学公式，并在处理重力场建模的数值实验中测试了它们的效率。由于无需解决相邻子域之间的特殊接口问题，在我们的应用程序中，我们使用重叠的DD方法。最后，我们介绍了使用FVM方法进行的数值实验，其中包含93 312 000 000个未知数，如果没有上述方法可以有效地降低问题的数值复杂性，将无法使用可用的计算工具来执行该未知数。