Analytic Integration of the Newton Potential over Cuboids and an Application to Fast Multipole Methods-Reference-Cited by-同舟云学术

Analytic Integration of the Newton Potential over Cuboids and an Application to Fast Multipole Methods

Published:2021-08-01 Issue:0 Volume:0 Page:
ISSN:1569-3953
Container-title:Journal of Numerical Mathematics
language:en
Short-container-title:

Author:

Kirchhart Matthias¹,Weniger Donat¹

Affiliation:

1. Applied and Computational Mathematics, RWTH Aachen University , Schinkelstraße 2 , Aachen , Germany

Abstract

Abstract We present simplified formulæ 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.

Publisher

Walter de Gruyter GmbH

Subject

Computational Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jnma-2020-0103/pdf

Reference14 articles.

1. W. Hackbusch. ‘Direct Integration of the Newton Potential over Cubes’. In: Computing 68.3 (May 2002), pp. 193–216. issn: 0010–485X. doi: 10.1007/s00607-001-1443-8.

2. W. Hackbusch. Direct integration of the Newton potential over cubes including a program description. Technical Report 68. Max Planck Institut Leipzig, 2001.

3. M. Kirchhart and C. Rieger. A Particle Method without Remeshing. Preprint. Oct. 2019. arXiv: 1909.07449 [Math.NA].

4. M. G. Duffy. ‘Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex’. In: SIAM Journal on Numerical Analysis 19.6 (Dec. 1982), pp. 1260–1262. issn: 0036–1429. doi: 10.1137/0719090.

5. S. Börm and W. Hackbusch. ‘Hierarchical Quadrature for Singular Integrals’. In: Computing 74.2 (Mar. 2005), pp. 75–100. issn: 0010–485X. doi: 10.1007/s00607-004-0076-0.