长方体上牛顿势的解析积分及其在快速多极方法中的应用

IF 3.8 2区数学 Q1 MATHEMATICS

Journal of Numerical Mathematics Pub Date : 2020-12-18 DOI:10.1515/jnma-2020-0103

Matthias Kirchhart, Donat Weniger

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引用次数: 1

摘要

摘要给出了二维和三维空间中多项式牛顿势解析积分的简化公式。这些都是在一个易于使用的c++库中实现的，该库允许任意精度的算术计算，这里也有文档。我们描述了如何将这些结果与快速多极方法相结合，以评估更一般的非多项式密度的牛顿势。

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Analytic integration of the Newton potential over cuboids and an application to fast multipole methods

Abstract We present simplified formulae for the analytic integration of the Newton potential of polynomials over boxes in two- and three-dimensional space. These are implemented in an easy-to-use C++ library that allows computations in arbitrary precision arithmetic which is also documented here. We describe how these results can be combined with fast multipole methods to evaluate the Newton potential of more general, non-polynomial densities.

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来源期刊

Journal of Numerical Mathematics 数学-数学

CiteScore

5.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Numerical Mathematics (formerly East-West Journal of Numerical Mathematics) contains high-quality papers featuring contemporary research in all areas of Numerical Mathematics. This includes the development, analysis, and implementation of new and innovative methods in Numerical Linear Algebra, Numerical Analysis, Optimal Control/Optimization, and Scientific Computing. The journal will also publish applications-oriented papers with significant mathematical content in computational fluid dynamics and other areas of computational engineering, finance, and life sciences.